Two masses on an inclined plane with a massless pulley

In summary: Great job!In summary, the conversation discusses a problem involving a block on a slope with coefficients of friction, connected to a hanging block via a massless string over a frictionless pulley. The minimum mass needed for the block to stick and not slip is 1.829 kg, and if the block is nudged slightly, it will start being pulled up the incline with an acceleration of 2.76 m/s^2. The solution involves writing equations for the sum of forces and solving for tension and acceleration.
  • #1
JefeNorte
9
0

Homework Statement


A block of mass m resting on a 20 degree slope. The block has coefficients of friction mu_s =0.80 and mu_k =0.50 with the surface. It is connected via a massless string over a massless, frictionless pulley to a hanging block of mass 2.0 kg.

What is the minimum mass m that will stick and not slip?

If this minimum mass is nudged ever so slightly, it will start being pulled up the incline. What acceleration will it have?

Homework Equations


T-f_k-(mg*sin(theta))=m*a
f_k=u_k*(mg*cos(theta))

The Attempt at a Solution


I completed the first part of the problem and determined that the minimum mass is 1.829 kg. I calculated the tension on the rope by multiplying the mass of the hanging block by 9.8. But when I plug these values into the equation I keep getting 2.76 m/s^2 which is not the correct answer. Is there something wrong with my equations or the tension value?
 
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  • #2
The tension in the rope is only equal to the weight of the hanging block if the objects aren't accelerating. You need to write the sum of the forces = ma for each object, where the sum of the forces includes the unknown tension T. Then you have two equations and two unknowns and you solve for T and a.
 
  • #3
Do you mean like T-(u_k*(mg*cos(theta)))-(mg*sin(theta))=m*a?
 
  • #4
I mean something exactly like that.
 

1. What is an inclined plane?

An inclined plane is a flat, sloped surface used to raise or lower objects. It is often used to make lifting heavy objects easier by changing the direction of the force needed to move the object.

2. What is a massless pulley?

A massless pulley is a pulley with negligible mass, meaning its weight can be ignored in calculations. It is often used in physics problems to simplify calculations and focus on the forces acting on the system.

3. How do the masses on an inclined plane with a massless pulley affect each other?

The masses on an inclined plane with a massless pulley are connected by a rope or string passing over the pulley. This means that the two masses are connected and their movements are dependent on each other.

4. What forces are acting on the masses on an inclined plane with a massless pulley?

The forces acting on the masses on an inclined plane with a massless pulley include the weight of each mass, the tension in the rope or string, and the normal force from the inclined plane. In some cases, friction may also be a factor.

5. How can the motion of the masses on an inclined plane with a massless pulley be calculated?

The motion of the masses on an inclined plane with a massless pulley can be calculated using Newton's second law of motion, which states that the sum of all forces acting on an object is equal to its mass multiplied by its acceleration. By setting up and solving equations for the forces on each mass, the motion of the system can be determined.

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