# Tension force and acceleration Problem

1. Dec 8, 2018

### chef99

1. The problem statement, all variables and given/known data
A block on an inclined surface is connected to another block that is hanging over the top edge of the incline, (as shown in the attached diagram). The system is moving in such a way that block B (mass = 3.0kg) is moving downwards, as block A slides up the ramp. The coefficient of kinetic friction between the sliding block and the ramp is 0.11. Determine the magnitude of the acceleration of the blocks and the magnitude of the force of tension in the string.

2. Relevant equations

a = m2g - m1g sinθ / m1 + m2

FT = ma

3. The attempt at a solution

For acceleration of the system.

a = (3.0kg)(9.8mls) - (2.0kg)(9.8m/s) sin35° / 3 +2

a = 3.63

The acceleration of the system is 3.63m/s {down}

b) Find tension force on the string.

m2, ma = mg -T

m1, ma = T

2ma =mg

so
a = g/2

T = mg/2

This is the only equation for tension force in my study materials, but I don't think it is right for this application. There is no part that requires the kinetic friction coefficient, and I don't believe it would be provided if not necessary. IF someone could provide some help on what formula to use for tension force that would be great, also I'm pretty sure part a) is right but I could be wrong. Thanks

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2. Dec 8, 2018

### Dewgale

This is what happens when you apply equations without understanding what they mean. Your equation for acceleration is wrong for this situation.

Analyze each block independently, each with their own equation $F_{net} = m a$, and each with the force T applied to it. If you do that, and factor in the frictional force, you should get two equations with two unknowns, $T$ and $a$. You can then solve for both variables.