# What Forces Affect the Motion in an Inclined Pulley System?

• azn_oohwee
In summary, the conversation discusses a problem involving a physics book and a coffee cup connected by a string on a slope. The book is given a push and released with a speed of 3.0 m/s. The coefficients of friction are Us = 0.50 and uk = 0.20. The conversation includes equations and calculations to find the distance the book slides, whether it sticks or slides back down at the highest point, and the magnitude of force needed to make the book stick or slide. The final answers are 0.65m for (a), slide back down for (b), and 4.63N for (c).
azn_oohwee
I am having a problem finding the last part of this problem, and I'm not really sure if I did the first part right.

The 1.0 kg physics book in Figure P8.38 is connected by a string to a 600 g coffee cup. The book is given a push up the slope and released with a speed of 3.0 m/s. The coefficients of friction are Us = 0.50 and uk = 0.20.

http://www.webassign.net/knight/p8-38.gif

(a) How far does the book slide?

(b) At the highest point, does the book stick to the slope, or does it slide back down?

If the book sticks, what magnitude of force along the incline is required to make it slide down? If the book slides, what magnitude of force along the incline is required to make the book stick?

So this is what I did.

For the cup
∑(Fc)y = T - mg = ma

For the book.
∑(Fb)y = N - mgcos(@) = 0
∑(Fb)x = -T - fk - mgsin(@) = ma
∑(Fb)x = -T - uk(m(b)*a + (m(b)*g) - m(b)sin(@) = m(b)a

I add the cup to the book.

-m(a)g - uk(m(b)*a + (m(b)*g) - m(b)sin(@) = m(b)a + m(c)a = a(m(b) + m(a))

-{ g(m(a) + uk(m(b)*a + (m(b)*g) - m(b)sin(@) } / { m(b) + m(a) = a

after solving for acceleration I use a to find delta x

Vf = 0, Vi = 3 so

0 = (3)^2 + 2a(deltaX)

deltaX = -9/2a

so that gives me (a)

For (b) I reason the book slides back down.

And for C I'm having trouble visualizing how to set up the problem

I'm setting it up like this

Components to the left:

Tension
Ma
Mgsin@

Components to the right:

static friction
and the force?

I just need a little help on this one. Anything will be greatly appreciated. Thanks.

azn_oohwee said:
The 1.0 kg physics book in Figure P8.38 is connected by a string to a 600 g coffee cup. The book is given a push up the slope and released with a speed of 3.0 m/s. The coefficients of friction are Us = 0.50 and uk = 0.20.

...

So this is what I did.

For the cup
∑(Fc)y = T - mg = ma

For the book.
∑(Fb)y = N - mgcos(@) = 0
∑(Fb)x = -T - fk - mgsin(@) = ma
∑(Fb)x = -T - uk(m(b)*a + (m(b)*g) - m(b)sin(@) = m(b)a

I do not understand your last equation. Why did you replace friction by uk(ma +mg)? Friction is N*uk.

ehild

oops sorry..

I meant to write..

∑(Fb)x = -T - fk - mgsin(@) = ma

∑(Fb)x = -T - ukN - mgsin(@) = ma

N = mgcos@ so

∑(Fb)x = -T - ukmgcos@ = ma

-m(a)g - uk(m(b)gcos@ - m(b)gsin@ = m(b)a + m(c)a

a = - { g(m(c) - uk(m(b)cos@) - m(b)sin@ } / {m(b) + m(c) }

That should be more correct.

I have the answers to the problems now. The last question was a bit vague on the wording, i'll have to ask my professor about that one.

(a) 0.65m
(b) slide back down
(C) 4.63N

## What is an inclined pulley system?

An inclined pulley system is a simple machine that consists of a pulley attached to a fixed point and a rope or cable that is looped around the pulley and attached to a load. The pulley is positioned at an angle, or incline, which allows for the load to be lifted or lowered using less force than if the load was lifted straight up.

## How does an inclined pulley system work?

The inclined pulley system utilizes the principles of mechanical advantage to reduce the amount of force needed to lift a load. The angle of the incline and the number of pulleys used determine the mechanical advantage. As the load is lifted, the force required to lift the load is spread out over the length of the rope, making it easier to lift.

## What are the advantages of using an inclined pulley system?

The main advantage of using an inclined pulley system is that it reduces the amount of force needed to lift a load. This makes it easier for individuals to lift heavy objects and can also increase efficiency and productivity in tasks that require lifting or pulling objects. Additionally, an inclined pulley system allows for more control and precision in lifting and lowering objects.

## Are there any limitations to using an inclined pulley system?

While an inclined pulley system can reduce the amount of force needed to lift a load, it does not eliminate the force completely. The weight of the load and the angle of the incline still require some amount of force to lift the load. Additionally, the rope or cable used in the system must be strong enough to support the weight of the load, and friction within the system can also affect its efficiency.

## How is an inclined pulley system different from a regular pulley system?

An inclined pulley system differs from a regular pulley system in that the pulley is positioned at an angle, rather than being parallel to the ground. This allows for a greater mechanical advantage and makes it easier to lift heavy objects. Additionally, an inclined pulley system allows for more control and precision in lifting and lowering objects, while a regular pulley system is typically used for lifting objects in a vertical direction.

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