Block-pulley system and rotational dynamics

In summary: Just solve for g.I do not see any difficulty. Just collect all the a terms on one side and all the g terms on the other. You have the values for r amd the masses. Just solve for g.
  • #1
Kennedy
70
2

Homework Statement


Two blocks, m1 = 1.0 kg and m2 = 2.0 kg are connected by a light string as shown in the figure. If the radius of the pulley is 1.0 m and its moment of inertia is of the system is 5.0 kg*m^2, the acceleration of the system is (expressed as a fraction of gravitational acceleration g):

Homework Equations


I believe that Newton's Second Law is the only relevant equation (F = ma).

The Attempt at a Solution


I have the acceleration to be in the direction of m2, because that's the heavier block. So, the m2g - T1 = m2a. Solving for T1 that leads to m2g - m2a = T1. On the other side of the pulley we have T2 - m1g = m1a. Solving for T2, we get T2 = m1a + m1g. Now the pulley, T2(radius) - T1(radius) = τ. We know that τ = Iα, and α = a/r.

Now, (m1a +m1g)(r) - (m2g -m2a)(r) = 5(a/r)

How do I solve this in terms of g?
 
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  • #2
Kennedy said:

Homework Statement


Two blocks, m1 = 1.0 kg and m2 = 2.0 kg are connected by a light string as shown in the figure. If the radius of the pulley is 1.0 m and its moment of inertia is of the system is 5.0 kg*m^2, the acceleration of the system is (expressed as a fraction of gravitational acceleration g):

Homework Equations


I believe that Newton's Second Law is the only relevant equation (F = ma).

The Attempt at a Solution


I have the acceleration to be in the direction of m2, because that's the heavier block. So, the m2g - T1 = m2a. Solving for T1 that leads to m2g - m2a = T1. On the other side of the pulley we have T2 - m1g = m1a. Solving for T2, we get T2 = m1a + m1g. Now the pulley, T2(radius) - T1(radius) = τ. We know that τ = Iα, and α = a/r.

Now, (m1a +m1g)(r) - (m2g -m2a)(r) = 5(a/r)

How do I solve this in terms of g?
Which mass is m1 and which is m2? tension produce by m1 is t1? Then write equation accordingly
 
  • #3
Abhishek kumar said:
Which mass is m1 and which is m2? tension produce by m1 is t1? Then write equation accordingly
The tension in the string attached to m1 is T1, and the tension in the string attached to m2 is T2.
 
  • #4
Kennedy said:
The tension in the string attached to m1 is T1, and the tension in the string attached to m2 is T2.
m1 is the 1 kg mass, and m2 is the 2 kg mass
 
  • #5
Kennedy said:
The tension in the string attached to m1 is T1, and the tension in the string attached to m2 is T2.
Kennedy said:
The tension in the string attached to m1 is T1, and the tension in the string attached to m2 is T2.
Kennedy said:
m1 is the 1 kg mass, and m2 is the 2 kg mass
Ok then t1-m1g=m1a(say equation 1)
m2g-t2=m2a(say equation 2)
and for rotational motion
t2-t1=Ia/r^2(say equation 3)
Then put the value t1 and t2 from equation 1and 2 in equation 3 you will get the acceleration
 
  • #6
Kennedy said:
, (m1a +m1g)(r) - (m2g -m2a)(r) = 5(a/r)

How do I solve this in terms of g
I do not see any difficulty. Just collect all the a terms on one side and all the g terms on the other. You have the values for r amd the masses.
 

Related to Block-pulley system and rotational dynamics

What is a block-pulley system?

A block-pulley system is a mechanical setup that consists of one or more pulleys and a block or multiple blocks connected by a rope or cable. It is used to change the direction of a force and lift or move objects.

What are the types of pulleys used in a block-pulley system?

There are three types of pulleys used in a block-pulley system: fixed, movable, and compound. Fixed pulleys are attached to a surface and do not move. Movable pulleys are attached to the object being lifted and move with it. Compound pulleys are a combination of fixed and movable pulleys, providing a mechanical advantage.

How does a block-pulley system work?

A block-pulley system works by using the principle of rotational dynamics, where the force applied to one end of a rope or cable is transferred and magnified to the other end. As the rope is pulled, the pulleys rotate, changing the direction of the force and allowing for the object to be lifted or moved.

What is rotational inertia in a block-pulley system?

Rotational inertia, also known as moment of inertia, is the resistance of an object to change its rotational motion. In a block-pulley system, it is the resistance of the pulleys to rotate and the block to move due to the force applied to the rope or cable.

How can the mechanical advantage of a block-pulley system be calculated?

The mechanical advantage of a block-pulley system can be calculated by dividing the force applied to the rope or cable by the weight of the object being lifted or moved. This will give the number of times the force is multiplied in the system, also known as the ideal mechanical advantage.

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