牛頓定律與動量：練習題

A car of mass \(1500\text{ kg}\) is travelling at a constant speed of \(20\text{ m s}^{-1}\) along a level road. The total resistive force acting on the car is \(600\text{ N}\). What is the useful power output of the car's engine to maintain this speed?

A ball is kicked from the ground with an initial velocity of \(20\text{ m s}^{-1}\) at an angle of \(30^{\circ}\) to the horizontal. Assuming negligible air resistance and \(g = 9.81\text{ m s}^{-2}\), what is the maximum height reached by the ball?

A trolley of mass \(2.0\text{ kg}\) moving at \(4.0\text{ m s}^{-1}\) collides with a stationary trolley of mass \(m\). After the collision, the \(2.0\text{ kg}\) trolley rebounds at \(1.0\text{ m s}^{-1}\) and the other trolley moves forward at \(2.0\text{ m s}^{-1}\). Calculate the loss in total kinetic energy during this collision.

An object of mass \(0.50\text{ kg}\) is initially at rest. A constant force of \(12\text{ N}\) acts on the object for a duration of \(0.25\text{ s}\). What is the kinetic energy gained by the object during this time interval?

A student uses a uniform metre ruler to measure the weight of an unknown object. The ruler is pivoted at the \(40\text{ cm}\) mark. A weight of \(2.0\text{ N}\) is placed at the \(10\text{ cm}\) mark to balance the ruler horizontally. If the weight of the ruler itself is \(1.5\text{ N}\), what is the weight of the object placed at the \(90\text{ cm}\) mark?

A uniform beam of length \(2.0\text{ m}\) is pivoted at its centre of mass. A weight of \(50\text{ N}\) is placed at a distance of \(0.80\text{ m}\) from the pivot. Calculate the magnitude of the force required to balance the beam if the force is applied vertically upwards at one of the ends of the beam.

A ball of mass \(0.15\text{ kg}\) is dropped from a height of \(2.0\text{ m}\) and rebounds to a height of \(1.5\text{ m}\). Calculate the magnitude of the change in momentum of the ball during the impact with the floor. (Take \(g = 9.81\text{ m s}^{-2}\))

A projectile is launched from ground level with an initial velocity \(V\) at an angle \(\theta\) to the horizontal. Show that the time taken to reach the maximum height is given by \(\frac{V \sin \theta}{g}\), and state one assumption made in this derivation.

A golf ball of mass \(0.045\text{ kg}\) is struck by a club. The ball, initially at rest, leaves the club face with a horizontal velocity of \(52\text{ m s}^{-1}\). The contact time between the club and the ball is \(0.65\text{ ms}\).

(a) Calculate the magnitude of the average force exerted by the club on the ball.
(b) Determine the impulse given to the ball.

A small motor is used to lift a weight of \(15\text{ N}\) through a vertical height of \(2.4\text{ m}\) at a constant speed. The time taken for the lift is \(6.0\text{ s}\). During this operation, the motor is supplied with a constant electrical power of \(12\text{ W}\).

(a) Calculate the useful work done by the motor in lifting the weight.
(b) Determine the useful power output of the motor.
(c) Calculate the efficiency of the motor system, expressing your answer as a percentage.