# Atwood's Machine and incline plane combined.

• unicornrose
In summary, the problem involves two packing crates connected by a string over a frictionless pulley. One crate has a mass of 10.0 kg and the other has a mass of 4.00 kg on a smooth incline. The task is to find the acceleration of the 4.00 kg crate and the tension in the string. The teacher's clue suggests using a combination of Atwood's machine and an incline plane and solving for 'a' and 'T' using equations for each object.

#### unicornrose

So here is the problem with the two parts and then the teacher's clue... I would be majorly appreciative if you could help me out.

Two packing crates of masses m1 = 10.0 kg and m2 = 4.00 kg are connected by a light string that passes over a frictionless pulley as in Figure P4.26. The 4.00 kg crate lies on a smooth incline of angle 40.0°. Find the acceleration of the 4.00 kg crate.

Part B is:
Find the tension in the string.

The clue that the teacher gave us is:
#4 (Pulley and incline) A combination of the Atwood’s machine and an incline plane.
Construct the equation for each object and solve for ’a’ and ’T’. Both objects
share the same ’a’ and ’T’.

Well, have you followed your teacher's hint? This is homework and, as such, we require that you show your work before we can help you.

The forces involves are T1, T2 and the components of mg. T1 is tension of the rope connecting the m1 and the 4kg crate, and T2 is the tension of the rope between m1 and m2.

Draw the free body diagram of m1, m2 and the 4kg crate. Make three equation and solve for a , T1 and T2.

## 1. How does Atwood's Machine work on an incline plane?

Atwood's Machine on an incline plane combines the principles of both Atwood's Machine and inclined plane. The incline plane reduces the force of gravity acting on the masses, making it easier to measure the effects of tension and acceleration. The machine works by using two masses connected by a string passing over a pulley. One mass is placed on an incline, while the other hangs vertically. As the incline angle increases, the acceleration of the system decreases, and the tension in the string increases.

## 2. What is the relationship between acceleration and the angle of the incline plane in Atwood's Machine?

The acceleration of Atwood's Machine on an incline plane is directly proportional to the angle of the incline. This means that as the angle increases, the acceleration of the system decreases. This relationship is described by the equation a = g * sinθ, where a is the acceleration, g is the acceleration due to gravity, and θ is the angle of the incline.

## 3. How is tension calculated in Atwood's Machine on an incline plane?

The tension in the string of an Atwood's Machine on an incline plane can be calculated using the equation T = (m1 - m2) * g * sinθ, where T is the tension, m1 and m2 are the masses, g is the acceleration due to gravity, and θ is the angle of the incline.

## 4. How does the mass of the incline plane affect Atwood's Machine?

The mass of the incline plane has a negligible effect on Atwood's Machine. This is because the incline plane only reduces the force of gravity acting on the masses, making it easier to measure the effects of tension and acceleration. The mass of the incline plane does not affect the acceleration or tension of the system.

## 5. What are the real-world applications of Atwood's Machine on an incline plane?

Atwood's Machine on an incline plane has several real-world applications, including measuring the coefficient of friction between surfaces and testing the accuracy of Newton's Second Law of Motion. It is also used in physics education as a hands-on demonstration of the principles of mechanics.