It is probably easy, but i don't know where to start
A hockey puck leaves a player's stick with a speed of 9.50 m/s and slides 27.0 m before coming to rest.
Find the coefficient of friction between the puck and the ice.
Thank You for helping me!!!
Compute the average force needed to stop a puck in 27.0 m. Here's how:
Work done against friction = initial kinetic energy.
M g mu X = (1/2) M V^2
'mu' is the number you want. Note that the mass m cancels out. g is the acceleration of gravity. X = 27.0 m
To find the coefficient of friction between the puck and the ice, we can use the following steps:
1. Identify the known values:
- Initial speed (u) = 9.50 m/s
- Distance traveled (s) = 27.0 m
- Final speed (v) = 0 m/s (since the puck comes to rest)
- Acceleration (a) = unknown
- Coefficient of friction (μ) = unknown
2. Apply the appropriate kinematic equation to relate the known variables:
We can use the equation: v^2 = u^2 + 2as, where v is the final speed, u is the initial speed, a is the acceleration, and s is the distance traveled.
Plugging in the known values into the equation, we get:
0^2 = (9.50)^2 + 2a(27.0)
3. Solve the equation for the acceleration (a):
Simplifying the equation, we have:
0 = 90.25 + 54a
Rearranging the equation, we get:
54a = -90.25
Dividing both sides of the equation by 54, we find:
a ≈ -1.674 m/s^2
4. Use the definition of friction and Newton's second law to find the coefficient of friction:
The definition of friction states that friction force (F_friction) = μ * N, where μ is the coefficient of friction, and N is the normal force. Since we are dealing with a horizontal surface, the normal force and the gravitational force cancel each other out, so we can assume N = mg, where m is the mass of the puck and g is the acceleration due to gravity (9.8 m/s^2).
Newton's second law states that the friction force is equal to the mass of the object multiplied by its acceleration: F_friction = ma
By equating both expressions for the friction force, we have:
μ * N = ma
Plugging in the known values, we get:
μ * mg = ma
Canceling out the mass on both sides of the equation, we find:
μ = a/g
Plugging in the value for acceleration (a) and acceleration due to gravity (g), we get:
μ ≈ -1.674 / 9.8
5. Calculate the coefficient of friction:
Evaluating the expression, we find:
μ ≈ -0.171
However, coefficients of friction cannot be negative, so we take the absolute value to get the positive coefficient of friction:
μ ≈ 0.171
Therefore, the coefficient of friction between the puck and the ice is approximately 0.171.