A.2 Forces and momentum：練習問題

A stationary gun of mass \(M\) fires a bullet of mass \(m\) horizontally with a velocity \(v\). What is the recoil velocity of the gun immediately after the bullet is fired?

A small mass is attached to a string and whirled in a horizontal circle of radius \(r\) at a constant speed \(v\). The tension in the string is \(T\). If the speed of the mass is doubled and the radius of the circle is halved, what will be the new tension in the string?

A book is resting on a horizontal table. If the weight of the book is considered the "action" force, what is the "reaction" force according to Newton's third law of motion?

A \(2.0\,kg\) trolley moving at \(3.0\,m\,s^{-1}\) collides with a stationary \(4.0\,kg\) trolley. After the collision, the trolleys stick together. What is their common speed immediately after the collision?

A wooden block of mass \(m\) rests on a rough horizontal table. A horizontal pulling force \(P\) is applied to the block, but it remains at rest. Which of the following correctly identifies the magnitude of the static friction force acting on the block?

A car of mass \(1200\,kg\) accelerates from rest to \(15\,m\,s^{-1}\) in \(5.0\,s\). Calculate the average net force acting on the car.

A \(0.5\,kg\) ball travelling at \(8.0\,m\,s^{-1}\) collides with and sticks to a stationary \(1.5\,kg\) block on a frictionless surface. Calculate the common velocity of the ball and block after the collision.

A $$0.15\,kg$$ baseball moving horizontally at $$40\,m\,s^{-1}$$ is hit by a bat, causing it to reverse direction and move at $$50\,m\,s^{-1}$$. If the bat is in contact with the ball for $$0.0020\,s$$, what is the average force exerted by the bat on the ball?

A 0.40 kg soccer ball is kicked. The force exerted by the foot on the ball varies with time. The force increases linearly from 0 N to 600 N in 0.05 s and then decreases linearly to 0 N in another 0.05 s.
(a) Calculate the total impulse delivered to the ball.
(b) Determine the speed of the ball as it leaves the foot, assuming it was initially at rest.
(c) If the ball was initially moving towards the kicker at 10 m s^-1, determine its final speed after the kick in the opposite direction.

A particle of mass \(m\) moving with velocity \(u\) collides with a stationary particle of mass \(2m\). After the collision, the first particle moves at a speed of \(v_1 = \frac{u}{\sqrt{3}}\) at an angle of \(30^\circ\) to its original direction. The second particle moves with velocity \(v_2\) at an angle \(\phi\) to the original direction of the first particle.
(a) Using the principle of conservation of momentum in the directions parallel and perpendicular to the initial velocity, find the magnitude of \(v_2\) in terms of \(u\).
(b) Calculate the angle \(\phi\).
(c) Determine, with a calculation, whether this collision is elastic or inelastic.