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习题练习：Space Time & Motion A.3 Work Energy and Power
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 作者: admin    总分: 53分  得分: _____________

答题人: 匿名未登录  开始时间: 23年11月13日 16:37  切换到: 整卷模式

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1#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A lead ball is dropped le;bt6r8 / oh ebtilq3r4la45from a height of $12\;m$ above the ground. Assuming that air resistance is negligible, which of the following expressions best describes the total energy of the ball when it is at a height of $3\;m$ above the ground in terms of its kinetic energy ($E_k$) and gravitational potential energy ($E_p$)?

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2#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Which of the following units is not a unit of power?

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3#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A builder uses a block and tackle pulley system to lift a bundle of materials of mass 15 kg to the top of a building of height 6 m in 9 s. What is the power delivered to the bundle?



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4#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The figure below shows Sankey's diagram for a small thermal plant. What is the efficiency of the system?



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5#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An object of mass M on a string moves in a circle of radius r at a constant speed.


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 velocity of the object is constant.


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6#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A box is pulled by a child with a horizontal force of $5\;N$. The box moves a horizontal distance of $4\;m$ in a time of $2\;s$. The average power delivered by the child to the box is

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7#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Which of the following is not a suitable SI unit of energy?

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8#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  
The Sankey diagram below shows the energy degraded at different stages of a nuclear power plant.
Which of the following sections corresponds to the stage with the highest energy degradation?


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9#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A coin is tossed vertically upwards from a height of 1.5 m. What is the maximum height reached above the ground if the coin was projected with an initial velocity of $3.0\;m\;s^{-1}$?(Take $g\;=\;10\;m\;s^{-2}$)

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10#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  1.State the law of conservation 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 masses $\frac{m_2}{m_1}$ =   

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11#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A spring with spring constant $k$ is extended by a distance $x$.

The uncertainty of $k$ is 2% and that of $x$ is 3%.
What is the uncertainty of the potential energy stored in the spring?


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12#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A box of mass m is pulled across a horizontal surface with a force $F$ as shown in the diagram. The coefficient of dynamic friction between the box and the surface is µ. What is the energy transferred to thermal energy while a box is moved by a distance of $d$?


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13#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The engine of a racing car provides a forward thrust of $800\;N$. The average of the total resistive forces acting on the car is $300\;N$ and the car covers a distance of $1.0km$ in $10s$. What is the average output power of the engine?

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14#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An electric motor is used to raise a block of mass 18.0 kg vertically to the top of a building at a constant speed of $1.5\;m\;s^{-1}$. If the power rating of the motor is 297 W, calculate the efficiency of the motor.

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15#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A box is pulled up a slope inclined at $30^{\circ}$ to the horizontal by a force of $F$.The angle between the direction of $F$ The angle between the direction of $30^{\circ}$.


The box is pulled a distance of d up along the slope. What is the work done by F on the box?

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16#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  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 $5.0\,m\,s^{-1}$. Calculate the maximum force exerted on the wall by the ball.  $N$
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 $3.0\,m\,s^{-1}$.
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    $J$ of the ball during the collision.
3.During this collision, the ball undergoes a change in momentum. the the law of conservation of momentum    in this situation.

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17#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A car engine has an input power of $P_{in}$ and efficiency of η. Which of the following gives the wasted energy from the engine in time of $t$.

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18#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A box of mass $2.0\;kg$ starts to move on a level surface under the effect of a varying force $F$. The variation of $F$ with the displacement $s$ of the object is shown in the graph below.

What is the speed of the box at $s=5\;m$?

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19#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A varying force acts on a spring. The variation of the extension $x$ of the spring with force $F$ acting on it is shown in the graph below.


The elastic potential energy stored in the spring is $E$ when the extension of the spring is $e$. What is the work done by force on the spring to increase the extension from $e$ to $3e$?

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20#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  While practising, a table tennis player 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 $8.0\;m\;s^{-1}$. The ball leaves the floor with an angle of $65^{\circ}$ to the floor as shown.

