# Velocity of an object on an inclined plane

• Prabs3257
In summary: Here's a neat trick. Maximising ##v## is the same as maximising ##v^2##. That makes the differentiation easier.
Prabs3257
Homework Statement
A body starts from rest on a long incline plane of slope 45 degree the coefficient of friction between the body and the plane varies as u=0.3x where x is the distance traveled down the plane the body will have maximum speed when x is
Relevant Equations
Work energy theorem
I used work energy theorem between initial top point and point x along the incline(downwards) i got the expression of v then diffrentiated it to get a maxima but it gives me a wrong ans which is 10/6 but the actual ans is 10/3 please tell me what i did wrong

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Prabs3257 said:
Homework Statement:: A body starts from rest on a long incline plane of slope 45 degree the coefficient of friction between the body and the plane varies as u=0.3x where x is the distance traveled down the plane the body will have maximum speed when x is
Homework Equations:: Work energy theorem

I used work energy theorem between initial top point and point x along the incline(downwards) i got the expression of v then diffrentiated it to get a maxima but it gives me a wrong ans which is 10/6 but the actual ans is 10/3 please tell me what i did wrong

There is a simple approach to this problem. Hint: what can you say about the forces when the body reaches its maximum speed?

PeroK said:
There is a simple approach to this problem. Hint: what can you say about the forces when the body reaches its maximum speed?
Ya i first did it using forces only and got the correct answer but i want to know what i did wrong with this

Prabs3257 said:
Ya i first did it using forces only and got the correct answer but i want to know what i did wrong with this

You'd need to post your working. I'm not sure if it's worth it, though.

PeroK said:
You'd need to post your working. I'm not sure if it's worth it, though.
I did post an img of it in the ques

Prabs3257 said:
I did post an img of it in the ques
There's almost no working there at all. You have an expression for ##v(x)## that you haven't justified. Did you integrate the friction force down the slope?

PS It looks like you just mixed up a factor of ##\sqrt 2## at some point.

Prabs3257 said:
I did post an img of it in the ques

Here's a neat trick. Maximising ##v## is the same as maximising ##v^2##. That makes the differentiation easier.

PeroK said:
There's almost no working there at all. You have a very simple expression for ##v(x)## that you haven't justified and is wrong in any case. Did you integrate the friction force down the slope?
Oh sorry i just forgot f was not constant and i integrated it now and got the correct ans thanks

## 1. What is the formula for calculating the velocity of an object on an inclined plane?

The formula for calculating the velocity of an object on an inclined plane is v = √(2ghsinθ), where v is the velocity, g is the acceleration due to gravity (9.8 m/s^2), h is the height of the inclined plane, and θ is the angle of inclination.

## 2. How does the angle of inclination affect the velocity of an object on an inclined plane?

The angle of inclination has a direct impact on the velocity of an object on an inclined plane. The steeper the angle, the faster the object will accelerate down the plane. This is because a steeper angle results in a greater component of the force of gravity acting in the direction of motion.

## 3. Can the velocity of an object on an inclined plane ever be greater than the velocity of a freely falling object?

No, the velocity of an object on an inclined plane can never be greater than the velocity of a freely falling object. This is because the velocity of a freely falling object is solely determined by the force of gravity, whereas the velocity of an object on an inclined plane is affected by other factors such as the angle of inclination and the object's mass.

## 4. Does the mass of an object affect its velocity on an inclined plane?

Yes, the mass of an object does affect its velocity on an inclined plane. The greater the mass of the object, the greater the force of gravity acting on it. This results in a greater acceleration and a higher velocity as the object moves down the inclined plane.

## 5. What is the difference between average velocity and instantaneous velocity on an inclined plane?

Average velocity on an inclined plane is the total displacement of an object divided by the total time taken to cover that distance. It gives an overall measure of an object's velocity over a given time period. Instantaneous velocity, on the other hand, is the velocity of an object at a specific moment in time. It takes into account the changes in velocity over extremely short time intervals and is affected by factors such as the angle of inclination and the object's mass.

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