The diagram below shows a tenn.n1y,s sdfqz/hk8 1o3t, mff/vfkph) is ball of mass $m$ striking a wall with an initial velocity, $u$, and rebounding with velocity $v$ . A second, softer ball of the same mass strikes the wall with the same speed but rebounds with a slower rebound speed.




Which of following statements is correct about the magnitudes of the impulse and change in momentum applied to the second ball compared to the first?

  An object of mass M on .mg m hizj+q3y6c ,whifn2m/4 a string moves in a circle of radius r at a constant speed.+mnq4m3/g 6ji.c2mhh fywi, z



Which of the following statements is true about the motion of the object:
I. The resultant work done on the object is zero.
II. The velocity of the object is constant.
III. The object is accelerating

  An object moves in a :bpw6xx rzvcmk, 7p s7 n-zg49circular path of radius $2 \, m$ with angular displacement of $\frac {π} {2}$ rad in $5 \, s$
What is the linear speed of the object?

  Consider the weight,8 ji; arbe mhdwhzz4; .oob0.2 $W$, of a skydiver falling through air with a drag force $F_{drag}$​ If the skydiver experiences terminal velocity, which of the following best represents the skydiver's motion by means of a free body diagram?

  A car of mass $m$ and a truck of mass $3 \, m$ travelling in opposite directions collide and stick together. The speeds of the car and the truck just before the crash are $2 \, v$ and $v$ respectively. What is their speed after the collision?

  A mass is attached to theotf cjc+d 6aebe 91q8):misky9j lzgq 87u-6 e mirror of a car by a string. As the car accelerates to the left, the string makes an angle with the vertical asyigsq-6: 9l6a8u 7t ej8dc9)zfe +oe mkqjb1c shown in the diagram below.



Which of the following shows the correct free-body diagram that represents the forces acting on this mass when it is accelerating?

  The graph below shows t i:g moxa3b tse+.,wt+he variation of the resultant force $F$ acting on a box with time$t$.



The box starts to move from rest. Which of the following graphs shows the variation of the momentum $p$ of the box with time $t$?

  As a truck is brought to rest, thegtfl8-4-orjf, 7+m utli3;xf*q td a pkgq -a) brakes apply a force of $5.1 \times 10^3N$ Which answer best describes the magnitude of the change in momentum of the truck if the brakes are applied for $3.0 \, s$?

  A football player bounced the ball off their hiq b- t6/yvaj, mzn)x2ead as shown while diving sideways ,2bxtn mz-yji6q) va/



Which of the following gives a Newton’s Third Law pair of forces that applies to this situation?

  A spring of negligibsv1 8 yeib4h1o gd.k-:j6 sngple mass and length of $l_o$ is attached to a fixed point. When the spring is extended by an external force $F$, the length of the spring increases to $l$. The graph shows how the length of the spring varies with the tension in spring. The tension in the spring is equal to where $k$ is a constant $k \Delta l$, and $\Delta l$ is the extension of the spring.

What are the gradient and y-intercept of the graph?

  1.State the law of cak1x- 1c bh1ep(:k;0hl9q yjsdt 1zehonservation of momentum.

2.A stationary body explodes into two pieces of mass as $m_1$​ and $m_2$​ in opposite directions.



Just after the explosion, the ratio of the kinetic energy of $m_1$​ to the kinetic energy of $m_2$​ is found to be 9. Calculate the ratio of mass $m_2$ to mass $m_1$.
$\frac{m_2}{m_1}$​​ =   

  A ball of mass $m$ is falling vertically through the air. The drag force acting on the ball is given by $kv^2$ where $k$ is constant and $v$ is the speed of the ball. What is the maximum speed reached by the ball?

  Two eggs of equal mass fall t b1p)-g7 yst :tenog:from the same height onto a padded floor. One of them is broken while the other one bounces upwards intact. The time of collision is the same for both. Which of the following correctly describes the egg that exerts more forcsp:nt b - tty1):o7ggee on the floor and the reason?

  A block of wood is placed on a ro nkm6z84f 9+bsjaek f7ugh inclined surface. Which of the diagrams below correctly represents the forcesje9n+4mfkfk7 az s86 b acting on the block when it is at rest?

  A jet aircraft is performing a “loop-the-loop” stunt ic,a9e2 9memyjz2 y* tpn which it moves in a vertical circular p*cmey2 99my2 zpt,jea ath as shown in the diagram.



Which of the following represents the free body diagram of the pilot at the top of the loop?

  A stone attached to o 3fmus)r5ss s3ne end of a rod rotates in a vertical circle at a constant spess3 )5 mrussf3ed. Two positions of the stone at two different instants, X and Y, are shown in the diagram below.



In the table below, which row is correct for the centripetal force acting on the stone at X and Y?

