Solving for Acceleration & Tension: Newton's Laws

In summary, the problem involves using Newton's Laws and Conservation of Energy to find the acceleration of each mass and the tensions in the cord for a system with a pulley and inclined plane. The coefficient of friction and masses of the objects are provided. The pulley is a frictionless solid disk. The first part of the problem involves using Newton's Laws to find the acceleration and tensions, while the second part involves using Conservation of Energy to find the speed and acceleration after one of the masses falls a certain distance. The pulley can be ignored in the calculations as it does not affect the solution.
  • #1
sweet_girl123
9
0

Homework Statement



1. For the system shown below use Newton’s Laws to clearly derive an expression for the
acceleration of each mass and the tensions in the cord. The coefficient of friction
between m1 and the incline is 0.100. The mass m1 is 3.00 kg, m2 = 8.00 kg, and θ = 35.0°.
The pulley is frictionless solid disk of mass 0.250 kg.


2. For the system shown below use only Conservation of Energy to clearly derive an
expression for the speed and acceleration of each mass after m2 falls a distance of
2.50 m. The coefficient of friction between m1 and the incline is 0.100. The mass m1 is
3.00 kg, m2 = 8.00 kg, and θ = 35.0°. The pulley is frictionless solid disk of mass
0.250 k


Homework Equations





The Attempt at a Solution



ƩF(x) = m a1

T1 - F - mgSinθ = m1 * a
T2 + m2g = m1a

ƩTorque = IAlpha
-RT1 + RT2 = IAlpha
R(T2-T1) = I (alpha/R)

This is not my homework. This was given to use for practicing for our finals.
Any help would be really helpful
Thank You\
 

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  • #2


You have made a decent start to solving the problem. I have a few comments:
sweet_girl123 said:

The Attempt at a Solution



ƩF(x) = m a1

T1 - F - mgSinθ = m1 * a
Good, but it looks like you mean to say m1 and not just m on the left side?
You can also look at ƩF(y), that will help you get the friction force F in terms of other quantities.

T2 + m2g = m1a
Think about the direction each force acts, and whether a + or - sign should be in front of each force. Also, I think you mean m2a on the right?
ƩTorque = IAlpha
-RT1 + RT2 = IAlpha
R(T2-T1) = I (alpha/R)
Why did you replace "Alpha" with "Alpha/r"? I think you meant something slightly different... otherwise this looks good.
This is not my homework. This was given to use for practicing for our finals.
Any help would be really helpful
Thank You\
That's okay, we pretty much like to see people show an attempt at solving the problem, which you did, even when it's not an assignment.

Final comment: I think to solve this they need to tell you what R is for the pulley -- or maybe they tell you what I is. Can you check the problem statement again, and see if I or R for the pulley is given?

Hope that helps.
 
  • #3


no there is no R or I is given and only the mass of the pulley is given which is making me confuse. and the part 2 of the quest with the conservation of the energy, I really do not have any idea about that how we do that can you please help me out with that??...:)
 
  • #4


If the pulley is frictionless then it won't rotate so it's only function is to redirect the forces, in that case the I and R don't matter and you can essentially forget it is there.
 
  • #5


ohhhkk thanks...and for the conservation energy is

1/2m1v^2 + 1/2 M2 V^2 = M1g h sin(X) - (mu)M2g hcos(X)- M2gh
??
 

What is Newton's Second Law and how is it related to acceleration and tension?

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass. This means that the greater the force applied to an object, the greater its acceleration will be. In the context of solving for acceleration and tension, this law can be used to calculate the acceleration of an object based on the net force acting on it and its mass, and therefore determine the tension in a system.

How do I calculate the acceleration of an object using Newton's Second Law?

To calculate the acceleration of an object, you will need to know the net force acting on the object and its mass. The formula for acceleration is a = F/m, where a represents acceleration, F represents force, and m represents mass. By plugging in the values for force and mass, you can solve for the acceleration of the object.

What is tension and how is it related to acceleration?

Tension is the force transmitted through a string, rope, or cable when it is pulled tight by forces acting at its ends. In the context of Newton's Laws, tension is related to acceleration because it is one of the forces that can act on an object, along with the force of gravity. Tension can either contribute to or counteract the force of gravity, resulting in a change in the object's acceleration.

Can Newton's Laws be used to solve for acceleration and tension in real-world scenarios?

Yes, Newton's Laws can be used to solve for acceleration and tension in real-world scenarios. These laws are fundamental principles of physics and can be applied to any situation where forces are involved. By understanding and applying these laws, scientists and engineers are able to solve complex problems and design systems that work effectively.

What are some common mistakes when solving for acceleration and tension using Newton's Laws?

One common mistake is forgetting to consider all the forces acting on an object. To accurately solve for acceleration and tension, all forces, including tension, must be taken into account. Another mistake is using incorrect units in calculations. It's important to pay attention to units and use consistent units throughout the calculation to get the correct answer. Additionally, not considering the direction of forces can lead to incorrect solutions, as forces can act in different directions and cancel each other out.

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