# Power, Torque, and Velocity in a Pulley System

• David112234
In summary, the conversation discusses a scenario where a textbook and a hanging book connected by a cord are released on a frictionless surface and observed to move a distance of 1.20 m over a time interval of 0.790 s. The questions asked pertain to the tension in the cord attached to each book and the moment of inertia of the pulley. The participant suggests using the equations F=ma, Torque=Iα, a=Rα, and I=mR2, and provides a step-by-step approach to finding the solutions.
David112234

## Homework Statement

A textbook of mass 1.99 kg rests on a frictionless, horizontal surface. A cord attached to the book passes over a pulley whose diameter is 0.150 m , to a hanging book with mass 2.97 kg . The system is released from rest, and the books are observed to move a distance 1.20 m over a time interval of 0.790 s .

A.What is the tension in the part of the cord attached to the textbook?
B.What is the tension in the part of the cord attached to the book?
C.What is the moment of inertia of the pulley about its rotation axis?

2. Homework Equations

F=ma
Torque= Iα
a=Rα
I=mR2

## The Attempt at a Solution

Forces on book 1 (on top/textbook)

mg and Normal force cancel each other so the only force is to the right, Tension

t1=m1a

Forces on book 2 (hanging one)

-t2 + m2g= -m2a

Forces on wheel pulley

The string will create a torque in the clockwise direction

T = Iα
a = Rα
a/R = α

T = I (a/R)

I am stumped as what to do, I can find the t1 by using the second equation and solving for a in terms of t2 and plugging it back into the first one but then I would have another unknown variable.

Before the books start to move the tension in the cable is the hanging mass X the acceleration of gravity. The tension in the cable is the same at all points in the cable when the books are at rest. Assume that the books accelerate at a constant rate. The distance traveled is equal to 1/2 the acceleration times the square of the elapsed time. Rearrange terms to find the acceleration. Compare that acceleration to the acceleration due to the masses and forces involved. Acceleration equals force divided by mass. Any difference between the two acceleration rates could be assumed to be the effects of the inertia of the pulley. That's as far as you can go without knowing either the mass or the radius of the pulley (or both mass and radius).

Once things start moving the forces on the cable will be different on each side of the pulley. You can calculate that using the observed acceleration and the mass of the books.

That should get you started.

## 1. What is the difference between power and torque?

Power is the rate at which work is done, or the amount of energy transferred per unit of time. It is measured in watts (W) or horsepower (hp). Torque, on the other hand, is a measure of rotational force and is measured in newton-meters (Nm) or foot-pounds (ft-lb). In simpler terms, power is the ability to do work, while torque is the force that causes an object to rotate.

## 2. How are power, torque, and velocity related?

Power, torque, and velocity are all related through the equation P = τω, where P is power, τ is torque, and ω is angular velocity. This means that the amount of power generated is directly proportional to both the torque and the angular velocity. In other words, increasing either torque or velocity will result in an increase in power.

## 3. What is the unit of measurement for velocity?

The unit of measurement for velocity is meters per second (m/s). Velocity is a vector quantity, meaning it has both magnitude and direction, and is used to describe the speed and direction of an object's motion.

## 4. How do power, torque, and velocity affect the performance of a vehicle?

Power, torque, and velocity all play important roles in determining the performance of a vehicle. Higher power and torque allow a vehicle to accelerate faster and tow heavier loads, while higher velocity allows for higher top speeds. However, it is important to find a balance between these factors, as too much power or velocity can compromise the vehicle's handling and stability.

## 5. Can power, torque, and velocity be increased in a vehicle?

Yes, power, torque, and velocity can be increased in a vehicle through various methods such as engine modifications, tune-ups, and gear ratio adjustments. However, it is important to note that these modifications should be done carefully and in accordance with the manufacturer's recommendations to ensure the safety and reliability of the vehicle.

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