  A box of mass m is pulled across a horizontal surface with a force F as show:a 6,qf yv+mjcn in the diagram. The coefficient of dynamic friction between the box and the surface is µ. What is the energy transferrm,c +yfjqa:6ved to thermal energy while a box is moved by a distance of d?

  n airplane in straight level flight expe u7/mz m:s1nderiences a lift force $L$ that is proportional to the speed of the plane and is perpendicular to the axis of the wings and as shown in diagram.






On a banked turn at the same speed, the wings make an angle $θ$ with the horizontal.
Which of the following gives the centripetal force on the airplane?

  An electric motor is used totim r* pmx-zz.yz8 ,gcuz ,7;s raise a block of mass 18.0 kg vertically to the top of a buildi8t-ygzzux;*c rzs m,z7p mi, .ng at a constant speed of $1.5\,ms^{−1}$. If the power rating of the motor is 297 W, calculate the efficiency of the motor.

  Two trucks X and Y are pulling a car out of thickq cyahctaxmyicj631jz2.8h 26 d/b0c mud along a straight path. The only other horizontal force acting on the car is a drag force opposite to the direction of motion. The diagramj. byz2t36cm6 /qi1a82 ccc hyhadx0j shows the direction of the force applied by truck X and the direction of motion of the car.



Which of the following vectors shows the direction of the force applied by truck Y?

  A box is sliding down an incli c4 n1ahchza oq-xw:,)r9. cykne at a constant speed of $2\,ms^{−1}$. The angle of the incline is $\theta$.



The magnitude of the total of the opposing forces is $16\,N$. What is the force of gravity acting on the box?

  A rocket ejects hot gas in space in a direction opposite to its travelling direction. What is correct for the magnitude of the momentum and the kinetic energy of the rocket?

  A table tennis ball of mass m is dropped on a level sn xku, 2s 6fco75*)rik txqi6gurface from a height $H$. The ball rebounds to a height $h < H$ after impact. Which of the following is correct about the nature of the collision and magnitude of the change in momentum $(\Delta p)$ of the ball as a result of this impact?

  1. Define distance. hdxt d6)( j/zi
2.An object moves in a straight line on a level road. The variation of the object's distance $d$ with time $t$ is shown on the graph below.

(1)Describe the motion of the object between $t=0.5\,s$ and $t=1.0\,s$.
(2)Calculate the instantaneous speed of the object at $t=0.5\,s$. $v$ =    $ms^{-1}$
(3)On the axes below, sketch a possible graph of the variation of velocity $v$ of the object with time $t$. There is no need to add values to the axes.

4.Determine the direction of the change in momentum of the object during the motion is  ----待选择----the same asopposite to  the direction of motion.

  A block of mass $m$, initially at rest, is acted upon by two unequal forces $F_1$ and $F_2$​ such that $F_1​>F_2​$ as shown in the diagram below. The forces act for a time $t$.


Which of the following correctly represents the magnitude of the final velocity of the block after time $t$?

  A cargo container is rele/l y)tkc8tgy 0ased from an airplane. A parachute is opened remotely a few seconds later to land it safely. Which graph shows the valy)g c08/yttkriation of the vertical acceleration with time $t$ for the cargo container from when it leaves the plane until landing?

  A car enters a roundac qapti+mtc 59;qr. z7, bpuo0bout with a speed $v$. The dotted line shows the path of the car. The road is slightly banked at an angle to the horizontal.



The coefficient of friction between the tires of the car and the road is $\mu$. When $\mu$ decreases, which of the following changes could prevent the car from slipping away on this roundabout?

  A car makes a U-turn on a flat horizontal73clg:i5 k0dh 2k qvic road at a speed of $9\,ms^{−1}$ as shown in the diagram.



The inner radius of the U-turn is $4\,m$ and its outer radius is $10\,m$.
What is the best estimate for minimum acceleration of the car when making the U-turn?

  An object with a weight t6 svh/pkf *dbbfy;b6/ s2yz($W$ connected to one end of a rod of negligible mass rotates at constant speed in a vertical plane.



When the object is at the top position of the circular path, the tension on the rod is zero. What is the magnitude of tension at the bottom position of the circular path?

  1. A ball of mass $0.20\,kg$ moving on a frictionless horizontal plane collides elastically with a vertical wall.



The variation of the force F acting on the ball during the collision with time t is shown on the graph below.



The speed of the ball just before the impact is $5.0\,ms^{−1}$. Calculate the maximum force exerted on the wall by the ball. $F_{Max}$ =    $N$


2.The wall is covered with a coating that causes an inelastic collision. The ball hits the wall with the same initial speed and bounces back with a speed of $3.0\,ms^{−1}$.

(1)Explain, by considering the moments just before and after the collision, how the principle of conservation of energy applies to the collision.
(2)Calculate the loss of the energy of the ball during the collision. $\Delta E_K$ =    $J$
(3)During this collision, the ball undergoes a change in momentum. Determine whether the the law of conservation of momentum  ----待选择----appliesdoes not apply  to the system of the ball and the wall.

