A railway operator studies the motion of an unpowered maintenance cart on a straight track. Fig. 1 shows the cart before it rolls into a sand-filled stoppin...
Question 1 Report
A railway operator studies the motion of an unpowered maintenance cart on a straight track. Fig. 1 shows the cart before it rolls into a sand-filled stopping box. The cart has a mass of 500 kg and enters the sand at 4.0 m/s. It comes to rest after travelling 1.6 m through the sand. Assume the retarding force is constant.
(a) Calculate the initial momentum of the cart. [2]
(b) Calculate the initial kinetic energy of the cart. [3]
(c) Calculate the magnitude of the deceleration of the cart in the sand. [3]
(d) Calculate the retarding force exerted by the sand. [2]
(e) Explain why using a longer sand box reduces the force on the cart. [3]
(f) State one change to the cart that would increase its momentum at the same speed. [1]
(g) Describe the main energy transfer as the cart stops. [2]
Answer Details
(a) Momentum is \(p=mv\):
\[p=500\times4.0=2000\text{ kg m/s}\]
The initial momentum is 2000 kg m/s. [2]
(b) Use \(E_k=\frac{1}{2}mv^2\):
\[E_k=\frac{1}{2}\times500\times4.0^2=4000\text{ J}\]
The initial kinetic energy is 4000 J. [3]
(c) Use \(v^2=u^2+2as\):
\[0=4.0^2+2\times a\times1.6\]
\[a=-5.0\text{ m/s}^2\]
The deceleration has magnitude 5.0 m/s². [3]
(d) \[F=ma=500\times5.0=2500\text{ N}\]
The retarding force is 2500 N. [2]
(e) A longer sand box gives a greater stopping distance. [1] This increases stopping time or reduces the deceleration. [1] Since \(F=ma\), a smaller deceleration requires a smaller resultant force. [1]
(f) Increase the cart's mass. Since \(p=mv\), this increases momentum at the same speed. [1]
(g) As the cart stops, its kinetic energy is transferred mainly to thermal energy in the sand and cart. [1] Some energy may also be transferred as sound. [1]
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