# Torque Plus Power In Relation to Velocity

• postfan
In summary: The maximum torque output from the engine of a new experimental car of mass m is τ . Themaximum rotational speed of the engine is ω. The engine is designed to provide a constant poweroutput P. The engine is connected to the wheels via a perfect transmission that can smoothlytrade torque for speed with no power loss. The wheels have a radius R, and the coefficient ofstatic friction between the wheels and the road is µ.Assuming no frictional losses, the car can drive at a maximum speed of v = 2P/(mg).
postfan

## Homework Statement

The maximum torque output from the engine of a new experimental car of mass m is τ . The
maximum rotational speed of the engine is ω. The engine is designed to provide a constant power
output P. The engine is connected to the wheels via a perfect transmission that can smoothly
trade torque for speed with no power loss. The wheels have a radius R, and the coefficient of
static friction between the wheels and the road is µ.
What is the maximum sustained speed v the car can drive up a 30 degree incline? Assume no
frictional losses and assume µ is large enough so that the tires do not slip.

(A) v = 2P/(mg)
(B) v = 2P/(√3mg)
(C) v = 2P/(µmg)
(D) v = τω/(mg)
(E) v = τω/(µmg)

## The Attempt at a Solution

I don't even know how to start on this. I'm supposing that the first step is finding a relationship between the torque, power, and velocity , but I don't know how to do that. Thoughts?

postfan said:
relationship between the torque, power, and velocity
Can you write a relationship for two of the three variables you've listed?

P=F*v*cos(theta).

And "F" is what?

Force

postfan said:
Force
Well, yes, I think we all guessed that, but which force?

The force is the one that the car provides.

postfan said:
The force is the one that the car provides.
The car's engine provides a torque, not a force.
I could guess you mean the propulsive force up the hill provided by friction, but then I don't know where the cos(theta) comes from.

I looked up the torque-velocity relation ,was I supposed to derive it somehow?

postfan said:
I looked up the torque-velocity relation ,was I supposed to derive it somehow?
If you mean P=Fv, no. Just explain exactly what F is in the present context and how cos theta comes into it.

F is the force produced from the power of the engine and the cos theta comes from the angle of the incline, the bigger the angle the less velocity.

postfan said:
F is the force produced from the power of the engine and the cos theta comes from the angle of the incline, the bigger the angle the less velocity.
You are still not explaining what you mean by "the force from the engine". Could you point to it on a diagram? As I wrote, the engine produces a torque, not a force.
When you apply a standard equation like P=Fv, you need to understand what relationship those entities must have for the equation to be applicable. In this case, F is a force applied to and driving the motion of an object, and v is the velocity of the object in the direction of that force. (And both need to be constant.)
Assuming you mean the v as given in the question, that's the velocity up the plane. If your F, when you have defined it, is acting up the plane also then it's going to be P=Fv, no role for theta.

Ok so F is the component of the weight that is parallel to the incline, is that right?

postfan said:
Ok so F is the component of the weight that is parallel to the incline, is that right?
Yes!
Small correction -it's equal and opposite to the component of the weight parallel to the plane.

Ok, so now what?

postfan said:
Ok, so now what?
So what is the component of the weight parallel to the incline, in terms of the given data?

## 1. What is torque?

Torque is a measure of the rotational force applied to an object. It is calculated by multiplying the force applied to an object by the distance from the axis of rotation.

## 2. How is torque related to power?

Power is the rate at which work is done or energy is transferred. Torque is a component of power, as it is one of the factors that determine the amount of work or energy that can be produced by an object.

## 3. How does velocity affect torque and power?

Velocity, or speed, is directly related to both torque and power. As velocity increases, so does the amount of torque and power that can be produced by an object. This is because an increase in velocity results in an increase in the rate at which work or energy is transferred.

## 4. What is the difference between torque and horsepower?

While both torque and horsepower are measures of power, they are calculated using different units and represent different types of power. Torque is a measure of rotational power, while horsepower is a measure of the overall power an engine or motor can produce.

## 5. How do torque, power, and velocity affect the performance of a machine?

The relationship between torque, power, and velocity is crucial to the performance of a machine. A machine with high torque and power output can produce more work or energy in a given amount of time, while a machine with high velocity can perform tasks faster. Balancing these factors is important for optimizing the performance of a machine.

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