# Inclined Plane with Pulley: Finding Velocity with Tension and Acceleration

• brake4country
In summary, the problem involves a 10 kg mass on a frictionless inclined plane, with a pulley and rope system attached to it. The tension is given as 75 N and the mass starts from rest. Using the equation T = mgsinθ + ma, the acceleration is found to be 2.5 m/s^2. Plugging this value into Vf=Vi + at, the final velocity after 2 seconds is calculated to be 5 m/s. The mistake in the previous attempt was not paying attention to the fact that it was a two part problem.
brake4country

## Homework Statement

A 10 kg mass is on a frictionless inclined plane 30 degrees to the horizontal. At the top of the plane is a pulley that has a rope attached to mass with tension T = 75 N. If the mass starts from rest, what is its velocity after 2 seconds?

F = ma
Vf=Vi + at

## The Attempt at a Solution

So my book lists the formula as T = mgsinθ + ma. I set the problem up pretty much the same as:
∑Fx = max
75 N - 10 N = (10 kg) a
My acceleration is 6.5 m/s2. Plugging this value into vf=vi + at, I get 13.0 m/s but my book says it's supposed to be 5 m/s. What am I doing wrong? Thanks in advance!

brake4country said:

## Homework Statement

A 10 kg mass is on a frictionless inclined plane 30 degrees to the horizontal. At the top of the plane is a pulley that has a rope attached to mass with tension T = 75 N. If the mass starts from rest, what is its velocity after 2 seconds?

F = ma
Vf=Vi + at

## The Attempt at a Solution

So my book lists the formula as T = mgsinθ + ma. I set the problem up pretty much the same as:
∑Fx = max
75 N - 10 N = (10 kg) a
Where did you get that 10 N from?

The x component of the weight: -mgsinθ

brake4country said:
The x component of the weight: -mgsinθ
m=10 kg, g=10 m/s2, θ=30° . How would it give 10 N ?

I see. Well, I redid this problem and I did a force table. My T is 75 N, my x component of the force is -50 N. If I set up the problem I get:
T - mgsinθ = ma
75-50 = 10 a
a = 2.5 m/s^2

I totally misread this problem and it serves me right for not paying close attention. This is a two part problem. I solved for the acceleration using F=ma, which is 2.5 m/s^2. Then with the known time (2 s), I plugged it into the equation Vf=Vi + at. Vf = 5 m/s.

Well done at the end!

brake4country

## 1. What is an inclined plane with pulley?

An inclined plane with pulley is a simple machine that consists of a flat, sloped surface (the inclined plane) and a wheel with a grooved rim (the pulley). It is used to help lift heavy objects by reducing the amount of force needed to lift them.

## 2. How does an inclined plane with pulley work?

The inclined plane with pulley works by allowing a force applied to the rope wrapped around the pulley to be spread out over a longer distance. This reduces the amount of force needed to lift a heavy object up the inclined plane. The inclined plane also reduces the amount of work needed to be done by the person lifting the object.

## 3. What are the advantages of using an inclined plane with pulley?

The main advantage of using an inclined plane with pulley is that it reduces the amount of force needed to lift a heavy object, making it easier for humans to lift heavy loads. It also allows for a longer distance over which the force is applied, reducing the amount of work needed to be done.

## 4. What are some examples of an inclined plane with pulley?

An inclined plane with pulley can be found in everyday objects such as a ramp used to load heavy objects onto a truck or a staircase with a railing. It is also commonly used in construction, such as in a crane or a pulley system for lifting materials to higher levels.

## 5. How is the mechanical advantage of an inclined plane with pulley calculated?

The mechanical advantage of an inclined plane with pulley is calculated by dividing the length of the inclined plane by the height of the inclined plane. This gives the ratio of the force required to lift an object up the inclined plane compared to the weight of the object being lifted. A higher mechanical advantage means less force is required to lift the object.

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