What is the velocity of the 250 pound mass when it hits the ground?

[chelito19]

Homework Statement

a 250 pound mass, is released in rest (hanging at 20 ft) and pulls a 400 pound mass up a ramp with a 30º angle, the coefficient of friction between the 400 pound mass and the ramp is 0.5. Determine the velocity as the 250 pound mass hits the ground

Homework Equations

for the 400 pound mass
T-Fk-mgsin30=m1a
N-mgcos30=0
for the 250 pound mass
T-W=m2a

The Attempt at a Solution

when i have two equations to solve, my acceleration is negative -26.5 m/s2, because the mass is going down, but when i attempt to integrate to find the velocity, I need to find the time which also comes out negative giving me a not very logical answer

 

[Doc Al]

I see two problems:

One is a sign problem. If the accelerations of m1 and m2 are a1 and a2, how are a1 and a2 related?

A bigger problem is that you seem to have the masses reversed. (Figure out the minimum force needed to lift that 400 lb mass up the ramp.)

 

[BAnders1]

First make sure all of your units agree. The forces described in the problem are in pounds, but your calculation for acceleration is in m/s^2. Considering -26.5 m/s^2 > g, and the acceleration should logically be smaller than g, I'm guessing you mistyped and meant to write -26.5 ft/s^2.

Also, since the acceleration is constant, there might be some useful equations for that condition which may save you from integrating (hint hint). To see if your answer makes sense in the end, compare it to the velocity of a free falling mass dropped from the same height.

 

[chelito19]

Yes, I also thought the masses were reversed but that´s how they are presented in the picture, which is a little confusing. Thanks for the help

 

[chelito19]

I think the acceleration are the same for a1 (going up the ramp) and a2 (going down the ramp)

 

[Doc Al]

Yes, I also thought the masses were reversed but that´s how they are presented in the picture, which is a little confusing.

Figure out the friction force and the component of the weight that acts down the ramp on the 400 lb mass. Then compare that to the 250 lb weight.

 

[Doc Al]

I think the acceleration are the same for a1 (going up the ramp) and a2 (going down the ramp)

Yes. But notice how you changed your sign. If up is positive, how would they relate?

 

[chelito19]

I get a larger number for the mass that's resting on the ramp initially than the one that is hanging being held by the cord. Which would make the mass hanging come up to meet the pulley as the larger mass slides down the ramp, wouldn´t it?
the a2 is going down, which is negative so i figured that part out, but the time is the variable that is giving me trouble since i get v=26.5t and i don't know neither the velocity or time