Finding acceleration and tension using Newton's laws

In summary, the problem involves two blocks connected by a massless rope on an inclined plane. Using Newton's laws of motion, the equations for the forces on each block can be written. However, there are three unknowns (T, F, and a) and only two equations, making it difficult to solve. It is assumed that tension is the same on both sides of the rope for a massless rope.
  • #1
Mangoes
96
1

Homework Statement



http://i.imgur.com/sPN07Hi.png

Homework Equations



Newton's laws of motion.

The Attempt at a Solution



I split up the entire thing into two pieces.

http://imgur.com/dMxfCZM

The left diagram illustrates the left block of 3 kg. I set the x-axis parallel to the ramp. The right is of the right block, where the x-axis is taken to be parallel to the horizontal surface.

Since accelerations occurs on the system,

By the left illustration,
ƩFx = T - w1sin30 = m1a

and by the right illustration,
ƩFx = Fcos20 - T = m2a

I can substitute the masses by their respective quantities, but my problem is that I have three unknowns (T, F, and a) and only two equations. I also don't really see how using the vertical components of motion will help me out.

Also, one thing I'm not even completely sure about is whether it's even correct to assume that tension is the same on both sides of the rope.

What am I doing wrong in here?
 
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  • #2
Mangoes said:
I can substitute the masses by their respective quantities, but my problem is that I have three unknowns (T, F, and a) and only two equations.
F is given. Look at the diagram.

Also, one thing I'm not even completely sure about is whether it's even correct to assume that tension is the same on both sides of the rope.
For a massless rope, that is a good assumption.
 
  • #3
Okay I think it's time to take a break then...

Thanks for the help.
 

FAQ: Finding acceleration and tension using Newton's laws

1. What is Newton's second law and how is it used to find acceleration and tension?

Newton's second law states that the net force on an object is equal to the product of its mass and acceleration. This means that if we know the mass of an object and the net force acting on it, we can use this equation (F=ma) to find the acceleration of the object. Additionally, we can also use this equation to find the tension in a string or rope that is attached to the object, as long as we know the mass and acceleration of the object.

2. How do you determine the net force on an object?

The net force on an object is determined by adding up all the individual forces acting on the object. This can be done using vector addition, where forces in the same direction are added together and forces in opposite directions are subtracted. Once we have the net force, we can plug it into Newton's second law to find the acceleration of the object.

3. Can Newton's laws be used to find acceleration and tension in any situation?

Yes, Newton's laws can be used to find acceleration and tension in any situation as long as the object is experiencing a net force. This means that the object is either accelerating or moving at a constant velocity.

4. Are there any other factors that can affect the acceleration and tension of an object?

Yes, there are other factors that can affect the acceleration and tension of an object. These include friction, air resistance, and the mass of the object. Friction and air resistance can act as additional forces on the object, which can affect its acceleration. The mass of the object also plays a role in determining its acceleration, as heavier objects require more force to accelerate.

5. How can you experimentally determine the acceleration and tension of an object using Newton's laws?

To experimentally determine the acceleration and tension of an object, you can set up a simple experiment where you measure the mass of the object and attach it to a string or rope. Then, you can apply a known force to the string and measure the acceleration of the object using a stopwatch or motion sensor. Once you have the acceleration, you can use Newton's second law to calculate the tension in the string.

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