Static friction - Cart on an incline plane Mass of the cart, M = 650 g Cart star

Question

Static friction - Cart on an incline plane

Mass of the cart, M = 650 g

Cart starts on a horizontal plane, now start increasing the incline angle ? by small increments (the static friction force will increase as well), until you reach some critical angle ?c when the cart starts sliding downhill.

Critical angle: 10.3 ± 0.05°

1. Calculate the coefficient of static friction.

2. Compare your calculated value with the given one (µS = 0.18) by calculating the discrepancy: 100%* (|calc. value– expect. value| / expect. value).

Explanation / Answer

Until motion starts, f = mgsin

As we increase , f increases and keeps the block motionless.

At = c, f = fmax = mgsinc = sN = mgcosc

=> s = mgsinc/mgcosc = tanc = tan(10.3o) = 0.1817

Error measurement:

tan(10.3o + 0.05o) = tan10.35o = 0.1826 = 0.1817 + 0.0009

tan(10.3o - 0.05o) = tan10.25o = 0.1808 = 0.1817 - 0.0009

Hence, coefficient of static friction, s = 0.1817 ± 0.0009

Discrepancy = (|calc. value - expect. value|/expect. value) * 100% = (|0.1817 - 0.18|/0.18)*100% = 0.944%

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