Is my solution for the acceleration of two blocks correct?

[ckboii89]

Homework Statement

Homework Equations

a= F/m

F= mgsinθ-Ffr

Ffr = $\mu$mgcosθ

d= 1/2gt^2

The Attempt at a Solution

a = (m1gsinθ+m2gsinθ)-($\mu$m1gcosθ+$\mu$m2gcosθ)/(m1+m2)

a = 3.72 m/s^2

t = 1.03s

I need someone to verify if this is correct, no anwser key was provided

d=

 

[ehild]

The Attempt at a Solution

a = [(m1gsinθ+m2gsinθ)-($\mu_1$m1gcosθ+$\mu$₂m2gcosθ)]/(m1+m2)

a = 3.72 m/s^2

t = 1.03s

I need someone to verify if this is correct, no anwser key was provided

d=

Take care with the formulation. The first term has to be divided by (m1+m2), too. Your result is not correct.

ehild

 

[ckboii89]

a=[gsinθ-(μ1m1gcosθ+μm2gcosθ)]
a=.298m/s^2

t=3.66

how about now?

 

[ehild]

a=[gsinθ-(μ1m1gcosθ+μm2gcosθ)]
a=.298m/s^2

t=3.66

how about now?

Still wrong. Did you divide the second term with m1+m2?

ehild

 

[ckboii89]

a=[gsinθ-g(μ1cosθ+μcosθ)]
a = 2.35 m/s^2

t = 1.30s

ck

 

[ehild]

a=[gsinθ-g(μ1cosθ+μcosθ)]
a = 2.35 m/s^2

t = 1.30s

ck

Correct the red part.

ehild

 

[ckboii89]

[gsinθ-μ1gcosθ-μ2gcosθ]
?

ehild i really appreciate the help

is the contact force the difference between the forces of the blocks? or the sum

 

[ehild]

The contact force is the magnitude of the force one block exerts to the other.

The common acceleration is the sum of all forces on the system divided by the sum of the masses. The internal forces (the force of block 1 on block 2 and the one block2 exerts to block 1 are opposite and of equal magnitude) cancel, so a=∑F_i(external)]/m_i.

If T is the contact force, Newton's second law applied to both blocks says that

m₁a₁=m1gsin(θ)-T-m₁μ₁gcos(θ) and

m₂a₁=m2gsin(θ)+T-m₂μ₂gcos(θ) .

If the blocks move together, a₁=a₂.
Add the equations:

a(m₁+m₂)=(m₁+m₂)g sin(θ)-(m₁μ₁+m₂μ₂)gcos(θ),
that is,

$$a=gsin(\theta)-\frac{m_1 \mu_1+m_2\mu_2}{m_1 +m_2}g cos(\theta)$$

ehild