A steel ball is dropped onto a hard floor from a height of 1.50 m and rebounds to a height of 1.

step 1 Hi, my name is Lance and I teach high school physics. I've been teaching for over 10 years and I

A steel ball is dropped onto a hard floor from a height of...

Key Concepts

Impulse-Momentum Theorem and Average Acceleration

This concept relates the change in momentum of an object to the impulse applied over a given time period. During a collision, the large change in velocity over a very short time interval results in a high average acceleration. Understanding this theorem is key to calculating the acceleration experienced by the ball during contact with the floor.

Collision Dynamics and Rebound Behavior

This concept deals with the behavior of objects during collisions, particularly in terms of how energy and momentum are transferred or lost. In problems involving rebounding objects, factors like the coefficient of restitution—which quantifies the loss of kinetic energy during impact—are considered to understand the difference between the incident and rebound velocities.

Deformation and Contact Time in Collisions

This concept focuses on the deformation and compression that occur during collisions, particularly when objects like balls compress against a rigid surface. By examining the short contact duration and applying kinematic relations, one can estimate the extent of deformation, even when the collision involves nearly rigid bodies.

Kinematics of Free Fall

This concept involves using the equations of motion to determine how objects move under the influence of gravity when they are in free-fall. It includes calculating velocities, displacements, and times based on a constant gravitational acceleration, and is crucial for understanding the motion of the ball as it falls towards and rebounds from the floor.

Conservation of Energy

This principle is applied to relate the gravitational potential energy at one height to the kinetic energy just before impact (or just after rebound). It allows one to determine the speed of an object from its height by equating potential and kinetic energies, assuming negligible energy losses in parts of the motion.

Transcript

00:04 Hi, my name is lance and i teach high school physics.

00:07 I've been teaching for over 10 years and i've been teaching ap physics for the last 3 to 4 years.

00:15 And i'm going to answer this interview question regarding a steel ball being dropped from a height of 1.5 m and show you how we solve this problem in physics.

00:28 So let's start with just a drawing.

00:35 So we have a steel ball and we dropped this ball from some hype maybe a tabletop right? of about 1.5 m.

00:50 Yes.

01:01 And so this ball we know will go down.

01:06 All right.

01:06 And now usually when we draw these diagrams, this could be a little bit misleading because what do we know about this ball? uh we know we have a bunch of formulas, right? and those formulas can can have one of you know, you know, many pieces missing.

01:24 Mm but we have to ask ourselves what we know what we can know.

01:31 Mhm.

01:32 So just thinking about properties.

01:35 Thank you.

01:37 Alright.

01:37 Properties of motion.

01:39 Right? and definitions of motion we know because we have we can have displacement.

01:44 We can have speed.

01:45 And that speed could change.

01:47 We could have an initial speed and a final speed.

01:54 If the if that speed is changing it can have an acceleration and how fast that speed changes would be determined by time.

02:07 So thinking about this ball and i think you know many times we'll write this you know we'll just show the direction that it's going down.

02:14 But that could be a little bit misleading about speed.

02:18 But we know this ball wolf when released will go down.

02:23 Yeah i'll go ahead and wow move that arrow away from that number as well.

02:31 Yeah.

02:33 And it will gain speed and as it gains speed and it will eventually reach the floor.

02:41 And so it will have some final speed.

02:45 Some unknown final speed.

02:47 But as we drop it initially before it does anything, it will have zero speed.

03:00 So initially we have a zero initial velocity.

03:03 That initial velocity because it is changing.

03:06 It goes from zero like no value at all to some value.

03:10 Later as it moves through this displacement at a higher and higher speed, we know that it's accelerating what's causing that acceleration.

03:19 Well, in this case, since we're dropping it right, that indicates that it's gravity.

03:25 So we know the displacement.

03:27 We know that it's going to displace from some point and go down 1.5 m to the floor.

03:34 We know that its initial velocity must be zero.

03:37 And we'll give, even though zero doesn't have units will give it meters per second to keep it consistent with the meters from the displacement, the final speed.

03:50 It is unknown.

03:52 But that's the question.

03:54 Yeah.

03:56 And we know just based on physics the acceleration is the gravitational constant in terms of acceleration.

04:07 So the acceleration due to gravity which we know to be 9.8 meters per second squared, again agreeing with our units for the velocity and in this case there is right, no, no time of fall given there is time in the problem.

04:27 But don't let that confuse you.

04:29 Oh, because the time of falling is not established.

04:36 So we have four of the five unknowns.

04:38 And luckily for us, our five kinetic equations give us a way of finding the variable in question, the unknown without having to have all of the variables.

05:03 So if we use this one sometimes called number three of three of the big five and we get rid of the zeros before we try to plug anything in, we find that the final velocity squared is two times the acceleration due to gravity times the displacement.

05:41 But we don't want the velocity squared want just the final velocity.

05:48 So it's the square root of two times the acceleration due to gravity times the displacement, which for this part two times 9.8 meters per second squared times the displacement of 1.5 m.

06:20 Yeah, it's a final velocity of five point four two.

06:31 And our unit analysis, we have meters times metres, which is meters squared over second squared.

06:38 And if we're taking the square root of that, that's just meters per second.

06:42 So that agrees with our units typically used for velocity.

06:49 So for part a.

06:56 Mhm.

06:57 The speed just before it hits the floor, right, when it runs out of space is 5.42 m per second for part b.

07:17 Now, after it's hit the floor, this ball is going to rebound with some initial speed but only reach a final height of 1.45 meters.

07:41 So how do we know how far it goes? what? how does that speed change again due to gravity? the gravitational pull, that acceleration is going to work opposite the direction of motion, meaning that it will slow down and it will go as high as it can until it has no ability to go any higher right? with no motion.

08:07 So it will have a final speed of zero.

08:15 Sorry, let me move this down a little bit.

08:19 Yeah.

08:22 Okay.

08:26 Why no? does not want to write on here for me? yeah.

08:46 Okay.

08:49 Oh there he comes or you.

08:56 So again, what do we know? we know that the displacement? this height is 1.45 m.

09:07 It will have a final velocity when it reaches that height of zero m per second.

09:13 The initial velocity is unknown.

09:19 And again the acceleration is due to gravity which has a constant acceleration of 9.8 m per second squared.

09:28 And in this case because the velocity, if i want upwards the upward direction to be positive, i'm going to have to identify that gravity is working opposite that.

09:40 So it has a negative direction...

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