# Sliding problems on a pulley

• Havenater23
In summary, the problem involves a 10.0 g mass suspended above the floor and attached to a 500.0 g mass through a string over a pulley. The goal is to determine the time it will take for the 10.0 g mass to hit the floor if it starts 1.50m above the floor. After setting up the problem, it is determined that the acceleration can be found by using the equation Mass B * G = a(Mass B + Mass A). The final acceleration value is 0.19 m/s^2. Using this value, the time can be calculated as 4 seconds using the formula Vf = Vi + at. A quicker method to determine the time is through the formula

## Homework Statement

A 10.0 g mass is tied to a string. The string is attached to a 500.0 g mass and stretched over a pulley , leaving the 10.0 g mass suspended above the floor. Determine the time it will take the 10.0 g mass to hit the floor if it starts out 1.50m above the floor.

## Homework Equations

I've set up the problem, but it seems almost impossible. There's just simply not enough info to solve it. You are missing : Force tension , Force Friction , and the overall acceleration.

## The Attempt at a Solution

My attempt isn't correct.

If someone could just tell me how to set it up in a simple way that would be great thanks

Could you please show a picture of the arrangement of the masses and pulley? Is the bigger mass on a horizontal table?

ehild

Isolate each mass and draw a free-body force diagram. Write the acceleration of each in terms of the tension in the string (an unknown force at this point).

Now, since they are connected by the (assumedly light, inextensible) string, the accelerations must be equal in magnitude. Solve for the tension.

What can you do once you've got the tension?

I honestly don't know, I was going to use the acceleration to find the time. In order to find the acceleration you need Force of friction; which I don't know how to find.

This is what I have once it is simplified :

Massb*g - Ff = a(Mass b + Mass A)

Which to find acceleration I need to know Ff. Once I know that I can plug the acceleration
into Vf^2 = Vi^2 + 2ad

Once I have found the Final Velocity I then can find time

Vf=Vi +at

Havenater23 said:
I honestly don't know, I was going to use the acceleration to find the time. In order to find the acceleration you need Force of friction; which I don't know how to find.

This is what I have once it is simplified :

Massb*g - Ff = a(Mass b + Mass A)

Which to find acceleration I need to know Ff. Once I know that I can plug the acceleration
into Vf^2 = Vi^2 + 2ad

Once I have found the Final Velocity I then can find time

Vf=Vi +at

So what happens if Ff = 0?

Then it would be unbalanced and accelerate based on the force of tension

Isn't that what is expected?

Hmm, true, I guess I didn't think about that, so if Ff = o then I can solve it like the way I have above ?

I'm going to make another attempt at it, when ever I'm done could you check my answer?

Havenater23 said:
Hmm, true, I guess I didn't think about that, so if Ff = o then I can solve it like the way I have above ?

Well, to be fair you didn't show your work as to how you arrived at the acceleration expression, but the expression itself looked okay.

Alright, well I got 4 secs technically 3.9 . If you could check it I would really appreciate it.

Havenater23 said:
Alright, well I got 4 secs technically 3.9 . If you could check it I would really appreciate it.

Can you show your work? In particular, show the final expression and value you obtained for the acceleration, and your calculation of the time.

For Mass A aka 500G

the equation what setup like this :

Ft=MassA * a
(Orginally Ft-Ff=MassA * a ; til I knew to just forget friction)

Mass B was set up like so :

Mass B * G - Ft =Mass B * a

Substituting Mass A for Ft : Mass B * G - Mass A * a = Mass B * a
Arranged all acclamations on one side and all Gravity's on one side :
Mass B * G = Mass B * a + Mass A * a
Then factored
Mass B*G = a(Mass B + Mass A)
Found the acceleration and did the following :

Massb*g = a(Mass b + Mass A)into Vf^2 = Vi^2 + 2ad

Once I have found the Final Velocity I then can find time

Vf=Vi +at

Sorry, I'm not seeing your final value for the acceleration. Can you give me a number?

Taking the Mass B * G = A(Mass B + Mass A)Mass B = 10g = 0.01 kg

Mass A = 500G = 0.5 kg

0.01*9.8 = A ( 0.01 + 0.5)
0.098 = A 0.51
A = 0.19 m/s^2

Vf^2 = Vi^2 + 2 ad
Vf^2 = o^2 + 2 0.19(1.50)

Vf = 0.76

Then use this formula
Vf = Vi + a T
0.76= 0+ 0.19(t)
T= 4 seconds

Okay.

You can get to the time a bit quicker by going via d = (1/2)*a*t2, so that

$$t = \sqrt{\frac{2d}{a}}$$

## 1. How does friction affect sliding problems on a pulley?

Friction can have a significant impact on sliding problems on a pulley. It can increase the resistance to motion, making it more difficult for the object to slide along the pulley. The amount of friction depends on the materials involved and the force applied.

## 2. What is the relationship between the mass of the object and sliding problems on a pulley?

The mass of the object can affect the sliding problems on a pulley in a few ways. A heavier object will require more force to overcome friction and slide along the pulley. Additionally, the mass of the object can also affect the tension in the rope or cable, which can impact the motion of the object.

## 3. How do you calculate the tension in a rope or cable during a sliding problem on a pulley?

To calculate the tension in a rope or cable during a sliding problem on a pulley, you can use the equation T = ma, where T is the tension, m is the mass of the object, and a is the acceleration. This equation takes into account the mass and acceleration of the object, as well as any external forces acting on it.

## 4. Can you increase the acceleration of an object during a sliding problem on a pulley?

Yes, there are a few ways to increase the acceleration of an object during a sliding problem on a pulley. One way is to decrease the mass of the object, as this will decrease the amount of force needed to accelerate it. Another way is to decrease the friction between the object and the pulley, which will reduce the resistance to motion and allow for a faster acceleration.

## 5. How does the angle of the pulley affect sliding problems on a pulley?

The angle of the pulley can have a significant impact on sliding problems. A steeper angle will increase the tension in the rope or cable, which can affect the acceleration of the object. Additionally, a larger angle can also increase the amount of friction between the object and the pulley, making it more difficult for the object to slide.

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