In a shuffleboard game,the puck slides a total of 12 m on a horizontal surface before coming to rest.If the coefficient of kinetic friction between the puck and board is 0.10,what was the initial speed of the puck?
A)4.8 m/s
B)48.5 m/s
C)3.8 m/s
D)4.3 m/s

Question

Quizplus · Accepted Answer

The initial speed of the puck can be found using the work-energy principle. The work done by friction is equal to the change in kinetic energy. The work done by friction is $W = f_k \cdot d = \mu_k \cdot m \cdot g \cdot d$, where $f_k$ is the force of kinetic friction, $\mu_k$ is the coefficient of kinetic friction, $m$ is the mass of the puck, $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$), and $d$ is the distance (12 m). The change in kinetic energy is $\Delta KE = \frac{1}{2} m v^2 - 0$ (since the puck comes to rest, the final kinetic energy is 0). Setting the work done by friction equal to the change in kinetic energy and solving for $v$ (initial speed), we don't need the mass of the puck as it cancels out. Plugging in the values, we get $v = \sqrt{2 \cdot \mu_k \cdot g \cdot d}$. Substituting $\mu_k = 0.10$, $g = 9.8 \, \text{m/s}^2$, and $d = 12 \, \text{m}$, we find $v \approx 4.8 \, \text{m/s}$.

In a Shuffleboard Game,the Puck Slides a Total of 12