  A brick of weight $100\,N$ rests on a rough horizontal surface. A varying horizontal force is applied to the brick. The graph shows the variation of the magnitude of the frictional force with the magnitude of the applied force.



What is the coefficient of the dynamic friction between the brick and the rough surface?

  A ball of mass $0.5\,kg$ strikes a vertical wall with a speed of $30\,ms^{−1}$. The magnitude of the change of the momentum of the ball is $22.5\,kgms^{−1}$. Calculate the speed of the ball just after it rebounds.

  An object is moving at constant vel .( -xq ,x9bt-akrauojocity. Which of the following could be the free-body diagram representing the forces acting 9t -aok xq(brux,aj-.on the object?

  An egg hits a wall ceoqqn+ rw7k 06overed with a soft material and sticks to it. The graph shows the variation of horizontal e0wqnkr 76+ oqforce $F$ acting on the egg with time $t$ during the collision.



The soft material on the wall is removed and an identical egg with the same initial speed collides with and sticks to the wall. Which graph shows the variation of horizontal force $F$ acting on the second egg with time $t$ during the collision? The graph for the first egg is shown as a dotted line.

  A roller coaster passes fmi r pl8hh 43dws:66ta vertical loop in a constant gravitational field. Friction and air resilh 6 sd4p86f h3rw:imtstance are negligible.



How do the kinetic energy of the roller coaster and the normal reaction force acting on the roller coaster compare at point X and Y?

  An object of mass $m$ rests on a rough surface. Another object of mass $M$ is connected to it with a rope.



The image below shows the free-body diagram of horizontal forces on the object of mass $m$.



Which of the following correctly describes the Newton's 3rd Law force paired with $F_2$​?

  A trolley is pushed in a level parking area of a markyq n at55++rgxet on a very rainy day. The rain q g++5n t5aryxfills the trolley at a rate of $R\,kgs^{−1}$. Ignoring frictional forces, what is the force needed to move the trolley at a constant speed of v?

  A box with a mass of M rests on a balance in an elevator that is moving downwi/gokz0k) 9rs9f vnr9 ard o9sk fi0/9rgk9) nrzvs. The elevator slows with an acceleration of $\frac{g}{4}$.



Which of the following gives the reading of the balance?

  Two blocks of masseshpes/ 6p: mf uk 3nw3q3i8vu)f $m$ and $2m$ approach each other and collide on a horizontal smooth surface. After the collision, they move together. The speeds of the blocks before the collision are $5v$ and $2v$ as shown.



Which of the following correctly gives the speed of the blocks after the collision and the nature of the collision?

  A ball is tied to a kz5p/(m s*+.a r br t1zdss3kw$10\,cm$ rope and rotates in a horizontal circular path starting from point $X$ with a linear speed of $20\,cm\,s^{−1}$. The rope is cut after $2\,s$ when the object is moving at point $Y$ as shown in the diagram.



Which of the following is correct about the angular displacement of the ball between $X$ and $Y$ and the direction of motion of the ball after the rope is cut?

  An airplane of weight jfph,a4z; 2bni egtxq*j x0tq :(,sj6 $3W$. Which of the following gives the magnitude of the force of the air on the plane?

  While practising, a table tennis pyo - d h(/k0jg(3ezpdelayer hits a ball of mass $2.8\,g$ that collides with the floor and then bounces back from the wall. The speed of the ball just before reaching the floor is $8.0\,ms^{−1}$. The ball leaves the floor with an angle of $65^{\circ}C$ to the floor as shown.



1. Due to the collision with the floor, the ball losses 30% of its initial kinetic energy. Calculate the leaving speed of the ball from the floor. $v$ =    $ms^{-1}$
2. The ball strikes the wall just as it reaches the highest point of its motion. Determine the horizontal distance between the bounce point and the wall. $d$ =    $m$
3.The ball collides elastically with the wall, with the time of contact during the collision is $0.040\,s$. Calculate the average horizontal force exerted by the wall on the ball during the collision. $F_{ave}$ =    $N$

  A roller coaster car with r4 :r,y)d1. of5hdjkqd1 cqlta mass of 80 kg moves on the track shown in the diagram starting from point yto, j df d1q:dkrc15 4.)lhrqA.



At points B and C, the track approximates a circular path so that the radii at at B and C are $12,m$ and $18\,m$ respectively.

1.Compare the normal force exerted by the track on the car at point B is  ----待选择----greater thanequal toless than  the corresponding force at point C.
2.Draw and label the free body diagram of the car at point C.
3.Calculate the maximum speed of the car at point C so that it could remain on the track. $v_{max}$ =    $ms^{-1}$

  1.
(1) A spacecraft is moving in a zero gravity zone in space with constant speed. Its pilot decided to accelerate by burning fuel. The burned fuel is ejected backwards from the rocket with a constant speed of $2.5\times10^2\,ms^{−1}$ relative to the rocket at a constant rate of $2.0\times10^{2}\,kgs^{−1}$.
Calculate the net force on the rocket due to the ejection of burnt fuel is $F$ =    $\times 10^4\,N$.