1.Due to the collision with the floor, the ball losses 30% of its initial kinetic energy. The leaving speed of the ball from the floor is around   $m\;s^{-1}$.
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.  $m$
3.The ball collides elastically with the wall, with the time of contact during the collision is $0.004\;s$. Calculate the average horizontal force exerted by the wall on the ball during the collision.  $N$



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21#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An elastic bungee cord of natural length $20\,m$ is being tested. A spherical object, originally at rest, is released from a platform. Air resistance and the mass of the cord are insignificant.


1.State the principle of conservation of energy.
2.Describe the eneryg changes that take place in the spherical object from the time it is released until it comes to rest for the first time.
3.The speed of the object just before the cord starts to extend is approximately   $m\,s^{-1}$.
4.The magnitude of the average net force acting on the object by the cord between the point the cord starts to extend and the point where it reaches maximum extension is $360\,N$ . The time taken during the fall of the object between these points is $0.28\,s$.
1.The mass of the object is approximately   $kg$
2.On the graph below, sketch how the the elastic potential energy $E_E$ of the spring changes with the vertical displacement $s$ as the cord stretches. There is no need to add values to the axes.

3.The extension of the cord at the point in time when the object has zero acceleration is $11\,m$. Determine the spring constant of the cord.  $N\;m^{-1}$




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22#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A block of mass 16 kg is pushed and released along a rough horizontal surface at an initial speed of $2\,m\;s^{-1}$.


The block travels through a distance of $16\,m$ and is brought to rest. What is the magnitude of the frictional force that brings the block to rest?

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23#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  1.Define momentum.
2.A golf ball of mass $45\,g$ moving with a constant velocity of $2.0\,m\;s^{-1}$ undergoes a head-on collision with a stationary ball of mass $2.0\;kg$. The line that joins the centres 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.

The magnitude of the change in momentum of the golf ball is approximately   $kg\,m\,s^{-1}$
3.Calculate the speed of the golf ball just after the collision.  $m\,s^{-1}$
4.Discuss whether the collision is elastic or inelastic.

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24#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  
A robot is used to move boxes in a factory. A box is pulled up a slope inclined at $30^{\circ}$ to the horizontal by a rope connected to the robot. The tension $T$ .


Ⅰ.Define work done by a force.
Ⅱ.The box is moving at a constant speed. It covers $1.2\,m$ in $3\,s$.
1.The output power of robot   $W$
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.  %
3.The emf of the battery is $32\,V$. Calculate the internal resistance of the battery.  $\Omega$
Ⅲ.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 $1.505\,m$ . Show that the work done by friction on the box after the break up to reach the maximum height is  $J$.
2.The coefficient of dynamic friction between the box and the incline  .
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.





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25#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A spring of spring constant $200\,N\;s^{-1}$ is compressed by $6.0\,cm$.

At the point where the box has moved $4.0\,cm$, how much work has been done by the spring on the box?

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26#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An object is thrown vertically upwards on the surface of the moon. The maximum height that the object can reach is h. When the object reaches the height of $\frac{h}{3}$ above the surface, what is the ratio


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27#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A car is moving with a kinetic energy of $10^5\;J$ .
Estimate the order of magnitude of its momemtum.

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28#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  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 change in kinetic energy of the ball and average net force on the ball?

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29#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A motor uses a cable to pull a trolley up an inclined plane at a constant velocity.


Which of the following statements about the energy changes of the trolley during its motion are correct?
Ⅰ.The work done by the engine has greater magnitude than the work done by friction.
Ⅱ.The total of kinetic and potential energy of the trolley increases.
Ⅲ.The gain in gravitational potential energy of the trolley has the same magnitude as the work done by the engine.

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30#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A ball is released from rest at a height h above the ground. At each bounce At each bounce $75^{\circ}$ of its kinetic energy is lost. Which graph represents the variation of the ball's velocity v with time t from the beginning of motion until the moment just before the third bounce? Assume the acceleration of the ball is in in the negative direction and that air resistance is negligible.



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31#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A box of mass $2\,kg$ is pushed with an initial speed of $10\,m\;s^{-1}$ on a rough horizontal floor. A uniform frictional force of $10\,N$ acts on the box. What is the distance travelled by the box at the instant when the kinetic energy of the box is halved?

