How Do Kinematics and Impulse Principles Apply in a Two-Particle Pulley System?

[songoku]

Homework Statement

Two particles of masses 8 kg and 5 kg are connected to the two ends of a light inextensible string which passes over a fixed smooth pulley. Initially each of the two particles are held at a position which is 5 m above a horizontal ground. The objects are then released from rest. Assuming that the particles never reach the pulley, and also that the particles do not rebound when thhey strike the ground.

(i) find the tension in the string and the acceleration of each particle
(ii) find the distance above the ground of the point H, the highest point reached by the 5 kg mass
(iii) find the speed with which the system is jerked into motion and the impulse experienced by the string during the jerk.

Homework Equations

F = ma
Kinematics
Impulse = change in momentum
p = mv

The Attempt at a Solution

I'm able to do part (i) and (ii). For part (i), I got T = 800/13 N and a = 30/13 ms^-2

I don't understand how to do the part (iii). What is the meaning of "which the system is jerked into motion"? I think maybe I have to find the speed when it moves for the first time, but no information about time given...

Thanks

 

[rl.bhat]

Find the velocities of masses when 8 kg mass hits the ground.
At that instant T becomes zero. 5 kg mass stops accelerating. That may be the point of jerk. After that 5 kg mass retards with g. You can find distance traveled by it before coming to rest.

 

[songoku]

Hi rl.bhat

Oh, that's the point of jerk. Then to find the impulse on the string, take the initlal velocity as the velocity of point of jerk and final velocity = 0?

Thanks

 

[cena]

Can u solve the question ii/ and iii/ a bit clearly...THx

 

[rwisz]

for any help!

I am happy to assist you with your question about kinematics and impulse.

For part (iii), the phrase "jerked into motion" refers to the initial acceleration of the system when it is released from rest. This is the moment when the forces acting on the particles suddenly change, causing them to start moving.

To find the speed at which the system is jerked into motion, we can use the equation v = u + at, where v is the final velocity, u is the initial velocity (which is 0 in this case), a is the acceleration, and t is the time.

Since we know the acceleration from part (i), we can plug it into the equation and solve for v. This will give us the speed at which the system starts moving.

To find the impulse experienced by the string during the jerk, we can use the equation impulse = change in momentum. Since the initial momentum of the system is 0, we can simply find the final momentum by using the equation p = mv, where m is the mass of the system (8 kg + 5 kg = 13 kg) and v is the final velocity that we found in the previous step. This will give us the final momentum of the system.

The impulse experienced by the string is then equal to the change in momentum, which can be calculated by subtracting the initial momentum (0) from the final momentum. This will give us the magnitude of the impulse experienced by the string.

I hope this helps you understand how to approach part (iii) of the problem. Let me know if you have any further questions.