A hockey puck on a frozen pond is given an initial speed of 11 m/s. If the puck always remains on the ice and slides 73 m before coming to rest, determine the coefficient of kinetic friction between the puck and ice. Use g equals 9.8 space bevelled m over s squared . Write your answer to 3 SF.
To determine the coefficient of kinetic friction between the puck and the ice, we can use the following equation:
Friction force (F_friction) = coefficient of kinetic friction (μ) * normal force (N)
The normal force (N) is equal to the weight of the puck, which can be calculated as:
Weight (W) = mass (m) * gravitational acceleration (g)
Given that the gravitational acceleration (g) is 9.8 m/s², we can calculate the weight of the puck using its mass.
Next, we need to determine the work done by the friction force, which is equal to the initial kinetic energy of the puck. The work done by friction is given by:
Work (W) = friction force (F_friction) * distance (d)
Since the work done by friction is equal to the change in kinetic energy (KE), we have:
W = KE_final - KE_initial
Since the puck comes to rest, the final kinetic energy (KE_final) is zero. Thus, we can rewrite the equation as:
KE_initial = W = F_friction * d
Now we can substitute the given values and solve for the coefficient of kinetic friction (μ).
Given:
Initial speed (v_initial) = 11 m/s
Distance (d) = 73 m
Gravitational acceleration (g) = 9.8 m/s²
Step 1: Calculate the weight of the puck (W):
W = m * g
Step 2: Calculate the initial kinetic energy (KE_initial):
KE_initial = W * d
Step 3: Rearrange the equation to solve for the coefficient of kinetic friction (μ):
μ = KE_initial / (m * g * d)
Let's now calculate the coefficient of kinetic friction using these steps.
Step 1: Calculate the weight of the puck (W):
Given that the mass is not provided, we cannot directly calculate the weight. However, we can cancel out the mass when solving for the coefficient of kinetic friction. So, we can skip this step.
Step 2: Calculate the initial kinetic energy (KE_initial):
KE_initial = 0.5 * m * v_initial^2
KE_initial = 0.5 * (11 m/s)^2
KE_initial = 0.5 * 121 m²/s²
KE_initial = 60.5 J
Step 3: Calculate the coefficient of kinetic friction (μ):
μ = KE_initial / (m * g * d)
μ = 60.5 J / (m * 9.8 m/s² * 73 m)
Since the mass (m) cancels out, we can simplify the equation:
μ = 60.5 J / (9.8 m/s² * 73 m)
μ ≈ 0.0891 (rounded to 3 significant figures)
Therefore, the coefficient of kinetic friction between the puck and ice is approximately 0.0891 (to 3 significant figures).
To determine the coefficient of kinetic friction between the puck and ice, we can utilize the concept of work and energy.
1. First, we need to identify the known variables:
- Initial speed (u) = 11 m/s
- Distance traveled (s) = 73 m
- Acceleration due to gravity (g) = 9.8 m/s²
2. The work done by the friction force is given by the equation:
Work = Force × Distance
In this case, the work done by friction force results in the kinetic energy of the puck being converted into thermal energy and is equal to the negative change in kinetic energy.
3. The initial kinetic energy of the puck can be calculated using the formula:
Initial Kinetic Energy = (1/2) × Mass × Initial Speed²
4. The final kinetic energy is given by:
Final Kinetic Energy = (1/2) × Mass × Final Speed²
5. Since the puck comes to rest, the final speed is zero, and the final kinetic energy reduces to zero.
6. By equating the initial kinetic energy to the negative work done by friction, we can solve for the coefficient of kinetic friction (μ) using the equation:
-Initial Kinetic Energy = Work
(1/2) × Mass × Initial Speed² = μ × Mass × Distance × g
7. Mass cancels out from both sides of the equation, so we can isolate μ:
μ = (1/2) × Initial Speed² / (Distance × g)
8. Plugging in the given values, we can calculate μ:
μ = (1/2) × (11 m/s)² / (73 m × 9.8 m/s²)
Calculating this expression will yield the coefficient of kinetic friction between the puck and ice. Rounding the result to three significant figures will give the final answer.