A 110 g hockey puck sent sliding over ice is stopped in 14.9 m by the frictional force on it from the ice. (a) If its initial speed is 7.8 m/s, what is the magnitude of the frictional force? (b) What is the coefficient of friction between the puck and the ice?
(a) Friction force * distance = (initial kinetic energy)
Solve for the friction force.
(b) Divide friction force by puck weight to get the coefficient of (kinetic) friction.
To find the magnitude of the frictional force between the hockey puck and the ice, we can use the equation:
Frictional force = mass * acceleration due to friction
First, let's calculate the acceleration due to friction using the given information. We know that the initial speed of the puck (v_0) is 7.8 m/s and it comes to a stop over a distance (d) of 14.9 m.
The equation to calculate acceleration (a) is:
v^2 = v_0^2 + 2ad
where v is the final velocity of the puck.
Since the puck comes to a stop, the final velocity (v) is 0. Substituting these values into the equation, we get:
0 = (7.8 m/s)^2 + 2a(14.9 m)
Rearranging the equation for acceleration (a), we get:
a = -((7.8 m/s)^2) / (2 * 14.9 m)
Now we can calculate the acceleration:
a = -5.136 m/s^2
Next, we can calculate the magnitude of the frictional force:
Frictional force = mass * acceleration
Given that the mass (m) of the puck is 110 g (or 0.11 kg), we can calculate the frictional force:
Frictional force = (0.11 kg) * (-5.136 m/s^2)
Frictional force ≈ -0.565 N
Note: The negative sign indicates that the frictional force is acting in the opposite direction of the initial velocity of the puck.
Now let's move on to finding the coefficient of friction (μ) between the puck and the ice.
The equation relating the frictional force to the normal force (N) and the coefficient of friction is:
Frictional force = μ * N
In this case, the normal force is equal to the weight of the puck (since it's on a horizontal surface). The weight (W) can be calculated using the mass (m) of the puck and the acceleration due to gravity (g).
Weight = mass * gravity
Weight = (0.11 kg) * (9.81 m/s^2)
Weight ≈ 1.0811 N
Now we can calculate the coefficient of friction:
μ = Frictional force / Weight
μ = -0.565 N / 1.0811 N
μ ≈ -0.523
Note: The negative sign in the coefficient of friction indicates that the frictional force is opposing the motion of the puck.
Therefore, the magnitude of the frictional force is approximately 0.565 N, and the coefficient of friction between the puck and the ice is approximately 0.523.