Question

during a hockey game on a pond, the defenseman passes a 114-g hockey puck over the ice to the center, who fails to catch it. the puck is traveling at an initial speed of 6.7 m/s. it stops in 18 m due to the frictional force on it from the ice.
a. the magnitude of the frictional force on the ice is
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b. the coefficient of kinetic friction between the puck and ice is
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Explanation:

Step1: Find the acceleration

Use the kinematic equation \(v^{2}=v_{0}^{2}+2ax\). Here, \(v = 0\) (stops), \(v_{0}=6.7\ m/s\), and \(x = 18\ m\).

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Step2: Calculate the frictional force

The mass of the puck \(m = 114\ g=0.114\ kg\). Using Newton's second law \(F = ma\).

$$F=0.114\times(- 1.25)=- 0.1425\ N$$

The magnitude of the frictional force is \(|F| = 0.14\ N\) (rounded to two significant figures)

Step3: Find the coefficient of kinetic friction

The normal force \(N = mg\) (since on a horizontal surface, \(N\) balances the weight), \(g = 9.8\ m/s^{2}\). The frictional force \(F=\mu_{k}N=\mu_{k}mg\).

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Answer:

a. \(0.14\)
b. \(0.13\)