Kinetic Friction - cart on an incline plane. Mass of cart, M = 550 g Acceleratio

Question

Kinetic Friction - cart on an incline plane.

Mass of cart, M = 550 g

Accelerations

Run 1: 0.025 m/s2

Run 2: 0.32 m/s2

Run 1

Move the cart close to the right end of the track. Adjust the incline angle ? = 5°. Give the cart a bump and it will begin to move. After being initially at rest, the cart is given some initial positive velocity by bumping which switches from static to kinetic friction.

Applying Newton’s second law for this system gives us: - Mgsin? + µk Mgcos? = Ma

Solving equation for µk gives: µk = (gsin? + a )/ gcos?

To calculate the coefficient of kinetic friction µk using equation you need the value of acceleration a of the system, which is given above.

Run 2

Repeat the experiment for an incline angle ? =7°. In this case the cart accelerates and runs all the way down

Question 1: Calculate the coefficient of kinetic friction for run 1 and 2, what are they?

Question 2: The average values of coefficient of kinetic friction from both runs is?

Question 3: The discrepancy between the experimental and theoretical values is?

Explanation / Answer

1.)
µk = (gsin + a )/ gcos
Run 1 -
µk = (9.8 * sin(5) + 0.025 )/ (9.8 * cos(5))
µk = 0.09

Run 2 -
µk = (9.8 * sin(7) + 0.32 )/ (9.8 * cos(7))
µk = 0.155

2)
Average Values of coefficient of kinetic friction = (0.155+0.09) /2 = 0.1225

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