Question

a 20 kg box falls from the back of a truck and hits the ground with a speed of 15m/s. it slides for a distance of 45m before coming to rest. determine the work done on the box by
friction

Answer 1

a 20 kg box falls from the back of a truck and hits the ground with a speed of 15m/s. it slides for a distance of 45m before coming to rest. determine the work done on the box by friction.

For any net force acting on a particle moving along any curvilinear path, its work equals the change in the kinetic energy of the particle, it is known as the work-energy theorem:

$$W = T _ {2} - T _ {1}$$ $$T = \frac {m v ^ {2}}{2} - \text {kinetic energy of the particle, therefore:} W = \frac {m v _ {2} ^ {2}}{2} - \frac {m v _ {1} ^ {2}}{2}$$ $$v _ {2} = 0 - \text {box coming to rest}$$ $$\text {So, } W = 0 - \frac {m v _ {1} ^ {2}}{2} \Rightarrow W = - \frac {m v _ {1} ^ {2}}{2}$$ $$v _ {1} - \text {initial speed}$$ $$W = - 2 0 * \frac {1 5 ^ {2}}{2} J = - 2 2 5 0 J$$

Answer: $W = -2250J$