Review. After a 0.300-kg rubber ball is dropped from a height of 1.75 m, it bounces off a concre

Review. After a 0.300-kg rubber ball is dropped from a...

Key Concepts

Impulse

Impulse is the product of force and the time period over which it acts and is equal to the change in momentum of an object. It is a vector quantity, meaning it has both magnitude and direction. In collision problems, impulse represents how the force applied over a short interval changes the momentum of the moving object.

Momentum

Momentum is the product of an object's mass and its velocity and is a vector quantity. It quantifies the motion of an object and plays a central role in analyzing collisions. In this context, momentum before and after impact is used to determine the impulse delivered during the collision.

Impulse-Momentum Theorem

The Impulse-Momentum Theorem states that the impulse on an object is equal to the change in its momentum. This theorem is crucial for solving problems where a force acts over a time interval, such as a ball bouncing off a surface, by linking the force exerted on the ball to the resulting change in its velocity.

Energy Conservation

Energy conservation, particularly the conversion between gravitational potential energy and kinetic energy, is fundamental in analyzing drop and bounce scenarios. As the ball is dropped, its potential energy is converted into kinetic energy just before impact, and upon rebounding, kinetic energy is converted back into gravitational potential energy, with some losses typically due to inelasticity of the collision.

Average Force

Average force in the context of collisions is defined as the total impulse divided by the duration of the collision. Estimating the time of contact between the colliding bodies allows for calculation of the average force during the collision, providing insight into the magnitude of the force exerted even when it may fluctuate over the impact duration.

Transcript

00:01 In this question, you have a ball that is dropped from the height of 1 .75 meters and it bounces off the floor and then comes back up to a height of 1 .5 meters.

00:23 And you want to calculate one, the force or the impulse that the floor exerts on the ball.

00:32 And then you want to estimate the size of the force that the floor is set on the bottom.

00:38 So for impulse, you know that the impulse, which is just a force times the time, is equal to the change in momentum.

00:48 So we know, so there's two separate incidences that you want to consider here.

00:56 So you want to consider the first part, which is this thing falling to the ground, and then the floor stopping it all the way to zero, and then the floor exerting another force to accelerate this thing back up to a certain speed so that it reaches 1 .5.

01:13 So this will make the situation slightly easier to calculate.

01:17 So in this case, i'm going to choose energy conservation laws to calculate the speed that this thing travels at.

01:27 So you know that if it's coming from a certain height and it reaches the floor.

01:33 By the time it reaches the flow, it has maximum kinetic energy, but all the potential energy is now been converted to kinetic energy, so the potential energy is zero.

01:43 So there's an exchange of energy that happens here.

01:46 So essentially what we can do is we can just say the kinetic energy or the potential energy that this mass has is now equal to the kinetic energy that this ball has by the time it strikes the floor.

02:01 So this says that all the energy, all the potential energy was converted into kinetic energy right before this thing hits the floor.

02:11 So the mass is common.

02:13 So what you find is that the velocity is just equal to 2gh, just a square root of that whole point.

02:24 So if we do this for this falling part, we can also do the same thing here, where this thing has kinetic energy at the bottom and it's going to lose that kinetic energy or convert it to financial energy by the time it gets to this height.

02:39 So we can use the same equation to calculate the velocity that this thing has going up as well.

02:45 So if you do this for the falling motion, you find that that velocity is around 5 .8 ,6 or something like that, meters per second.

03:01 And then if you use the same equations for the return motion, you'll find that that velocity is going to be equal to now two times the gravitational constant times the height that you get.

03:22 And then you can get that velocity as well...

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