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How to Calculate the Coefficient of Kinetic Friction for a Sliding Baseball Player
Physics
High School Grade 10-12
Question Content
A baseball player with mass m = 79.0 kg, sliding into second base, is retarded by a frictional force of magnitude 490 N. What is the coefficient of kinetic friction μₖ between the player and the ground?
Correct Answer
0.631 (unitless)
Detailed Solution Steps
1
Step 1: Recall the formula for kinetic friction force: $F_f = \\mu_k F_N$, where $F_f$ is the kinetic friction force, $\\mu_k$ is the coefficient of kinetic friction, and $F_N$ is the normal force.
2
Step 2: For an object on a horizontal surface, the normal force equals the object's weight. Calculate the weight: $F_N = mg$, where $m = 79.0\\ kg$ and $g = 9.81\\ m/s^2$. So $F_N = 79.0\\ kg \\times 9.81\\ m/s^2 = 774.99\\ N$.
3
Step 3: Rearrange the kinetic friction formula to solve for $\\mu_k$: $\\mu_k = \\frac{F_f}{F_N}$. Substitute the known values: $\\mu_k = \\frac{490\\ N}{774.99\\ N} \\approx 0.631$.
4
Step 4: Confirm that the coefficient of kinetic friction is a unitless quantity, as the units of force cancel out.
Knowledge Points Involved
1
Kinetic Friction Force Formula
The formula $F_f = \\mu_k F_N$ describes the force that opposes the motion of a sliding object. $\\mu_k$ is the coefficient of kinetic friction (a dimensionless value specific to the two surfaces in contact), and $F_N$ is the normal force pressing the surfaces together. It applies only when the object is in sliding motion.
2
Normal Force on Horizontal Surfaces
For an object resting or moving horizontally on a surface with no vertical acceleration, the normal force $F_N$ is equal in magnitude to the object's weight ($F_N = mg$). Weight is calculated as the product of mass $m$ and the acceleration due to gravity $g$ (typically taken as $9.81\\ m/s^2$ near Earth's surface).
3
Dimensionless Quantities
Coefficients of friction are dimensionless, meaning they have no units. This is because they are ratios of two forces (friction force and normal force), so their units cancel out, leaving only a numerical value that represents the frictional relationship between two surfaces.
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