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32#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  
  • 1.Define power
  • 2.A mass of $2.0\,kg$ is pulled by a variable horizontal force $F$ on a smooth surface. A thread attached to the mass passes over an ideal pulley and supports another mass of $3.0\,kg$.

The variation of $F$ with the distance $d$ moved by the mass of $2.0\,kg$ is shown in the graph.

  • 1.Calculate work done, in $J$, on the $2.0\,kg$ mass by the force $F$ when the mass travelled $0.90m$.  $J$
  • 2.Calculate the final speed of the $2.0\,kg$ mass.  $m\;s^{-1}$
  • 3.On another occasion, the horizontal force is no longer applied and the $2.0\,kg$ mass is replaced with a motor which pulls the $3.0\,kg$ mass with a constant speed of $0.50\,m\;s^{-1}$.

  • 1.On the graph, show the variation of the change in gravitational potential energy Δ$E_p$ of the mass with time $t$.(no need to add values to the axes)

  • 2.The power supplied to the motor is $20\,W$. Calculate the efficiency of the motor.  %


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33#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Ⅰ.The diagram below shows a water slide. As a test, an object is released from point $A$,$\,6.0\,m$ above the ground level. Point $B$ at the end of the slide is $2.0\,m$ above the ground level. Location $C$ is the point of contact of the slide with the ground. The slide approximates a circular shape at this point.

Air resistance and friction on the object are negligible.
1.Draw the free-body diagram of the forces acting on the object as it passes point $D$.

2.At the instant the object passes point $C$, explain why there is acceleration and yet no work is done.
Ⅱ.The object slides from point $A$ to point $B$ and is launched from point $B$ with an angle.
1.The speed of the object at point $B$ is approximately   $m\;s^{-1}$
2.At point $B$, on the object is launched into the air and lands in a pool of water that is $2.2\,m$ below point $B$.
After $1.1\,s$, it reaches the surface of the water. The angle $\theta$ of the launch above the horizontal is approximately   $^{\circ}$.
3.Calculate the horizontal distance travelled by the object between losing contact with the slide and reaching the water.  m

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34#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An electric motor lifts containers through a vertical distance of $30\,m$.Each container weighs $200\,N$ and takes 60 seconds to lift.If the motor operates at $100N$ and has an efficiency of 40%,what current must be delivered to the motor?

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35#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A box half filled with sand is pulled by a motor at a constant speed of $2.0\,m\;s^{-1}$ on a frictionless surface. During the motion, sand is added to the box from above at a constant rate of $\sigma\;kg\;s^{-1}$

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 $F_{net}=\frac{Δp}{t}$
2.The force applied by the motor on the box is $0.11\,N$. Determine $\sigma$.  $kg\;s^{-1}$
3.The motor has an efficiency of 75%. Calculate the total power provided to the motor.  $W$

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36#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A body with maximum potential energy $E_p$ undergoes simple harmonic motion with amplitude $X_0$. The body is released from rest from maximum displacement. What is the magnitude of the change in potential energy of the system after the body has moved a distance of $\frac{X_0}{4}$?

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37#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  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?

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38#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Two blocks of masses $3.0\,kg$ and $4.0\,kg$ are held stationary with a thread connecting the blocks. The mass of $43.0\,kg$ is on a rough incline that makes an angle of $30^{\circ}$ with the ground and it starts to slip up when the other mass is slightly more than $4.0\,kg$.

1.State two differences between static friction and dynamic friction
2.Calculate the coefficient of static friction between the mass of $3.0\,kg$  $N$ and the rough surface.  
3.The thread connecting masses breaks and the mass of $3.0\,kg$ slides down. The acceleration of the mass of $3.0\,kg$ is around   $m\;s^{-2}$. The coefficient of dynamic friction between $3.0\,kg$ mass and the rough surface is 0.40.
4.The speed of the mass of $3.0\,kg$ after it has moved through a vertical height of $1.0\,m$.  $m\;s^{-1}$

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39#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  The graph shows the variation of length of a spring of original length $l_0$ as it is stretched to length $l$ by a variable force



The work done against the spring is represented by which of the following?

