Acceleration of a system with 2 Blocks and a Wedge

In summary, the block B is initially at rest on the top of a 20kg wedge A. A 2kg block C is connected to block B by a cord which passes over a pulley of negligible mass. The software was used to determine the accelerations for values of m $ 0.01 increments until the wedge did not move and then 0.1 increments until no motion occurred. The results showed that the acceleration of block B was less than the acceleration of block A. The difference in acceleration was due to the friction between the blocks.
  • #1
goukishin
3
0

Homework Statement


Block B of mass 10 kg is initially at rest as shown on the upper surface of a 20-kg wedge A which is supported by a horizontal surface. A 2-kg block C is connected to block B by a cord which passes over a pulley of negligible mass. Using computational software and denoting by m the coefficient of friction at all surfaces, use this program to determine the accelerations for values of m $ 0. Use 0.01 increments for m until the wedge does not move and then use 0.1 increments until no motion occurs.
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Homework Equations


ƩF = ma
Tc/Tb = e(μ x β) (In this case β = 120*pi/180

The Attempt at a Solution


Taking each block as a system, finding Tc then Tb in terms of μ
Assuming the acceleration of Block C is the same as the acceleration of block B

Stuck at studying Wedge A. What are the forces acting on it and the equations?
Is the acceleration of the wedge the same as the acceleration of B?
 
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  • #2
goukishin said:
Stuck at studying Wedge A. What are the forces acting on it and the equations?
Is the acceleration of the wedge the same as the acceleration of B?
What forces do you think are acting on it?
If B is sliding on A, it will have a different acceleration; otherwise it will be the same.
 
  • #3
Can we chooses different axes to study Block B and wedge A ?
 
  • #4
You can, but it might be confusing, particularly for anyone trying to check your work.
 
  • #5
Well no, it is not confusing, it's the opposite. When we choose different axes according to the position of each block, it is much easier to find the Normal force acting on the system and the acceleration since a(y) becomes zero. But since Block B is in contact with the wedge, I wonder if that's allowed. And I really doubt it.
 
  • #6
Sounds like you and I mean different things by 'using different axes'. pls post your working so that I can get some idea of what you're doing.
 

Related to Acceleration of a system with 2 Blocks and a Wedge

1. What is the equation for calculating the acceleration of a system with 2 blocks and a wedge?

The equation for calculating the acceleration of a system with 2 blocks and a wedge is a = (m1g sinθ - μk(m1 + m2)g cosθ) / (m1 + m2 + m3), where m1 and m2 are the masses of the blocks, m3 is the mass of the wedge, θ is the angle of the wedge, g is the acceleration due to gravity, and μk is the coefficient of kinetic friction between the blocks and the wedge.

2. How does the angle of the wedge affect the acceleration of the system?

The angle of the wedge affects the acceleration of the system by changing the direction and magnitude of the force exerted on the blocks. As the angle increases, the force exerted on the blocks becomes more vertical, resulting in a greater acceleration. Conversely, as the angle decreases, the force becomes more horizontal and the acceleration decreases.

3. What is the role of friction in the acceleration of this system?

Friction plays a major role in the acceleration of this system. The coefficient of kinetic friction, μk, affects the acceleration by creating a resistance force that opposes the motion of the blocks and the wedge. The greater the coefficient of friction, the smaller the acceleration of the system will be.

4. Can the acceleration of the system be negative?

Yes, the acceleration of the system can be negative. This would occur if the force of friction is greater than the force of gravity acting on the blocks, resulting in a net force in the opposite direction of motion. This can happen if the angle of the wedge is too steep or if the coefficient of friction is high enough.

5. How does the mass of the blocks and the wedge affect the acceleration of the system?

The mass of the blocks and the wedge have a direct impact on the acceleration of the system. The greater the mass, the more inertia the system has, making it more difficult to accelerate. This is reflected in the equation, where a larger mass in the numerator will result in a smaller acceleration. Additionally, the total mass of the system (m1 + m2 + m3) will also affect the acceleration, as a greater mass will require a greater force to accelerate.

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