Blocks moving on frictionless incline at constant speed, accleration

In summary: C) = m(B)cosQ - m(A)In summary, the masses of blocks A, B, and C can be found by setting up equations for the forces acting on each block and solving for the unknown mass in each case. In Part A, the mass of block C is equal to the sum of the mass of block B multiplied by the cosine of the angle of the incline, minus the mass of block A. In Part B, the mass of block C is equal to the sum of the mass of block B, multiplied by two times the cosine of the angle of the incline, plus three times the mass of block A.
  • #1
joemama69
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Homework Statement



There is no friction

Part A) Find the mass of block C so that block B moves up the incline with a constant speed

Part B) fint he mass of block C so that Block B moves up the incline with a constant accleration a = g/2

Homework Equations





The Attempt at a Solution



Block A

Fy = T(2) -m(a)g = m(a)a T(2) = m(a)a + m(a)g

Block B

Fx = T(1) - m(b)gsinQ - T(2) = m(b)a T(1) = m(b)a + m(b)gsinQ + T(2)

Block C

Fy = T(1) - m(c)g = m(c)a

Do i just plug them all tother and solve for m(c)
 

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  • #2


joemama69 said:
Block A

Fy = T(2) -m(a)g = m(a)a T(2) = m(a)a + m(a)g

Block B

Fx = T(1) - m(b)gsinQ - T(2) = m(b)a T(1) = m(b)a + m(b)gsinQ + T(2)
OK. (Looks like you switched labels for the strings.)

Block C

Fy = T(1) - m(c)g = m(c)a
Careful with signs. Make sure "a" is going in the same direction in all equations.

Do i just plug them all tother and solve for m(c)
You could. Just plug the given values into each equation and see what you end up with.
 
  • #3


since it is moving with constant speed, that makes a = 0.

but since a is 0, doesn't that put it in equalibrium and make its not moving

Part B a = g/2

A = T(1) - m(A)g = 1/2 m(A)g
B = T(2) - T(1) - m(B)gcosQ = 1/2 m(B)g
C = m(c)g - T(2) = 1/2 m(c)g

T(1) = 1/2 m(A)g + m(A)g
T(2) = m(c)g - 1/2 m(c)g

m(c)g - 1/2 m(c)g - 1/2 m(A)g - m(A)g - m(B)gcosQ = 1/2 m(B)g

m(c) = m(B) + 3m(A) + 2m(B)cosQ
 
Last edited:
  • #4


joemama69 said:
since it is moving with constant speed, that makes a = 0.
Right.
but since a is 0, doesn't that put it in equalibrium and make its not moving
Since a = 0 it is in equilibrium, but that doesn't mean it's not moving. (It's moving with constant velocity.) What's the net force in this case?
 
  • #5


so then Part A

A = T(1) - m(A)g = 0
B = T(2) - T(1) - m(B)gcosQ = 0
C = m(C)g - T(2) = 0

T(1) = m(A)g
T(2) = m(C)g

m(A)g - m(C)g - m(B)gcosQ = 0

m(C) = m(B)cosQ - m(A)
 
  • #6


joemama69 said:
so then Part A

A = T(1) - m(A)g = 0
B = T(2) - T(1) - m(B)gcosQ = 0
C = m(C)g - T(2) = 0

T(1) = m(A)g
T(2) = m(C)g
All good.

m(A)g - m(C)g - m(B)gcosQ = 0
You have the first two terms reversed. (Compare to your equation for B above.)
 

1. What is a frictionless incline?

A frictionless incline refers to a surface or plane that has no friction, meaning there is no resistance to motion when an object slides or moves along it. This type of surface is often used in physics problems to simplify calculations and focus on the effects of other forces such as gravity.

2. How does a block move on a frictionless incline at constant speed?

A block on a frictionless incline will move at a constant speed if there are no external forces acting on it. This means that the forces of gravity and the normal force (perpendicular to the incline) are balanced, resulting in no acceleration. The block will continue to move at a constant speed unless acted upon by an external force.

3. What is acceleration on a frictionless incline?

Acceleration on a frictionless incline can refer to two different things: the acceleration of the block itself or the acceleration due to gravity. If the block is moving at a constant speed, there is no acceleration of the block. However, the acceleration due to gravity is still present and can be calculated using the angle of the incline and the acceleration due to gravity on Earth (9.8 m/s²).

4. How does the angle of the incline affect the block's motion on a frictionless incline?

The angle of the incline affects the block's motion by changing the components of the forces acting on it. As the angle increases, the force of gravity acting parallel to the incline increases, causing the block to accelerate down the incline. On the other hand, as the angle decreases, the force of gravity acting parallel to the incline decreases, resulting in a slower acceleration or even a constant speed if the angle is small enough.

5. Can a block move up a frictionless incline?

Yes, a block can move up a frictionless incline if it is given an initial velocity or if an external force is applied to it. However, the block will eventually come to a stop unless the applied force is continuous or if the incline is angled downward. This is because the force of gravity is always acting downwards, making it difficult for the block to move against it without additional forces.

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