Question

A 4kg package is released from rest at point A and slides down a frictionless track until it reaches point B with a speed of 4.20 m/s. From point B it slides on a level surface with friction coefficient a distance of 3.00 m to point C, where it comes to rest. Calculate the height H Calculate the coefficient of kinetic friction on the horizontal surface.

Answer 1

Explanation:

(a)   According to the law of conservation of energy,

               Potential energy = Kinetic energy

                     mgh = $\frac{1}{2}mv^{2}$

Putting the given values into the above formula as follows.

               mgh = $\frac{1}{2}mv^{2}$

    $4 \times 9.8 \times h = \frac{1}{2} \times 4 \times (4.2)^{2}$

                    h = 0.9 m

Therefore, the height H is 0.9 m.

(b)   For the given situation,

             Kinetic energy = work done by friction

       $\frac{1}{2} \times mv^{2} = \text{friction} \times d$

       $0.5 \times mv^{2} = u \times mg \times d$

       $0.5 \times 4 \times 4.2^{2} = u \times 4 \times 9.8 \times 3$

                   u = 0.3

Thus, we can conclude that the coefficient of kinetic friction on the horizontal surface is 0.3.