# Find Acceleration of Wedge with Rope Pulled by Constant Force T

• Vibhor
In summary, the problem involves finding the acceleration of a wedge pulled by a constant force T, with all surfaces being smooth and the pulley and rope being massless and frictionless. By resolving forces on the block and using the equations ∑F = Ma and N = mgcosθ, it is found that the acceleration is actually 2.28ms-2 towards the right, not towards the left as initially calculated. This is because the block does have a component of acceleration perpendicular to the wedge, as pointed out in the conversation. The correct answer is 1.3ms-2.
Vibhor

## Homework Statement

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In the attached picture, the rope is being pulled by a constant force T. All the surfaces are smooth. The pulley and the rope are massless and frictionless. Find the acceleration of the wedge.(use g=10ms-2)

## The Attempt at a Solution

The normal force between the block and wedge is represented by N and acceleration of the wedge by 'a'.

Writing ∑F = Ma for the wedge in horizontal direction , ##Nsinθ + Tcosθ -T = Ma## .

Resolving forces on the block in direction perpendicular to the surface of wedge , ##N=mgcosθ##

Using the above two equations , a = ##\frac{mgcosθsinθ + Tcosθ -T}{M}## .

This gives a = 2.28ms-2 towards left. But the answer given is 1.3ms-2 .

Could somebody help me identify the mistake .

Thanks

#### Attachments

• wedge.PNG
3.3 KB · Views: 433
Why is there any acceleration to the left? It would seem that gravity and the rope would both apply forces to the right. And the rope and pulley are said to be frictionless -- but what about between the block and ramp?

Vibhor said:
Resolving forces on the block in direction perpendicular to the surface of wedge , ##N=mgcosθ##

Looks like you are assuming that the block has no component of acceleration perpendicular to the wedge. Is that so?

Vibhor
TSny said:
Looks like you are assuming that the block has no component of acceleration perpendicular to the wedge. Is that so?

Terrible mistake on my part

Thanks a lot !

## What is the formula for finding the acceleration of a wedge with a rope pulled by a constant force T?

The formula for finding the acceleration of a wedge with a rope pulled by a constant force T is a = T/m, where a is the acceleration, T is the constant force, and m is the mass of the wedge.

## How do you determine the direction of acceleration for a wedge with a rope pulled by a constant force T?

The direction of acceleration for a wedge with a rope pulled by a constant force T is always in the direction of the force T. This is based on Newton's Second Law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

## What factors can affect the acceleration of a wedge with a rope pulled by a constant force T?

The acceleration of a wedge with a rope pulled by a constant force T can be affected by several factors, including the magnitude of the force T, the mass of the wedge, and the coefficient of friction between the wedge and the surface it is on.

## How can the acceleration of a wedge with a rope pulled by a constant force T be calculated if there is friction present?

If there is friction present, the formula for finding the acceleration of a wedge with a rope pulled by a constant force T becomes a = (T - μmg)/m, where μ is the coefficient of friction and g is the acceleration due to gravity (9.8 m/s^2).

## Are there any real-life applications of calculating the acceleration of a wedge with a rope pulled by a constant force T?

Yes, there are many real-life applications of calculating the acceleration of a wedge with a rope pulled by a constant force T. For example, this concept can be used in engineering to design machines that require wedges and ropes, such as cranes and pulley systems. It can also be used in physics experiments to study the principles of motion and forces.

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