Impulse momentum and morequestion

In summary: Impulse is the change in momentum, which can be calculated by multiplying the force applied by the time it is applied for. In this case, the impulse would be the force applied by the falling object multiplied by the time it takes for the impact to occur. In summary, a 200g block is suspended through a vertical spring that stretches by 1cm when the block is in equilibrium. A 120g particle is dropped on the block from a height of 45cm and sticks to it after impact. The goal is to find the maximum extension of the spring. There are two possible methods to solve this problem, using either the equation k|x| = mg or the work-energy theorem. However, using the work-energy theorem would
  • #1
atavistic
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Homework Statement

A block of mass 200g is suspended through a vertical spring.The spring is stretched by 1cm when the block is in equilibrium.A particle of mass 120g is dropped on the block from a height of 45cm.The particle sticks to the block after the impact.Find the max extension of the spring.

The attempt at a solution

Well in the beginning my aim was to find the force constant k.But i am stuck ..should i use k|x| = mg or work done by spring = loss in gravitational PE i.e (kx^2)/2 = mgx.Getting diff result in both. After that I must find out the velocity of the system due to the impulse but how?Then i can apply conservation of mechanical energy I guess i.e KE just after the collision + spring PE_1 = mgh + spring PE_2. (where spring PE_1 is the spring PE before the impact and spring PE_2 is spring PE when it is max stretched.)

Plz help
 
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  • #2
atavistic said:
... should i use k|x| = mg or work done by spring = loss in gravitational PE i.e (kx^2)/2 = mgx.Getting diff result in both. ...
You should not use (kx^2) / 2 = mgx because, if the weight is allowed to fall freely under gravity, the GPE will be translated into spring PE (SPE) plus KE (as you said when considering conservation of mechanical energy):
GPE + SPE + KE = constant

atavistic said:
... After that I must find out the velocity of the system due to the impulse but how? ...
It may help to recall the definition of impulse.
 
  • #3


I would suggest approaching this problem by first considering the principles of impulse and momentum. The impulse-momentum theorem states that the change in momentum of an object is equal to the impulse applied to it. In this case, the impulse would be the product of the force and the time over which it is applied.

So, to find the velocity of the system after the collision, we can use the equation:
m1v1 + m2v2 = (m1 + m2)v
where m1 and v1 are the mass and velocity of the block before the collision, and m2 and v2 are the mass and velocity of the particle before the collision. We can then solve for the final velocity, v, which would be the velocity of the combined system after the collision.

Next, we can consider the conservation of mechanical energy. In this system, we can assume that there is no external work done, so the total mechanical energy before and after the collision should be the same. This means that the initial kinetic energy of the particle (m2v2^2/2) will be transferred to the combined system as kinetic energy (mv^2/2) and potential energy stored in the spring (kx^2/2).

Using this information, we can then set up the equation:
(m2v2^2/2) = (mv^2/2) + (kx^2/2)
where m2 and v2 are known from the given information, and m, v, and x can be solved for using the equations from before.

Finally, to find the maximum extension of the spring, we can use the equation:
F = kx
where F is the force applied by the system and k is the spring constant. We can solve for x using the values we have already calculated.

I hope this helps guide you in your problem-solving process. Remember to always consider the relevant principles and equations, and carefully track your units to ensure a correct solution.
 

1. What is the difference between impulse and momentum?

Impulse and momentum are both terms used to describe the motion of an object. Momentum is a measure of an object's mass and velocity, while impulse is a measure of the force applied to an object over a certain amount of time. In simpler terms, momentum is the quantity of motion an object has, while impulse is the change in momentum due to a force.

2. How is impulse related to force?

Impulse is directly related to force through the equation FΔt = mΔv, where F is the force applied, Δt is the time over which the force is applied, m is the mass of the object, and Δv is the change in velocity of the object. This means that the greater the force applied or the longer the time over which it is applied, the greater the change in momentum, or impulse, will be.

3. Can momentum be conserved in a closed system?

Yes, momentum is conserved in a closed system, meaning that the total momentum of all objects in the system will remain constant. This is known as the law of conservation of momentum and is a fundamental principle in physics.

4. How does impulse affect the motion of an object?

Impulse can change the motion of an object by changing its momentum. If an object experiences a large impulse, its momentum will change significantly, causing it to speed up, slow down, or change direction. This is why forces such as braking or pushing can cause an object to change its motion.

5. What are some real-life examples of impulse and momentum?

Some examples of impulse and momentum in everyday life include a car crash, where a large force is applied to the car over a short amount of time, resulting in a change in its momentum and motion. Another example is a baseball being hit by a bat, where the force of the bat on the ball causes a change in its momentum, resulting in it flying in a different direction.

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