# Halliday, Resnick & Krane Chapter 5: Force on Pulley

• vibha_ganji
In summary, the tension on a pulley can be found by adding the equations for m1 and m2, resulting in 2T + N = (a+g)(m1+m2). The masses will have the same acceleration and the next step is to solve for T. A hint for solving for T would be to use the equations for m1 and m2 to eliminate variables.
vibha_ganji
Homework Statement
Someone exerts a force F directly up on the axle of the pulley shown in Fig. 5-45. Consider the pulley and string to be massless and the bearing frictionless. Two objects, m1 of mass 1.2 kg and m2 of mass 1.9 kg, are attached as shown to the opposite ends of the string, which passes over the pulley. The object m2 is in contact with the floor. (a) What is the largest value the force FB may have so that m2 will remain at rest on the floor? (b) What is the tension in the string if the upward force F is 110 N? (c) With the tension determined in part (b), what is the acceleration of m1?
Relevant Equations
F=ma
Force on pulley = 2(tension)
As the force on a pulley is equal to twice the tension, I just have to find the tension to solve part A. To do so, I first wrote the equations for both m1 and m2.

m1 * a = T - m1g

m2 * a = T + N - m2g

The tension must have the same values for both equations so I added both equations to find the tension.

m1a + m2a = 2T + N - g(m1 + m2)
a(m1+m2) + g(m1+m2) = 2T + N

(a+g)(m1+m2) - N = 2T

I’m not sure what to do next. Can I have a hint?

Last edited:
Delta2
vibha_ganji said:
m1 * a = T - m1g

m2 * a = T + N - m2g
How are you defining a? Will the masses have the same acceleration?

## 1. What is the concept of a pulley?

A pulley is a simple machine that is used to lift or move heavy objects. It consists of a wheel with a groove around its circumference and a rope or belt that runs through the groove. When one end of the rope is pulled, the object on the other end is lifted or moved.

## 2. How does a pulley change the direction of force?

A pulley changes the direction of force by redirecting the force applied to the rope or belt in a different direction. This allows for the force to be applied in a more convenient or advantageous direction, such as lifting an object straight up instead of pulling it horizontally.

## 3. What is the difference between a fixed pulley and a movable pulley?

A fixed pulley is attached to a stationary object and the rope or belt runs through it, while a movable pulley is attached to the object being lifted or moved and the rope or belt runs through it and back down to the ground. A fixed pulley changes the direction of force, while a movable pulley also reduces the amount of force needed to lift an object.

## 4. How does the number of pulleys affect the amount of force needed to lift an object?

The more pulleys used in a system, the less force is needed to lift an object. This is because each additional pulley reduces the amount of force needed by half. For example, using two pulleys reduces the force needed by half, using three pulleys reduces it by one-third, and so on.

## 5. Can a pulley system create a mechanical advantage?

Yes, a pulley system can create a mechanical advantage by reducing the amount of force needed to lift an object. This is because the force is distributed among multiple ropes or belts and each additional pulley reduces the force needed by half. However, the trade-off is that the distance the rope or belt needs to be pulled is increased.

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