Impulse and momentum problem

[Mikejax]

Homework Statement

A ball of mass 0.150 kg is dropped from rest from a height of 1.25 m. It rebounds from the floor to reach a height of 0.960 m.* What impulse was given to the ball by the floor?

Homework Equations

impact speed is given by (1/2)mv^2 = mgh1.
rebound speed is given by (1/2)mv^2 = mgh2.
The impulse of the floor is the change in momentum.
mv2(up) - mv1(down) = m(v1 + v2)up

The Attempt at a Solution

using the speed impact speed equations, I have solved for v in both cases.* The ball hits the ground with a speed of 4.94 m/s.* Using mgh2 from its rebound height, one can find the potential energy and then solve for the velocity that the ball had when leaving the floor, which, algebraically, comes to 4.33 m/s.

So then, momentum just before hitting floor is mv = 0.15kg*4.94m/s = 0.741 kg-m/s.
momentum just after hitting floor = mv = 0.15kg*4.33m/s = 0.6495 kg-m/s.

My textbook describes "impulse" as the change in momentum of an object. So I took the difference, which is .741 - .6495 = 0.0915.

The correct answer, according to my book is 1.36 kg-m/s.Why did they add the momentums?

My understanding is that impulse, is a difference, not a sum of momenta.I realize that, if one uses Impulse = momentum(final) - momentum(initial), you get the answer (because both - signs make the operation an addition)...but then the whole conecpt isn't very clear to me.It seems to me that the impact of the ball on the floor, is reducing the ball's momentum and velocity, thus, conceptually it's as if the floor is "taking away" energy from the ball. But mathematically, in this problem, it seems we are required to "add' this energy to the initial momentum of the ball...it doesn't make sense to me, I was wondering if someone could clarify the issue.

 

[Doc Al]

So then, momentum just before hitting floor is mv = 0.15kg*4.94m/s = 0.741 kg-m/s.
momentum just after hitting floor = mv = 0.15kg*4.33m/s = 0.6495 kg-m/s.

My textbook describes "impulse" as the change in momentum of an object. So I took the difference, which is .741 - .6495 = 0.0915.

The correct answer, according to my book is 1.36 kg-m/s.Why did they add the momentums?

Realize that momentum is a vector quantity--direction counts.

Let's call the up direction to be positive (+) and the down direction to be negative (-).

The initial momentum is 0.741 kg-m/s down, thus -0.741.
The final momentum is 0.6495 kg-m/s up, thus +0.6495.

The difference, final - initial, is: (+0.6495) - (-0.741) = + 1.39 kg-m/s, which means an upward impulse. (I'm using your numbers; I didn't check your calculations.)

Note that momentum and energy are two very different things. What changes the momentum of something is a force acting over some time. The ground smacks the ball upward, changing its momentum.

 

[thomate1]

I can understand your confusion and I will try my best to clarify the concept of impulse and momentum for you.

First, let's define impulse and momentum. Impulse is the change in momentum of an object, which is defined as the product of its mass and velocity. Momentum is the quantity of motion an object has, and it is also defined as the product of its mass and velocity.

Now, let's look at the problem at hand. The ball is initially at rest, so its initial momentum is zero. When it hits the floor, it experiences a change in momentum due to the impact. The floor exerts a force on the ball, causing it to change its velocity and therefore its momentum. This change in momentum is the impulse given to the ball by the floor.

To calculate the impulse, we can use the following formula: Impulse = Final momentum - Initial momentum. In this case, the final momentum is the momentum of the ball just after it rebounds from the floor, and the initial momentum is zero. So, the impulse given to the ball by the floor is equal to its final momentum, which is 0.6495 kg-m/s.

Now, let's address your concern about adding the momenta. In this case, we are not adding the momenta, but rather subtracting them. The reason for this is that momentum is a vector quantity, meaning it has both magnitude and direction. When we subtract the initial momentum from the final momentum, we are essentially taking into account the direction of the momentum.

To better understand this, let's look at the direction of the momenta in this problem. The initial momentum of the ball is zero, so we can say it is in the downward direction. The final momentum, on the other hand, is in the upward direction. When we subtract these two momenta, we are essentially taking into account the change in direction of the momentum, which is the result of the impact.

I hope this helps to clarify the concept of impulse and momentum for you. Remember, impulse is the change in momentum, and when we calculate it, we are taking into account both the magnitude and direction of the momentum.