Question

0.46KG block is held in place against a spring by a 30N horizontal external force. The external force is removed and the block is projected with a velocity v1 1.2m/s upon separation from the spring. The block descends a ramp and has a velocity v2 equal to equal 1.5m/s at the bottom. The track is frictional between point A and B. The block enters a rough section at B extending to E. The coefficient of kinetic friction is 0.38. The velocity of the block v3 is 1.4m/s at C. The block moves unto D, where it stops. Calculate the distance the block travel between point B to D

Answer 1

Since we know velocity of the block at the bottom, and from the bottom of the ramp till point B there is no friction, until point B the block moves with constant velocity (since no other forces are acting on it) of 1.5 m/s. 1.4 m/s at the point C doesn't matter because the distance from B to C is unknown and the block must reach 1.4 m/s anywhere between 1.5 m/s and 0 m/s. Then we can simply apply work-energy theorem, assuming that whole kinetic energy converted to work done by friction:

$$\frac{1}{2}mv_2^2=\mu mgx,$$

$$x=\frac{mv_2^2}{2\mu mg}=\frac{1.5^2}{2\cdot0.38\cdot9.8}=0.3\text{ m}.$$