Pulley system on an inclined plane with friction.

In summary, the problem involves two blocks connected by a string over a frictionless pulley, with one block on an incline. The acceleration of gravity is 9.8 m/s2 and the blocks have a combined mass of 147 kg. The question asks for the coefficient of kinetic friction between the left block and the incline, given that the blocks move at 1.9 m/s under an acceleration of 4.1 m/s2. Using the equation ƩF=(m1+m2)a, and accounting for tension, gravity, and friction, the solution is μ=1.412400969.
  • #1
cmcraes
99
6

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
Ff=μk*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 traveling 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!
 

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  • #2
cmcraes said:

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
Ff=μk*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 traveling 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.

cmcraes said:
(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
 

1. What is a pulley system on an inclined plane with friction?

A pulley system on an inclined plane with friction is a mechanical device that uses a combination of an inclined plane and one or more pulleys to lift or move objects. The inclined plane provides a sloped surface, while the pulleys help to distribute the weight of the object and make it easier to lift or move.

2. How does the pulley system on an inclined plane with friction work?

The pulley system on an inclined plane with friction works by using the inclined plane to reduce the amount of force needed to lift or move an object. The pulleys then distribute this force evenly, making it easier to lift or move the object. The friction on the inclined plane also helps to prevent the object from sliding back down.

3. What is the purpose of using a pulley system on an inclined plane with friction?

The purpose of using a pulley system on an inclined plane with friction is to reduce the amount of force needed to lift or move an object. This can make it easier for humans to lift heavy objects, or it can be used in machines to lift or move heavy loads more efficiently.

4. How does friction affect the efficiency of a pulley system on an inclined plane?

Friction can affect the efficiency of a pulley system on an inclined plane by causing some of the force applied to be lost due to the resistance of the surface. This means that the amount of force needed to lift or move an object may be slightly higher than the theoretical amount needed without friction.

5. What are some real-world examples of a pulley system on an inclined plane with friction?

Some real-world examples of a pulley system on an inclined plane with friction include elevators, cranes, and ramps. Elevators use a combination of an inclined plane and pulleys to lift people or objects between floors. Cranes use a pulley system on an inclined plane to lift and move heavy objects at construction sites or in warehouses. Ramps use an inclined plane with friction to make it easier for people or vehicles to move from one level to another.

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