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40#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  
A cart of mass $M$ enters a smooth vertical loop the loop or radius $R$ with a horizontal speed $u$ at the bottom of the track, as shown. The cart just manages to stay in contact with the track at the top most point of its path.
Its speed at the bottom of the loop $u$, is given by:


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41#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  
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 $\theta$.
Which of the following statements are correct for this motion?
  • I. Centripetal force = $mg\;\tan (\theta)$
  • 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.


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42#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  
A race car starts to race on a straight horizontal race track from rest. The car's engine has a constant power output and the car experiences a resistive force 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?


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43#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A motorised toy car starts from rest, with the motor delivering increasing power to the car over time as shown in the graph below.


Assuming no energy losses, which of the following gives the kinetic energy of the car after 8.0 seconds?

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44#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A small ball of mass $m$ is attached to a string and moves in a vertical circular path of radius $r$.



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?

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45#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An object of mass $m$ with a speed of $3.0\,m\;s^{-1}$ collides horizontally with a stationary box of mass $2\,m$. After the collision, the object and the box move together.



The friction acting on the box and the object is $6.0\,N$.
Which expression gives total distance travelled by the combined objects before coming to rest after the collision?


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46#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A trapeze artist is swinging from position A to position C as shown in the diagram.



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?


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47#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A roller coaster loop has a radius $R$ as shown in the diagram. The combined mass of 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?

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48#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An object is released from rest from a very high building. Air resistance is not negligible. Which of the following graphs shows the variation of the gravitational potential energy of the object with time?



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49#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  Two masses of $2kg$ and $4kg$ are connected with a string that passes over a pulley. They are released from rest. Energy is lost in the pulley due to friction.



When the $2kg$ mass has gained a gravitational potential energy of $E$, the $4kg$ mass has a kinetic energy of $\frac{1}{2}E$. How much energy has been lost to friction up to that point in time?

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50#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A metal ball of mass $m$ is released from a height of $h$ above a massless platform attached to a vertical spring.

The spring constant of the spring is given by $\frac{mg}{h}$. The ball hits the spring and compresses it. When the spring is compressed by a distance $h$, what is the speed of the ball?(Energy transfer only happens between spring and ball and the kinetic energy of the spring can be ignored)

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51#
 
填空题 ( 1.0 分) 切至整卷模式 搜藏此题  
  1.Define potential energy.
2.A body of mass $2.0\,kg$ is pushed with an initial speed of $1.2\,m\;s^{-1}$ down the slope of a frictionless $30^{\circ}$ incline from a height of $h$. As soon as it reaches the bottom of the incline, it begins to move on a rough horizontal table where it comes to rest momentarily after colliding with a spring of spring constant $32\,N\;m^{-1}$.

1.The speed of the body is $3.06\;m\;s^{-1}$ when it reaches the bottom of the incline. Calculate $h$  $m$.
2.The distance between the bottom of the slope and the body's position is $x$. On the graph, sketch the variation of the square of the speed $v^2$ of the body with distance $x$.(no need to add values to the axes)

3.At the instant that the body stops momentarily, the spring is compressed as $0.43\,m$. The coefficient of friction between the body and the rough surface is 0.40. The distance that the body covered on the horizontal rough surface between the point of leaving the ramp and stopping momentarily.  
3.The incline is replaced with one of a steeper gradient. The body is pushed at the same speed from the same height. Explain the effect of the increase in gradient on the maximum compression of the spring in comparison to the maximum compression in the original situation.

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52#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  A 74 kg boy starts to ride a 6.0 kg bicycle from rest. The graph shows how the acceleration $a$ of the bicycle varies with the distance travelled $x$.


What is the total work done by the boy?

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53#
 
单选题 ( 1.0 分) 切至整卷模式 搜藏此题  
  An object of mass $1.0\,kg$ rests on a rough surface. Another object of mass $2.0\,kg$ is connected to it 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 $1.0\,kg$ mass is $40\,J$. Which of the Magnitude of the force of friction and N Distance travelledis following is correct for the $1.0\,kg$ mass during this period?

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