Impulsive force due to a falling chain

Click For Summary
SUMMARY

The discussion focuses on calculating the impulsive force exerted by a falling uniform chain of mass M and length L on the floor when a length x has reached the ground. The initial calculations suggested an impulsive force of 2Mgx/L, but the correct answer is 3Mgx/L. The discrepancy arises from neglecting the normal force exerted by the floor, which is crucial in determining the total force during the impact.

PREREQUISITES
  • Understanding of classical mechanics, specifically impulse and momentum.
  • Familiarity with the concepts of normal force and gravitational force.
  • Knowledge of kinematics, particularly the equations of motion under gravity.
  • Basic calculus for handling mass elements in continuous systems.
NEXT STEPS
  • Study the principles of impulse and momentum in detail.
  • Learn about normal force and its role in impact scenarios.
  • Explore kinematic equations related to free-falling objects.
  • Investigate the dynamics of continuous mass distributions in physics.
USEFUL FOR

Physics students, educators, and anyone interested in mechanics, particularly those studying dynamics and impulse forces in continuous systems.

vikvaryas1
Messages
2
Reaction score
0
A uniform chain of mass M and length L is held in vertically in such a way that its lower end just touches the floor. The chain is released from rest in this position. Any portion that strikes the floor comes to rest. Assuming that the chain does not form a heap on the floor, calculate the force exerted by it on the floor when a length x has reached the floor.


I assumed chain that the chain is made up of many small mass elements and an impulsive force exerted by the floor brings each of these to rest.
Velocity of the mass element at height of x when it reaches the ground is √2gx
Impulse is change in momentum by time that is (m*v-m*0)/dt.
m=M*dx/L
So Impulse = Mv*dx/dt*(1/L)
=Mv2/L
v=√2gx
so 2Mgx/L
But the answer was given as 3Mgx/L
Please show where i was wrong
 
Physics news on Phys.org
You missed the normal force due to floor. :wink:
 
Ok i got it thanks.
 

Similar threads

Weight of gold chain when dropped on a weighing scale
  • · Replies 12 ·
Replies
12
Views
3K
Analyzing the Fall of a Chain: Problem 103 of 200 Puzzling Physics Problems
  • · Replies 7 ·
Replies
7
Views
3K
U-shaped length of chain falling when one end is released
  • · Replies 30 ·
2
Replies
30
Views
3K
Why is m*dv/dt 0 in the Falling Chain Problem?
  • · Replies 5 ·
Replies
5
Views
4K
Why is the tension in a falling chain not equal to ρgy?
  • · Replies 4 ·
Replies
4
Views
2K
Finding the Force Applied by a Support on a Falling Chain
  • · Replies 2 ·
Replies
2
Views
2K
Work done by gravity on a hanging chain?
  • · Replies 22 ·
Replies
22
Views
2K
Analyzing Velocity and Force of a Chain in Motion
  • · Replies 15 ·
Replies
15
Views
2K
Force due to a chain falling on a table
  • · Replies 11 ·
Replies
11
Views
3K
What is the force exerted by a falling chain on a table?
  • · Replies 2 ·
Replies
2
Views
4K