A cart is set rolling across a level table , at the same speed on every trial. If it runs into a patch of sand, the cart exerts on the sand an average horizontal force of `6N` and travels a distance of `6 cm` through the sand as it comes to a stop. If instead the cart runs into on a path of gravel on which the cart exerts an average horizontal force of `9 N` how far into the gravel will the cart roll before stopping?

Options

A. `9 cm`
B. `6 cm`
C. `4 cm`
D. `3 cm`

Answer

C

Explanation

The system consisting of the cart 's fixed , initial kinetic energy is the mechanical energy that can be transformed due to friction from the surface . Therefore , the loss of mechanical energy is
`Delta E _(mech) = - f_(k)d = - (6N) (0.06 m) = 0.376 J`. The procuct must remain the same in all cases . For the cart rolling through gravel, ` - (9 N) (d)= 0.36 J` rells us `d = 4 cm`.