How do you calculate acceleration and angular acceleration with pulleys?

In summary, the heavier block with a mass of 500 g and the lighter block with a mass of 460 g are attached to a pulley with a radius of 5.00 cm and a frictionless wire. When released from rest, the heavier block falls 75.0 cm in 5.00 seconds. Using kinematic equations, the acceleration of the blocks can be found to be 6.00 cm/s^2 and the angular acceleration of the pulley is 1.20 rad/s^2. The mass of the pulley is not needed to solve this problem."
  • #1
DeadFishFactory
25
0

Homework Statement


A block has a mass of 500 g, another block has a mass of 460 g. Both are attached to a pulley with a frictionless wire that does not slip. The pulley, which is mounted in horizontal frictionless bearings, has a radius of 5.00 cm. When released from rest, the heavier block falls 75.0 cm in 5.00 seconds. What is the magnitude of the blocks' accleration? What is the magnitude of the pulley's angular acceleration?

Fig: http://i212.photobucket.com/albums/cc150/deadfishfactory/1.jpg


Homework Equations


Torque = Moment of Inertia * Angular Acceleration
Force = Mass * Acceleration
Acceleration = Angular Acceleration / Radius
Moment of Inertia = (1/2)MR^2

The Attempt at a Solution


T=tension; W=weight; A=accleration; R=radius; I=moment of inertia
M(1) = left box; M(2) = right box; M(3) = pulley

A(1) = A(2) = a/R = A

1. T(1) - W(1) = m(1) * A; T(1) = W(1) + M(1) * A
2. T(2) - W(2) = -m(2) * A; T(2) = W(2) - M(2) * A
3. T(1)R - T(2)R = I * A / R
T(1) - T(2) = M(3) * A
W(1) + M(1) * A - W(2) + M(2) * A = M(3) * A
Solved for A.

Well, I started plugging things in and stuff, but I can't solve the problem because the mass of the pulley is unknown. I'm pretty sure I did it wrong so can someone point out my mistake or show me how to do it if I did it completely wrong? Thanks!

answer: a) 6.00 cm/s^2 b) 1.20 rad/s^2
 
Physics news on Phys.org
  • #2
Using kinematic formula, find the acceleration of the falling body. Using this value find the angular acceleration of the pully. In this problem mass of any object is not needed
 
Last edited:
  • #3
Still having trouble finding the acceleration of the blocks.

I found the angular acceleration of the pulleys by using the constant acceleration equation like you said. I got 1.22 rad/s^2, which is close enough. I can't figure out how to find the acceleration of the blocks since I used gravity for the block's acceleration to find the angular acceleration. My physics skills aren't too good, can you explain it to me very precisely since I'm kinda slow.
 
  • #4
Heavier block falls 75.0 cm in 5.00 sec. (The system was released from rest.) Can you find A from the basic equations of Kinematics. (Remember those s-u-v-a-t equations??)
 
  • #5
Ohhhh. Pfft. When you said "heavier block falls 75.0 cm in 5.00 sec," it immediately smacked into me. Haha. I'm such an idiot for not noticing. Anyways, I got the answer. Thank you very much!
 

FAQ: How do you calculate acceleration and angular acceleration with pulleys?

What is rotation with pulleys?

Rotation with pulleys is a mechanical system in which a rotating motion is transferred from one pulley to another using a belt or chain. This allows for the use of a smaller driving pulley to rotate a larger driven pulley, resulting in a change in speed, direction, or both.

What are the different types of pulleys used in rotation systems?

There are two main types of pulleys used in rotation systems: fixed pulleys and movable pulleys. Fixed pulleys are attached to a stationary point and do not move, while movable pulleys are attached to the load being moved and move along with it.

What are the advantages of using pulleys in rotation systems?

Pulleys offer several advantages in rotation systems, including the ability to transfer a rotational motion over a distance, the ability to change the direction of rotation, and the ability to change the speed of rotation. Pulleys also allow for the use of smaller and more efficient motors or engines for driving the system.

How do you calculate the mechanical advantage of a pulley system?

The mechanical advantage of a pulley system is equal to the number of supporting ropes or strands in the system. For example, a system with one fixed and one movable pulley has a mechanical advantage of 2, while a system with two fixed and two movable pulleys has a mechanical advantage of 4.

What are some common applications of rotation with pulleys?

Rotation with pulleys is used in a wide range of applications, including lifting heavy loads, moving objects along an inclined plane, and powering machinery in factories. It is also commonly used in transportation systems, such as elevators and escalators, and in various types of exercise equipment.

Similar threads

Back
Top