A 4-kg cart starts up an incline with a speed of 3 m/s and comes to rest 2 m up the incline.The total work done on the cart is:

Question

Quizplus · Accepted Answer

The total work done on the cart can be calculated using the work-energy principle, which states that the work done on an object is equal to its change in kinetic energy. Initially, the cart has kinetic energy due to its speed, and it comes to rest at a higher elevation, which means all its initial kinetic energy is converted into potential energy (and possibly overcoming friction, but this is not specified). The initial kinetic energy (KE) of the cart is given by $KE = \frac{1}{2}mv^2$, where $m = 4 \, \text{kg}$ and $v = 3 \, \text{m/s}$. So, $KE = \frac{1}{2} \times 4 \times (3)^2 = 18 \, \text{J}$. Since the cart comes to rest, all this energy is used to move up the incline and possibly overcome friction. Therefore, the work done on the cart is negative (since it's losing kinetic energy), and the magnitude of this work is equal to the initial kinetic energy, which is -18 J.

A 4-Kg Cart Starts Up an Incline with a Speed