# Pulley system on an inclined plane with friction.

## Homework Statement

Two blocks are connected by a thin inextensible string over a frictionless massless pulley
as shown on the picture below
The acceleration of gravity is 9.8 m/s2

Given that the two blocks move at 1.9 m/s
under an acceleration of 4.1 m/s2,
calculate the coeﬃcient µk of kinetic friction between
the left block and the incline.

## Homework Equations

*
ƩF=MA
Ffk*Fn
m2-T = m2*a

*(any and all derived equations as well)

## The Attempt at a Solution

Tension minus parallel force of gravity minus force of friction equals zero because its travelling at a constant velocity.

(110kg*(9.8m/s2-4.9m/s2)) - (37kg*9.8m/s2*sin(33)) - (μ*9.8m/s2*37kg*cos(33))

after doing the arithmetic and algebra i got to:
429.5138859N = (μ*9.8m/s2*37kg*cos(33))

Dividing both sides by (9.8m/s2*37kg*cos(33))
i got μ=1.412400969

I got this incorrect twice before and know have noticed my previous errors and fixed them, but was wondering if anyone can verify with me that this is the right/ wrong answer? thanks!

#### Attachments

• pully.png
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ehild
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## Homework Statement

Two blocks are connected by a thin inextensible string over a frictionless massless pulley
as shown on the picture below
The acceleration of gravity is 9.8 m/s2

Given that the two blocks move at 1.9 m/s
under an acceleration of 4.1 m/s2,
calculate the coeﬃcient µk of kinetic friction between
the left block and the incline.

## Homework Equations

*
ƩF=MA
Ffk*Fn
m2-T = m2*a

*(any and all derived equations as well)

## The Attempt at a Solution

Tension minus parallel force of gravity minus force of friction equals zero because its travelling at a constant velocity.

The text of the problem is confusing, but the blocks do not move with constant velocity: There is acceleration of 4.1 m/s2. v=1.9 m/s at an instant.

(110kg*(9.8m/s2-4.9m/s2)) - (37kg*9.8m/s2*sin(33)) - (μ*9.8m/s2*37kg*cos(33))

The equation is not correct. It should be ƩF=(m1+m2)a, the sum of all external forces is equal to the acceleration of the whole system multiplied by the mass of the whole system. What is that 4.9 m/s2?

ehild