(2) The spacecraft has a mass of $4.2\times10^3\,kg$ at the instant that it starts to burn the fuel. Calculate the acceleration of the spacecraft after $1.0\,s$ has passed. $a$ =    $ms^{-2}$


2.The spacecraft enters the atmosphere of Mars and slows down due to friction. To decelerate its speed more to reach a safe landing speed, the operator runs the propeller that pushes against the gas in the atmosphere.
(1) By referring to Newton's Third Law, outline why there is a force acting on the spacecraft due to the propeller.

(2)The average density of the Mars atmosphere is $0.020\,kgm^{−3}$. The radius of the propeller blades is $1.2\,m$. At a given instant, the average force slowing force from the propeller to is $140\,kN$. Assuming that the propellor causes all gas that it passes through to come to rest relative to the falling spaceship, estimate the speed of the spaceship at this instant. $v$ =    $ms^{-1}$

(3).The landing legs of the spacecraft have springs that can compress as the spacecraft makes contact with the ground. Explain how this decreases the average force acting on the spacecraft as it lands.

  1.Define momentum.

2.A golf ball of mass $45\,g$ moving with a constant velocity of $2.0\,ms^{−1}$ undergoes a head-on collision with a stationary ball of mass $2.0\,kg$. The line that joins the centers of the balls is along the direction of the velocity of the golf ball.



(1) Use Newton's Third Law and Second Law to deduce why the change in momentum of the golf ball is equal and opposite to the change in momentum of the stationary ball during the collision.

(2) The variation of force acting on the golf ball $F_g$​ with the time t during the collision is shown in the graph.



Calculate the magnitude of the change in momentum of the golf ball is approximately $\Delta p$ =    $kg\,ms^{−1}$.

(3) Calculate the speed of the golf ball just after the collision. $v$ =    $ms^{-1}$
(4) Determine whether the collision is  ----待选择----elasticinelasticit depends .

  A mass $m$ is moving on a circular path at the end of a rope of constant length. The centripetal force acting on the mass is $F$. The frequency of the motion is gradually increased. Which graph correctly shows the change of the centripetal force as the frequency is increased?

  A robot is used to mov,tx5t :w:md*s2zlfyv l;2r m ce boxes in a factory. A box is pulled up a slope inclined at l5r c vsm,:dw* :f;ltt2y2zxm$30^{\circ}C$ to the horizontal by a rope connected to the robot. The tension T in the rope is 45N. Friction acts between the box and the ramp.



1.Define work done by a force.

2.The box is moving at a constant speed. It covers $1.2\,m$ in $3.0\,s$.
(1) Calculate the output power of robot. $P$ =   $W$
(2) During the pull, the robot has a potential difference of $24\,V$ across the terminals of its battery and a current of $3.0\,A$ derived from the battery. Determine the efficiency of the robot in this situation. The efficiency(percentage) is:    %
(3) The $emf$ of the battery is $32\,V$. Calculate the internal resistance of the battery. $r$ =    $\Omega$​

3.The rope connecting the robot and the box breaks at a height of $1.5\,m$ from the ground level.
(1) The maximum height above the ground level reached by the box is $1.505\,m$. Calculate the work done by friction on the box after the break up to reach the maximum height. $W_f$ =    $J$
(2) Determine the coefficient of dynamic friction between the box and the incline. $\mu$ =   
(3) The box experiences friction both on the way up the slope and also as it slides back down the slope. On the graph below, sketch the variation of the speed $v$ of the box with the time $t$ passed from when the rope breaks until the box reaches the ground level.

  The motion of an object relyb/5qsqo;2t a eased from a high place in a vacuum is observed. The variation of its vel ;q/52sqty boaocity with time is recorded and the following graph is obtained.



1.Discuss the role that observations play in the development of scientific understanding.

2.Other than velocity and time, Can both displacement and acceleration be obtained from the graph?  ----待选择----yesno 

3.
(1) The height of the release point is $70\,m$. Calculate the speed $v_1$​ of the object just before the contact with the ground. $v_1$ =    $ms^{-1}$
(2)The object rebounds from the ground with a speed $v_2$​ of $17\,ms^{−1}$. The mass of the object is $8.0\,kg$ and the contact time during the rebound is $0.50\,s$. Calculate the average force acting on the object from the ground. $F$ =    $N$

  1.A small glass marbw 9q5;xgrmsh3-un87 cnkhzx;bkj b tec4o7 .)le of mass $5.0\,g$ is dropped into the ocean.

