Dynamics：練習題

A mass of \( 0.50 \, kg \) is suspended from a spring and is at rest. The mass is then pulled down by a force \( F \) so that the spring extends further by \( 0.10 \, m \). If the spring constant is \( 100 \, N \, m^{-1} \), what is the net force acting on the mass at the instant it is released?

A jet of water of cross-sectional area \( A \) strikes a vertical wall normally with a speed \( v \). The water does not rebound but runs down the wall. The density of water is \( \rho \). What is the force exerted by the water on the wall?

A trolley of mass \( 2.0 \, kg \) moving at \( 4.0 \, m \, s^{-1} \) collides head-on with a stationary trolley of mass \( 3.0 \, kg \). The collision is perfectly elastic. What is the velocity of the \( 2.0 \, kg \) trolley after the collision?

A helicopter of mass \( 1500 \, kg \) accelerates vertically upwards at \( 2.0 \, m \, s^{-2} \). Air resistance is negligible. The blades of the helicopter push a volume of air downwards. What is the magnitude of the force exerted by the air on the helicopter blades?

A uniform wooden block of mass \( m \) is placed on a rough plane inclined at an angle \( \theta \) to the horizontal. A force \( P \) is applied parallel to the plane to move the block up the plane at a constant velocity. The frictional force between the block and the plane is \( f \). Which expression correctly defines the force \( P \)?

Which fundamental property of an object is a measure of its reluctance or resistance to a change in its state of motion?

A metal sphere of mass \( 0.40 \, kg \) is moving with a velocity of \( 6.0 \, m \, s^{-1} \). It collides with a stationary sphere of mass \( 1.2 \, kg \) and stays in contact with it.
What is the loss in total kinetic energy of the system as a result of this collision?

A rocket of mass \( 2500 \, kg \) ejects exhaust gases at a constant rate of \( 40 \, kg \, s^{-1} \) with a relative speed of \( 800 \, m \, s^{-1} \).
Ignoring the effect of gravity, calculate the initial acceleration of the rocket.

Two blocks, X and Y, are connected by a light inextensible string passing over a smooth pulley. Block X has a mass of \( 3.0 \, kg \) and sits on a smooth horizontal surface. Block Y has a mass of \( 5.0 \, kg \) and hangs vertically.
(a) Calculate the acceleration of the system when released from rest.
(b) Calculate the tension in the string.
(c) If the surface for block X is replaced with a rough surface providing a constant frictional force of \( 4.5 \, N \), calculate the new acceleration.

A trolley of mass \( 0.80 \, kg \) moves at a velocity of \( 2.5 \, m \, s^{-1} \) to the right. It collides with a second trolley of mass \( 1.2 \, kg \) moving at \( 1.5 \, m \, s^{-1} \) in the opposite direction. After the collision, the \( 0.80 \, kg \) trolley moves to the left at \( 1.8 \, m \, s^{-1} \).
(a) Calculate the final velocity of the \( 1.2 \, kg \) trolley.
(b) Determine whether the collision is elastic or inelastic by calculating the total kinetic energy before and after the impact.
(c) Explain the significance of the relative speed of approach and relative speed of separation in this context.