Why Is My Calculation Result for Acceleration Incorrect?

[nicky670]

Homework Statement

In another set up where mass of block A is 𝑚𝐴 = 10.0 kg and the mass of block B is 𝑚𝐵 =12.0 𝑘𝑔. A spring with constant𝑘 = 90 𝑁 / 𝑚 is attached to block A as shown. The incline plane is 𝜃 = 37∘ and the coefficient of kinetic friction between the block A and theincline is 𝜇𝑘 = 0.30 as before. Block B is moving down and block A moving up the slope. (The magnitude of the spring force is
given by |𝐹𝑠𝑝| = 𝑘𝑥 where 𝑥 is the extension.)

Relevant Equations

For Ma(perpendicular) = FN - Magcos(titre) = 0
Ma (Parallel) = Fsp + T - Ffriction - Magsin(titre) = Ma(a)

For Mb: Mbg - T = Mb(a)

Fsp = 90 x 0.12 = 10.8
Ffriction = Magcos(titre) x 0.30
I got the answer 2.09ms2 when the correct answer is 1.11ms2. What am i doing wrong here?

 

[Chestermiller]

Isn't the spring force opposite to T?

 

[nicky670]

Isn't the spring force opposite to T?

But wouldn't the spring force push the block forward?

 

[haruspex]

But wouldn't the spring force push the block forward?

It says the spring has an extension of 0.12m.

 

[nicky670]

It says the spring has an extension of 0.12m.

When the spring extends, wouldn't it exert a force in the same direction as the tension force?

 

[Chestermiller]

When the spring extends, wouldn't it exert a force in the same direction as the tension force?

When you stretch a spring, doesn't it pull back on you in the opposite direction?

 

[haruspex]

When the spring extends, wouldn't it exert a force in the same direction as the tension force?

Is an extended spring under tension or under compression?

 

[nicky670]

When you stretch a spring, doesn't it pull back on you in the opposite direction?

Oh, means to say when its extended it will have a tension pulling it back and if compressed there will be a force pushing the block forward?

 

[nicky670]

Is an extended spring under tension or under compression?

tension.

 

[haruspex]

Oh, means to say when its extended it will have a tension pulling it back and if compressed there will be a force pushing the block forward?

Yes.

 

[nicky670]

Yes.

Thank you haruspex :)