# Accleration of 2blocks

## 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=

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ehild
Homework Helper

## 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

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

t=3.66

how about now?

ehild
Homework Helper
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

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

t = 1.30s

ck

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

t = 1.30s

ck

Correct the red part.

ehild

[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
Homework Helper
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=∑Fi(external)]/mi.

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