Find Tension: Solve Homework on Frictionless Slope w/m1=3kg & m2=0.86kg

[Rey4312]

Homework Statement

In the figure below, assume that the slope is frictionless and that the two blocks are connected by a massless cord. Assume the following:
θ1 = 37°
θ2 = 45°
m1=3kg
m2=0.86kg.
What is the tension in the cord?.

Homework Equations

F=ma , w=mg, trig

The Attempt at a Solution

i know that you need to find acceleration. Which i did (a=3.04) and i found it by ((m1)(m2)g)/(m1+m2)

you'll have to use trig functions but I'm not sure which one to use.
And wouldn't you set it equal to each other?

 

[Doc Al]

i know that you need to find acceleration. Which i did (a=3.04) and i found it by ((m1)(m2)g)/(m1+m2)

Where did that formula come from?

In any case, try analyzing the forces on each block separately. Draw a FBD for each and apply Newton's 2nd law. Then combine the two equations to solve for the acceleration and the tension.

 

[Rey4312]

I was given it...

Could you use the trig function tangent?
so then your equations would be:
w tan(37)=3 a
and
w tan(45)=.86 a

but then you're only left with acceleration, and there's two different ones.

 

[Doc Al]

I was given it...

It doesn't apply to this problem.

What forces act on m1 parallel to the surface?

What forces act on m2 parallel to the surface?

 

[Rey4312]

It doesn't apply to this problem.

oh okay...


the only force that i can think of would be friction, at least that is parallel

 

[Doc Al]

the only force that i can think of would be friction, at least that is parallel

No. You are told that the slope is frictionless.

There are two other forces with components parallel to slope. What are they?

 

[Rey4312]

w=mg, tension?, or would it be the normal force (though i thought that was perpendicular)

 

[Doc Al]

w=mg, tension?,

Right, those are the two forces with parallel components. What is the component of the weight parallel to the slope?

or would it be the normal force (though i thought that was perpendicular)

Yes, the normal force is perpendicular. So you won't need it.

 

[Rey4312]

W= mg (mass*gravity)

 

[Doc Al]

W= mg (mass*gravity)

What direction does the weight act?

 

[Rey4312]

directly down parallel with the slope

 

[Doc Al]

directly down parallel with the slope

Directly down, yes. But that's not parallel to the slope. (The slope isn't vertical.) You need to find the component parallel to the slope.

You might want to read this: Inclined Planes

 

[Rey4312]

the component parallel would be tension.

 

[Doc Al]

the component parallel would be tension.

The tension in the string is a different force, but yes it is parallel to the slope. You still need the component of the weight parallel to the slope. (Read the link I gave.)

 

[Rey4312]

Read the link I gave.

Sorry didn't see that the first time..

so it would be net force?

 

[Rey4312]

solved it... thanks for the help