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Center of Mass : Introduction 0/4
Momentum Conservation & Collision 0/4
Impulsive & Non-impulsive Forces
The force of relatively higher magnitude and which act for a relatively short time and can change the momentum significantly in a very short duration than the force is called as impulsive force.
Normal reaction acting during the collision is always impulsive.
Effect of impulsive force can be cancelled by another impulsive force only.
Similar to normal reaction tension force can also be impulsive.
Find out the height achieved by the ball after the collision with the floor. Assume that e = 0 and all surfaces are smooth.
In this scenario, before hitting the surface ball is in circular motion with the circle of radius L. As e=0, velocity of separation will be zero along the line of impact after collision with the ground. After hitting the ground tension in the string will become zero as length between ground and ceiling is less than L. Because of this object will move in straight line for some time until tension in the string becomes non-zero.
The moment, tension in the string is greater than zero; object will start moving in circular motion again with the circle of radius L.
We can find out velocity of object at this point and will apply energy conservation after this point to find out maximum height attained by the object.
Let’s find out velocity of object by drawing impulse force diagram at various points.
When the object hits the ground component of velocity along the line of impact will become zero. Similarly when object is just leaving the ground there will be an impulse force in the form of tension force will act and component of velocity along this line will become zero.
Let’s apply energy conservation now,
Friction force acting between two colliding objects will be impulsive if the normal reaction acting on the same point is impulsive.
A force of relatively smaller magnitude and which cannot change momentum significantly in very short duration. Examples are spring force, gravitational force, and electrostatic force.
Momentum conservation can be applied in presence of external force for approximate calculations if the external force is non-impulsive and the duration of process is very small.
Let’s consider a hypothetical situation where a block of mass 2M is at rest and a block of mass M is moving in upward direction with the velocity of U m/s just before the collision. Find out velocity of both objects just after the collision.
As the duration of collision is very short we can apply momentum conservation for a short period in the presence of gravitational force.
Apply equation of elasticity,
Solving both equations,
Variable mass system
Whenever some mass is added or subtracted to or from a system with some relative velocity with respect to system than it exerts impulsive force on the system called as thrust force whose magnitude is equal to
A cart is moving with velocity u at given moment. Due to a hole in the cart, sand is leaking from the cart with a speed of lambda kg/s. Find out velocity of cart after time t.
External force on the system = 0
Relative velocity of sand particles with respect to cart = 0, hence thrust force = 0
As acceleration is zero, velocity will be constant. Hence, V = u
Cart will move with constant velocity after time t.
How to solve problems on variable mass system
- Identify the system and draw the boundaries of system.
- System is taken for the general time t or general position r.
- Identify if at the next instant dt, whether the mass of system is increasing or decreasing.
- If the mass of the system increases or decreases than find out the rate.
- Identify whether there is change in velocity of the mass just before and just after it added or subtracted to or from the system.
Get above force balance equation and solve it to find out required information.
Chain is released from shown position. Find out normal reaction at any time t on weighing machine.
l is the length of chain accumulated on weighing machine in time t =