What is the acceleration of the 10 kg block on the frictionless ramp?

[JustAverageSkill]

Homework Statement

The ramp in figure is frictionless. If the blocks are released from rest, which way does the 10 kg block side and what is the magnitude of its acceleration? θ=40°
https://s.yimg.com/hd/answers/i/b94e08c806334d908a6afee7b8761bbd_A.png?a=answers&mr=0&x=1456730351&s=946fcf963764a48cb25be59052f47790

Homework Equations

The Attempt at a Solution

m1=10kg, m2= 5kg[/B]
For m1:
ΣF_x=m₁a₁
T-m₁gsinθ
For m2
ΣF_x=m₂a₂
I'm unsure how to proceed from here. Other online solutions seem to assume that a1=a2, is that true? Why/why not? Please help me in how to continue. Thanks!

 

[Qwertywerty]

Provided the string is in-extensible, as can be assumed here, a₁ must equal a₂.
The letters in bold should provide a clue to the reasoning behind this.

Hope this helps,
Qwertywerty.

 

[JustAverageSkill]

Provided the string is in-extensible, as can be assumed here, a₁ must equal a₂.
The letters in bold should provide a clue to the reasoning behind this.

Hope this helps,
Qwertywerty.

Given that fact, how should I proceed?

 

[Qwertywerty]

Given that fact, how should I proceed?

You have two unknowns - Tension and acceleration(Tension is same throughout the string).

You need two equations - Write Newton's law for both masses, and solve the two equations to obtain a.

 

[JustAverageSkill]

You have two unknowns - Tension and acceleration(Tension is same throughout the string).

You need two equations - Write Newton's law for both masses, and solve the two equations to obtain a.

I tried to write out the equations as follows:
m1ax=T - m1gsinθ
m2ax=T - m2g

Is this correct? Upon solving this I got an answer that is different than the one in the book

 

[Qwertywerty]

Edit : Keep in mind, the directions of both accelerations. We have already arrived at a conclusion regarding the accelerations. What is that?

 

[JustAverageSkill]

Keep in mind, the directions of both accelerations. Assume one common direction for both(Why?).

I'm not sure what you mean by this. For m1, I have defined positive x to be up and parallel to the ramp. For m2, positive x is directly up.

 

[Qwertywerty]

I'm not sure what you mean by this. For m1, I have defined positive x to be up and parallel to the ramp. For m2, positive x is directly up.

If one block goes up, the other one goes...Where?

 

[JustAverageSkill]

If one block goes up, the other goes down, I suppose. But how do I quantitate that idea?

 

[JustAverageSkill]

If one block goes up, the other one goes...Where?

See above please

 

[Qwertywerty]

For one block, acceleration would be in the direction of tension; in the other, not. You have to thus be careful while applying Newton's law.

 

[JustAverageSkill]

For one block, acceleration would be in the direction of tension; in the other, not. You have to thus be careful while applying Newton's law.

Could you please write out the correct force equations that I should use to solve for tension and acceleration?

 

[Qwertywerty]

I'd rather you tried it for yourself.

Assume that the 10kg mass goes up and the 5kg one down. Try the equations again.

P.S - I have noted that you had made an attempt in post #5, but I'd like for you, to give it another go.

 

[JustAverageSkill]

I'd rather you tried it for yourself.

Assume that the 10kg mass goes up and the 5kg one down. Try the equations again.

P.S - I have noted that you had made an attempt in post #5, but I'd like for you, to give it another go.

Here's another attempt, which yielded the right answer.
For m1:
m1ax=T-m1gsinθ
For m2:
m2(-ax)=T-m2g
m1ax+m1gsinθ=m2(-ax)+m2g
ax(m1+m2)=m2g-m1gsinθ
ax=(m2g-m1gsinθ)/(m1+m2)=(5*9.8-10*9.8*.64)/15=-0.92

 

[Qwertywerty]

That seems to be correct. Congrats!