Pullies, masses, and acceleration

In summary, the first statement is true because when m1 > m2, m2 will be pulled up with an acceleration of g. The second statement is cannot tell because the masses are not given. The third statement is true because when m2 moves to the right, m1 will move to the left and the frictional force will be to the right. The fourth statement is cannot tell because it is unclear what is meant by a 10 N weight and a 10 N force applied to the rope.
  • #1
LadyTwi
8
0

Homework Statement


Answer True, False, or Cannot tell to each of the four statements below.

A) If m1 > m2 in the diagram below, then |a2| = g.
http://www.learning.physics.dal.ca/dalphysicslib/Graphics/Gtype09/pulley02.2.gif" [Broken]

B) In the diagram below, a1y = a2y.
http://www.learning.physics.dal.ca/dalphysicslib/Graphics/Gtype09/pulley02.2.gif" [Broken]

C) The diagram below shows two blocks, 1 and 2, at rest, connected to a rope and pulley system. There is friction between the blocks, but block 2 rests on a frictionless surface. An external force Fext is applied; the tension in the rope is T and the frictional force is F. The frictional force on block 2 points right.
http://www.learning.physics.dal.ca/dalphysicslib/Graphics/Gtype09/pulley02.4.gif" [Broken]

D) Block 1 rests on a frictionless table. In case A, a 10 N weight is attached; in case B, a 10 N force is applied to the rope. Block 1 accelerates faster in case B.
http://www.learning.physics.dal.ca/dalphysicslib/Graphics/Gtype09/pulley02.3.gif" [Broken]

The Attempt at a Solution



A) I think this one would be true because all objects fall toward the Earth with an acceleration of g, so m2 would be pulled up with an acceleration of g.
B) I don't know about this one. Maybe it's cannot tell because we don't know the mass of each of the masses?
C) I think this one is true because because when m2 moves to the right, m1 would move to the left so its frictional force would be to the right.
D) I'm really unsure about this one. Is there a difference between a 10 N weight and 10 N of tension? I didn't think there was.

I keep getting this question wrong, so if someone could help me, that would be great. <:
 
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  • #2
Sorry for the double post, but this question is due in 17 minutes and I'd really like some help. Thanks!
 
  • #3


A) True - According to Newton's Second Law, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In this case, m2 has a greater mass, so it will experience a smaller acceleration compared to m1, which has a smaller mass. Since the only force acting on m2 is its weight (mg), its acceleration (a2) will be equal to g.

B) Cannot tell - The diagram does not provide enough information to determine the acceleration in the y-direction for both masses. The acceleration in the x-direction may be different, but we cannot make any conclusions about the y-direction.

C) True - The frictional force on block 2 points to the right because it opposes the motion of block 2. This means that the external force applied must be greater than the frictional force in order to overcome it and cause the block to move to the right. This also means that the tension in the rope (which is equal to the external force) must also be greater than the frictional force.

D) True - In case A, the only force acting on block 1 is its weight (mg), which is equal to 10 N. In case B, an additional external force of 10 N is applied, which will cause the block to accelerate faster since the net force acting on it is now 20 N (10 N from its weight and 10 N from the external force). The 10 N of tension in the rope is not relevant since it is acting on block 2, not block 1.
 

1. How do pulleys affect the acceleration of a mass?

Pulleys can either increase or decrease the acceleration of a mass, depending on the number and arrangement of pulleys. In a simple pulley system with one fixed pulley and one movable pulley, the acceleration of the mass will be equal to the acceleration due to gravity, or 9.8 m/s^2. However, if multiple pulleys are used in a system, the acceleration can be decreased by increasing the number of supporting ropes.

2. What is the relationship between the mass and acceleration in a pulley system?

The mass of an object does not affect its acceleration in a pulley system. The acceleration will always be equal to the acceleration due to gravity, regardless of the mass of the object. This is because the force of gravity acting on the object is balanced by the tension in the rope, resulting in a net force of zero and therefore no change in acceleration.

3. How does the arrangement of pulleys affect the force needed to lift a mass?

The arrangement of pulleys can greatly affect the force needed to lift a mass. In a simple pulley system with one fixed pulley and one movable pulley, the force needed to lift the mass is equal to its weight. However, using multiple pulleys in a system can distribute the weight of the mass among multiple ropes, resulting in a decrease in the force needed to lift the mass.

4. What is the mechanical advantage of using pulleys in a system?

The mechanical advantage of using pulleys in a system is the ratio of the output force to the input force. In a simple pulley system with one fixed pulley and one movable pulley, the mechanical advantage is equal to 1, as the output force is equal to the input force. However, using multiple pulleys in a system can increase the mechanical advantage, making it easier to lift heavy objects.

5. Can pulleys violate the law of conservation of energy?

No, pulleys cannot violate the law of conservation of energy. The mechanical advantage gained by using pulleys is always balanced by an increase in the distance over which the force is applied. Therefore, the work done and energy used in a pulley system will always be equal to the work output and energy gained.

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