[填空题]
1.In an Atwood machi2s k4awg7 bg2fne, two blocks of masses 2.0kg and 4.0khm770mdu e7u yg are connected with a mass0ymu ud e77h7mless string that passes over a pulley. The pulley has a radius r of 0.25m.
The masses are released from rest and the tensions created on the strings attached to the masses of 2.0kg and 4.0kg are $T_1$ and $T_2$ respectively. The acceleration of the mass of 2.0kg is 2.3$ms^{−2}$.
(1)Determine the values for $T_1$ and $T_2$. $T_1$ = N $T_2$ = N
(2)Show that the angular acceleration of the pulley is approximately 9rads$^{−2}$. $α$ = rads$^{-2}$
(3)Calculate the angular speed of the pulley after 3.0s. $ω_f$ = rads$^{-1}$
(4)By using the answer in (i) and the information in (ii), calculate the moment of inertia $I$ of the pulley. $I$ = kg m$^2$
(5)Discuss whether the pulley is in rotational equilibrium or translational equilibrium.
2.On another occasion, the same pulley's rotation is controlled by a motor. The variation of the pulley's angular velocity with time is shown on the graph below.
(1)Identify the quantities that are represented by the area under the graph and the gradient of the graph.
(2)On the graph below, sketch the variation of torque T on the pulley with time. (There is no need to add values to the axes.)
(3)The system starts from rest and the angular velocity of the pulley at t=4.0s is 4.0rads$^{−1}$. Calculate the number of revolutions made by the pulley between t=0s and t=4.0s. n =
