Question

A 200-g hockey puck is launched at an initial speed of 16 m/s up a metal ramp that is inclined at a 30° angle. The coefficients of static and kinetic friction between the hockey puck and the metal ramp are µs = 0.40 and µk = 0.30, respectively. What vertical height does the puck reach above its starting point

Answer 1

h = 8.588 m

Step-by-step explanation:

Given:

Mass of hockey puck: m = 200 g = 0.2 K g

Angle of incline: θ = 30º (with respect to horizontal)

Coefficient of static and kinetic friction between the puck and ramp:

μ s = 0.4 and μk = 0.3

initial speed:

v = 3.5 m /s

Let h be the vertical height reached by the puck, above the ground. This corresponds to a distance of

d = h *sin 30º = 2 *h

along the incline. As the puck is moving, only kinetic friction comes into play as it climbs up the incline. Let N be the normal reaction exerted by the metal ramp on the ball. Then,

N = m*g *cos θ = 0.2 *9.8 1*cos 30 º = 1.6991 N

Therefore, kinetic friction acting on the puck is:

F k = μ k *N = 0.3 *1.6974 = 0.50974 N

From work energy theorem, the change in kinetic energy should equal the work done by friction and gravity. Therefore,

0.5* 0.2 *16² = 0.50974 *2h + 0.2*9.81*h

⇒ h = 8.588 m