The following data are available:

The radius of the marble = $5.0\times10^{−3}\,m$
The average density of sea water = $1.03\times10^3\,kgm^{−3}$
The viscosity of the sea water = $1.1\times10^{−3}\,Pa\,s$

(1) On the diagram below, draw and label a free-body diagram of the forces on the marble when it is moving at a constant speed.



(2) Calculate the magnitude of the buoyant force acting on the marble. $F_{buoyant}$ =    $\times10^{-3}\,N$
(3) Determine the speed $v$ that is would be obtained using Stokes' Law in this situation. $v$ =    $ms^{-1}$
(4) The actual value of $v$ is significantly different than the calculated value in (3). Demonstrate why the calculated value is inaccurate.

2.The depth of the region where the marble was released is $9.2\times10^2\,m$. Calculate the pressure of the ocean on the ocean floor. $P$ =    $\times10^7\,Pa$

  A ball with mass $m$ is released from a height of $h$ and undergoes free fall. The ball hits the ground and rebounds vertically. On rebound, the ball reaches a maximum height of $h'$. The time taken for the collision is $T$. What are the magnitude of the average net force on the ball and change in kinetic energy of the ball?

  A roller coaster car of mass m approximates circular motion at point A as shown in the diagram.

  A stationary nucleus of uranium-238 undergoes alpha decay to form thorium-234. The initial speed of the alpha particle is v. What is correct about the magnitude of the thorium-234 velocity and its direction?What is Magnitude and what is Direction

  A ball of mass 0.1kg moves horizontally with a speed 5.0$ms^{-2}$, hits a vertical wall and rebounds with speed of 3.0$ms^{-2}$ The graph records the variation of force with time t.


What is $F_{max}$?

  A block of mass 4.0 kg rests on an inclined plane.

The coefficient of static friction between the block and the plane $\mu_s$ is 0.4.
Which of the following gives the angle of inclination at which the block will start to slide?

• 
  

  Two objects of mass M and m are connected via a frictionless pulley. The rope attached to the object of mass M makes an angle $\theta$ with the horizontal. The objects are at rest.
For the large mass, which expressions are correct for the force of friction $F_f$ and the normal force N
What is $F_f$ and what is N

  A point P is subjected to three simultaneous forces of magnitudes $F_A$>$F_B$>$F_C$ $F_A$>$F_B$>$F_C$. Point P is in equilibrium. Which of the following statements is not always true about the magnitudes of the forces?
I.$F_A$=$F_B$+$F_C$
II.$F_A$≤$F_B+F_C$
III.$F_A$＞$F_B$-$F_C$

  

  A car enters a horizontal circular roundabout as shown with a speed of ${35kmh^{-1}}$. The radius of the roundabout is 15m.

• State the force which provides the centripetal force for the circular motion of the car.
  1
• Calculate the minimum coefficient of static friction between the tyres of the car and the road for the car to safely complete its motion around the roundabout.  
  3
• State and explain any change in your answer to part (b) if:
  
  • The mass of the car increases.  ----待选择----changeNo change 
    2
  • The road is banked at an angle so that the car is tilted towards the center of the roundabout.
    2
  • The speed of the car increases.
    

  A box half filled with sand is pulled by a motor at a constant speed of2${2ms^{-1}}$ on a frictionless surface. During the motion, sand is added to the box from above at a constant rate of ${{\sigma}kgs^{-1}}$

• State the condition related to the mass of an object in order for the equation ${F_{net}}$=ma to be equivalent to the equation ${F_{net}}$=${\frac{{\Delta}p}{t}}$.
  1
• The force applied by the motor on the box is 0.11N. Determine ${\sigma}$  ${kgs^{-1}}$
  2
• The motor has an efficiency of 75%. Calculate the total power provided to the motor.  (数值) W
  2
  

  Two bodies of masses 2 kg and 3 kg are connected by a thread and pulled in the upward direction with an acceleration of g due to an upward force F
The thread between the masses is cut. Which of the following is correct for the bodies just after the cut?
What is Acceleration of 3 kg mass and what is Acceleration of 2kg mass

  A stationary object explodes and splits into two parts of masses m and 2m. Mass m moves north with a velocity of 2v and mass 2m moves south with a velocity of v. Calculate the total change in linear momentum of the system as a result of the explosion.

  A spherical raindrop falls at a termj,05a+wdrrh-m ea1 l8g0u h zminal speed of v. Its density is ρ and its radius is r Which of the following expressions is correct for v? (Buoyancy acting on the raindrop is insignificant)

  An object of mass m rests on a rough surface. Another object of mass M is connected to it via a frictionless pulley. The coefficient of dynamic friction between the surface and the object of mass m is μ.

When the object of mass M is released, the objects accelerate. What is the acceleration of the system?

