Question

A warm hockey puck has a coefficient of restitution of 0.50, while a frozen hockey puck has a coefficient of restitution of only 0.35. In the NHL, the pucks to be used in games are kept frozen. During a game, the referee retrieves a puck from the cooler to restart play but is told by the equipment manager that several warm pucks were just put into the cooler. To check to make sure he has a game-ready puck, the referee drops the puck on its side from a height of 2 m. How high should the puck bounce if it is a frozen puck

Answer 1

the required height is 0.2449 m only

Step-by-step explanation:

Given the data in the question;

Initial height = 2m

so speed of the puck before hitting the ground will be;

u² = 2gh

Initial speed u_ball = √2gh

u_ball = √( 2 × 9.8 × 2 )

u_ball = √39.2

u_ball = 6.26 m/s

given that; FOR THE FROZEN PUCK, coefficient of restitution = 0.35 only

R = - (v_ball - v_ground / u_ball - u_ ground)

so

0.35 = - (v_ball - 0 / 6.26 - 0)

0.35 = -v_ball / - 6.26

-v_ball = 0.35 × (- 6.26)

-v_ball = -2.191 m/s

v_ball = 2.191 m/s

to get the height;

v² = 2gh

h = v² / 2g

we substitute

h = (2.191)² / 2×9.8

h = 4.800481 / 19.6

h = 0.2449 m

Therefore, the required height is 0.2449 m only