What is the acceleration in this case? At your job at a warehouse, you have desi

Question

What is the acceleration in this case?

At your job at a warehouse, you have designed a method to help get heavy packages up a 15 ramp. The package is attached to a rope that runs parallel to the ramp and passes over a pulley at the top of the ramp. The other end of the rope is attached to a counterweight that hangs straight down. The mass of the counterweight is adjusted to always be twice the mass of the package. However, your boss is worried that the acceleration of the package will make it too difficult to handle at the top of the ramp and tells you to calculate it. To determine the influence of friction on the package by the ramp, you run some tests and find that using a horizontal force of 250 N, you can push a 50 kg package at a constant speed along a level floor made of the same material as the ramp.

Explanation / Answer

Let m1 be the mass over ramp and m2 ne the hanging mass

m2 = 2m1

The net force will be:

Fnet = W2 - w1 = 0

a = (m2g - m1g sin(theta))/(m1 + m2)

a = gm(2 - sin15)/3m = 5.69 m/s^2

Hence, a = 5.69 m/s^2

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