  A cannonball is fired horizontally from a cannon positioned at the edge of a cliff.
1.In the context of Newton's Laws, explain why the cannon recoils to the left when the cannonball is fired.
2.The initial recoil speed of the cannon is 1.0$ms^{-1}$ and its mass is 1200 kg.
(1)The total of opposing forces acting on the cannon during the motion of the cannon is 8.0 kN. Determine the distance covered by the cannon after the firing.  m
(2)The mass of the cannonball is 9.0 kg. Calculate the magnitude of the firing velocity of the ball is approximately   $ms^{-1}$.
(3)Calculate the magnitude of the displacement of the cannonball after 5.0s. Air resistance can be ignored.  m

  A system that consists of two light identical springs connected in series stores a total elastic potential energy $E_p$when a load is added to the springs. One of the springs is then removed and the same load is added to the remaining spring.

In terms of$E_p$, what is the total elastic potential energy stored in the single spring situation?

  Two blocks of masses 3.0 kg and 4.0kg are held stationary with a thread connecting the blocks. The mass of 3.0 kg is on a rough incline that makes an angle of 30° with the ground and it starts to slip up when the other mass is slightly more than 4.0 kg.

• State two differences between static friction and dynamic friction
  2
• Calculate the coefficient of static friction between the mass of 3.0 kg and the rough surface.   
  3
• The thread connecting masses breaks and the mass of 3.0 kg is around 1.5 kg mass and the rough surface is 0.40.   ${ms^{-1}}$
  2
• Determine the speed of the mass of 3.0 m.   ${ms^{-1}}$
  2
  

  A CD stores data on its surface on a number of concentric circular tracks of different radii. The radius of the first track is 24 mm and that of the last track is 60 mm as shown in the diagram.

  The diagram shows the forces acting on a block as it slides down an inclined plane with constant acceleration. W is the weight of the block, F is the friction force, μd​ is the coefficient of dynamic friction and g is the gravitational field strength. The plane is inclined at an angle θ to the horizontal.

Which expression gives the acceleration of the block?

  Three identical cylinders sit inside a cup. Their radius of each is 5 cm ana8g 55qiez.n nd their centres of mass are marked in the diagram. The lines connecting the centres of the masses pass through the contact points between the cylinders. z8n55aq i.gne

1.Draw and label the free-body diagram for the cylinder $M_3$
2.1For analysis purposes, the three cylinders can at times be considered as a single object consisting of the mass of the all cylinders. Explain why this simplification may be useful.
2.2The reaction force of the ground on $M_3$ is 30N Show that the mass of each cylinder is around 1.0 kg  kg
3.Determine the force that mass $M_3$ exert on $M_1$  N

  Block A of mass $m_A$=3.0 kg $m_A$=3.0kg rests above the flat horizontal surface of block B of mass $m_B$=6.0kg, which in turn rests on a smooth horizontal surface as shown.

The coefficients of static and kinetic friction between A and B are $\mu_s$​=0.2 and $\mu_k$​=0.1 respectively. A horizontal force of F=7.0N is applied towards the right on block A. Assuming acceleration due to gravity g≈10$ms^{-2}$ the direction and magnitude of acceleration $a_B$of blockB are:

  

• A conical pendulum consists of a 22cm string that makes an angle θ with the vertical as shown in the diagram.
  Mass of the bob = 8.0g
  
  Angle with the vertical θ=$20^{\circ}$
  
  
  Show that angular velocity $\omega$ is given by $\omega=\sqrt{\frac{g\tan \theta}{\tau}}$
  2.2Calculate the linear velocity of the bob   $ms^{-1}$
  
  2.3Determine the tension in the string.   N
  
  3.1Explain the effect of increasing the angular speed ω on the angle θ.
  
  3.2The maximum tension the string can provide is 1.5N. Determine the maximum angular speed.  $rads^{-1}$
  
  

  

  A ball of mass m strikes a vertical wall with a speed of v. It bounces back with the same speed. The angle between the wall and the trajectory of the incoming ball is $\theta_2$​. The angle between the wall and the trajectory of the ball after the bounce is $\theta_2$. During the collision, the only force that acts on the ball is normal to the wall.


What is the magnitude of the change in momentum of the ball?

  A ball of mass 1.6kg is dropped from a very high building. The only forces acting on the ball are the force of gravity and air resistance. The graph shows the variation of the vertical velocity v of the ball with time t.

• 
  
  • Define terminal speed.
    1
  • State the terminal speed of the ball.   $ms^{-1}$
    1
    
• Estimate the vertical displacement of the ball during the t=2.0s  $ms^{-2$}
  2
• Determine the magnitude of the vertical component of air resistance at t=2.0s  N
  3
  

  A mass m attached to a string is moving in a horizontal circular motion as shown. The tension on the string is T, and the angle with the vertical is θ.

• I. Centripetal force = mg tan(θ).
• II.Total gravitational and kinetic energy of the mass is constant.
• III. If the rope is cut, the mass will fall downwards with a straight line trajectory.
  

