Acceleration and Tension of two masses on an inclined plane with friction.

In summary, the conversation discusses a situation involving two masses, with known values for mass one, mass two, and the coefficient of friction between mass one and an inclined plane. The goal is to find the magnitude of acceleration for the masses and the tension in the cord. The equations Fk= μkFnormal and Fnetx=Mg*Sinϑ-Fk=Ma are used to solve for the acceleration and tension. However, the original solution did not take into account the hanging mass, which can be used to calculate the tension accurately. By incorporating the hanging mass, the correct answers are found to be a=2.4m/s/s and t=37N.
  • #1
Imuell1
10
0

Homework Statement


In the attachment there is a drawing of the situation.
Mass one = 4kg and Mass two = 5kg
The coefficient of friction between mass one and the inclined plane = 0.24
Find the magnitude of the acceleration of the masses and the tension in the cord.

Homework Equations


Fk= μkFnormal
Fnetx=Mg*Sinϑ-Fk=Ma
Fnormal=Mg*Cosϑ

Fnetx=Fk+Mg*Sinϑ-T=Ma ?

The Attempt at a Solution



a=(Sinϑ-μkCosϑ)g... a=9.8(Sin30-0.24*Cos30)=2.86m/s2
t=MgSinϑ-MgCosϑ*μk-Ma... t=33.9481-8.1476-14.3=11.5NI'm not sure if the equation I ended up with for acceleration is correct and I am pretty sure that my equation for tension is completely wrong.

The book is giving me the answers a=2.4m/s/s and t=37N
 

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  • #2
Imuell1 said:
Fnetx=Mg*Sinϑ-Fk=Ma
Fnetx=Fk+Mg*Sinϑ-T=Ma

How can this be?

a=(Sinϑ-μkCosϑ)g... a=9.8(Sin30-0.24*Cos30)=2.86m/s2
t=MgSinϑ-MgCosϑ*μk-Ma... t=33.9481-8.1476-14.3=11.5N

What you're doing here is calculating an acceleration of a system that has a gravity towards sky. And using the acceleration from that to determine the tension of a completely different system.

Hint: Your completely ignoring the hanging mass. You can use it to your advantage.
 
Last edited:
  • #3
Awesome this helped me a lot. GOD bless you all.
 

1. What is acceleration on an inclined plane?

Acceleration on an inclined plane refers to the rate of change of the velocity of an object as it moves along the plane. It is typically measured in meters per second squared (m/s^2).

2. How does friction affect acceleration on an inclined plane?

Friction is a force that opposes motion and it can significantly affect the acceleration of an object on an inclined plane. Friction acts in the opposite direction of motion, so it will slow down the acceleration of the object. This is because some of the force that would contribute to the object's acceleration is being used to overcome the force of friction.

3. What is the equation for calculating acceleration on an inclined plane?

The equation for calculating acceleration on an inclined plane is a = (m1-m2)sinθ / (m1+m2) + µcosθ, where m1 and m2 are the masses of the two objects on the inclined plane, θ is the angle of the incline, and µ is the coefficient of friction.

4. How does the angle of inclination affect the tension on the string connecting the two masses?

The angle of inclination can affect the tension on the string connecting the two masses by changing the weight of the objects and the normal force acting on them. As the angle increases, the weight component parallel to the incline increases, causing a greater tension in the string. However, if the angle is too steep, the objects may slide down the incline, decreasing the tension in the string.

5. How does the mass of the objects affect the acceleration on an inclined plane?

The mass of the objects can affect the acceleration on an inclined plane through the equation a = (m1-m2)sinθ / (m1+m2) + µcosθ. As the mass of the objects increases, the acceleration will decrease, as there is more mass to overcome the force of friction. However, the acceleration can be increased if the angle of the incline is decreased or if the coefficient of friction is decreased.

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