A block of mass m_1m1 = 11.1 kg, sliding down a ramp inclined at angle \\theta =

Question

A block of mass m_1m1 = 11.1 kg, sliding down a ramp inclined at angle heta = 23 degrees, is connected by a light string over a pulley to a second mass, m_2 m2 = 1.7 kg, suspended along the vertical side of the incline. There is a (kinetic) frictional force on the first mass: F_{fr, ~ ramp ~ on ~ 1} = 0.1 cdot F_{N, ~ ramp ~ on ~ 1} (The frictional force is proportional to the normal force.) Calculate the acceleration of the first mass, m_1m1. Your answer should be positive if the acceleration is up the ramp, and negative if the acceleration is down the ramp. Give your answer in the units of m/s2 to at least three significant digits. You won't be graded on the number of digits, this is just so your answer is not counted as incorrect due to rounding. Note: Initially the mass m_1m1 is sliding down the ramp and the mass m_2m2 is moving upwards.

Explanation / Answer

m1a = m1gsin23-f-T

f = mue*n = mue*m1gcos23 = 0.1*11.1*9.8*cos23 = 10.01 N

m2a = T-m2g

m1a = 42.5-10.01-m2a-m2g

a(m1+m2) = 42.5-26.67 = 15.83

a = 1.24 m/s^2

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