  A mass Y attached to a rope is moving in uniform circular motion on a frictionless table as shown on the diagram. The circular path of constant radius r is shown with the dotted line. The mass X is hanging from the lower end of the rope.

The masses of X and Y can be adjusted. What independent adjustments to mass X and mass Y could produce uniform circular motion at a lower speed v, but with the same radius r?

  A mass moving with a constant speed u encounters a rough surface and comes to a stop. The mass takes a time t to stop after encountering the rough surface.




The coefficient of dynamic friction between the rough surface and the mass is 0.40. What which of the following expressions gives the initial speed u?

  A firecracker is at rest v1fi,rfd +l( )mqra mf 3fq,+bjust before exploding. Upon exploding, the firecracker splits into two unequal pa qm)f3qfadb ffr+ ,m(v l+ir,1rts which are projected in exactly opposite directions. Which of the following must be true?

• 
  

  A race car starts to ryz0z-6b-p) nj co7ff sace on a straight horizontal race track from rest. The car's engine has a constant power output and the car experiences a resistive fo67-)nzo cfs pbyf0-j zrce that increases proportionally with its speed.
Which graph represents the variation with distance s of the power P required by the engine to overcome the resistive force?

  A small ball of mass m is attached to a string axypi((g dko(q;vpt /j 0rm;(tx,ygu wgt-(5 end moves in a vertical circular path of radiusyk/wotrex( pg0 (((d,;qg;pjymxt( 5t guv- i r

What is the minimum velocity v at the lowest point of the path for the ball to continue moving in a circular path at top of the circle?

  Three identical masses are con,cd0yb g7o, *lrw0qocnected as shown with a string that passes over an ideal pulley. The tension in the string c ylgo0c 7r0w*o,d ,bcqonnecting $m_1$ and $m_2$ is $T_1$
. The tension of the string attached to $m_3$ is $T_2$
The acceleration of the $m_3$ is $\frac{g}{4}$
Which of the following is correct for $T_2$ and the acceleration of $m_1$

  An object of mass m withd4vyb87ybc a* a speed of 3.0$ms^{-1}$ collides horizontally with a stationary box of mass 2m ,After the collision, the object and the box move together.
The friction acting on the box and the object is 6.0N.
Which expression gives total distance travelled by the combined objects before coming to rest after the collision?

  A trapeze artist is swinging from positil5ows6vpy: xkgn:-aduq1 c /)on A to position C as shown in the diagram.o cvyuw5:p)6:s xqg/1d-klan


[Source: Image created using Images by OpenClipart-Vectors from Pixabay - https ://pixabay.com]
The combined mass of the artist and the swing is 70 kg and the length of the rope of the swing is L Which expression gives the kinetic energy at position B?

  A roller coaster loop has a radius R ;rrez jrif0*p3l3 ;in as shown in the diagram. The combined mass ofjlnie rr3i pfr30z;*; a car and the passengers is M


When the car goes around the top of the loop, the normal reaction force of the track on the car is equal to half of the weight of the car and passengers.
Which expression gives the kinetic energy at the top of the loop?

  A 200g ball is moving in a horizouvai k+,3lz*lv7)kdju8- r eantal circle shown with the dotted path in the diagram. The diameter of the bol+ikv8, *l)z7u u3rda v-keajwl is 40 cm and the angular speed is $4\pi rads^{-1}$

What is the magnitude of the ball's centripetal acceleration?

  An object starts to move in a straightut(b6x i .k u-,uw)lxm line under the effect of two opposite force)mx,t 6b(- wkx uu.iuls of 12N and 16N


After 5s, the displacement of the object is 25m. What is the mass of the object?

  1.Define Newton's First Law.A block of mass taeao,qi8+t,f6 ;es -4a f90sdoej 5vwz )nzw 2.0 kg slides at the constant speed of v on a rough inclined plane. A string attached to the hanging mass of 0.50 kg 2.passes over a pulley and supports the block. The slope ofeawastw -,fi0s+e9)f nv86z; 4jdazqo,toe5 the incline is 25°.


[Source: Created with Chemix - https://chemix.org/]
1.Show that the direction of the motion of the box is down the slope.
2.Draw and label a free-body diagram for the forces acting on the block.

3.Determine the coefficient of dynamic friction between the block and the inclined plane.  
4.In reality, air resistance will also have an effect on the motion of the block and the calculated coefficient of friction. If air resistance were taken into account for this constant speed scenario, discuss how the calculated value would be affected.

  washing machine contains a cylinder thaj0xt-u- ah 1noh,eyk8t carries clothes and rotates in a circular motiohak-xujeh-,0 1oyt n8n about a horizontal axis as shown in the diagram. Frictional forces act between the clothes and the inner surface of the cylinder.

The radius of the cylinder is 0.27m and its linear speed of rotation of the outside of the cylinder is$1.6ms^{-1}$
1.Draw the free body diagram for the piece of clothing at the position shown.
2.1The laundry machine cylinder is designed to make the piece of clothing lose contact with the cylinder at an angle θ above the horizontal as shown.


The free body diagram for the piece of clothing at this position is given below.



Give an expression for the centripetal force at the position shown.  
2.Calculate the angular speed, expressing your answer to the correct number of significant figures  $rads^{-1}$
3.Show that θ=75° when the piece of clothing loses contact with the cylinder.
4.Determine the time taken for a piece of clothing to move from the lowest point of the cylinder (point A) to the point where it loses contact.  s

  A rocket is moving in the absence of a gravitaq z9ar 82huxn6.5 vo-lyzg v)ltional field with constant speed. It starts to accelerate by burning fuel. At the start, the fuel contributes to most of the mass of the rocket. The burned fuel is ejected backwards from the rocket with a constn zaq x yzo.ug)v5rl8l9hv- 62ant speed of v relative to the rocket and a constant rate of σ $kgs^{-1}$
. Which graph shows the variation of acceleration a of the rocket with time t as most of the fuel is used?

  A jet of water with a cross sectional area of A strikes perpendiculaj- bx v-hfd70jr to a wall at a speed of v After the collision, the water loses all of its horizontal speed and falls to the ground. The magnitude of the force created on the wall due to the watervf 0h bd-jj7x- is F Which expression give the density of the water?

  An apple falls 5 m in height from a tree. e 2s3,.mfuf,d7 m;uyljakx(u It rebounds from the ground with a quarter of its striking speed. The apple is in contact with the ground for approxim3 k.xj(,7f f,memdyas u2ul;uately 0.1
s. What is an estimate of the magnitude of the average net force on the apple when it strikes the ground?

  A box of mass 3kg is pl9q pri8 4dfdw td)+x7hg1qbq9aced on a box of mass 7kg. The coefficient of static friction between the surfaces of the boxes is 0.5. A horizontal forceF is applied to the 7kg box which p qd9g7+h )q fd8rxw9qt d4i1bsits on a frictionless surface.

What is the maximum value of F that can move the boxes without the 3kg box slipping?

  1.Define Newton's Thicyshp*:ecw .oi (gp *-rd Law.
2.A block of mass 2.0 kg is placed on another block of mass 5.0 kg. The blocks sit on a frictionless surface, but the coefficient of static friction between the blocks is 0.50. The block at the top is pulled with a varying horizontal force F


2.1Calculate the magnitude of the maximum force $F_{max}$ which results in both of the blocks moving together without slipping.  N
2.2On the graph, sketch how the force of static friction $F_f$ acting on the bottom block varies with the force F
(no need to add values on the axis)



$F_{max}$ is your answer to (b)(i) and draw your graph up to $F_{max}$
2.3According to Newton's Third Law, there must be another force paired with the weight of the top block. Describe this force.
3.On another occasion, the blocks are moved with the help of a force of 12N acting on the block at the top. The drag force D on the blocks is given by D=2.5*$10^{-2}v^2$where v is the speed of the blocks. Calculate the top speed of the blocks for this force.  $ms^{-2}$

  A 74 kg boy starts to ride a 6.0 kg t.k:fy,sjgc n/k83xu bicycle from rest. The graph shows how the acceleration a of t gyusk: cnx k.tjf83,/he bicycle varies with the distance travelled x

What is the total work done by the boy?

  An object of mass 1.0kg rests on a rough surface. Another object of masu.dq9s(kaaxi 2)h :wts 2.0kg is connected to i)ti2(9u :wqhska dx.at with a string.

When the objects are released, the masses accelerate at $\frac{g}{2}$The work done by the tension of the string on the 1.0kg mass is 40J. Which of the following is correct for the 1.0kg mass during this period?
What is Magnitude of the force of friction /N and Distance travelled

  A piece of metal of weight W is suspended by two identical strings. Each strih(n kzom j(;g7u5) b5i0.khyw2mj wzc ng passes thro5 (uwj;k( bw5i c2mygz0km )o.h nzjh7ugh a pulley and is attached to a block of mass m. The system is in equilibrium

What must be true for m such that the two strings attached to the piece of metal are almost horizontal?

  A ball of mass 0.4kg is attachez)9t ;a/bx.o n9 a7s+cvn e-hn9h tidyd to a string of length 0.2m and is moving in a verticstobn;ay7 zexh/nh n -a. +99vt9i)dcal circular path with tangential speed of $\sqrt3ms^{-1}$ at the instant shown in the diagram.

Given that$\sin (60^{\circ})$=$\frac{\sqrt3}{2}$ and $\cos (60^{\circ})$=$\frac{1}{2}$,what is the tension in the string at the shown position?