Question

a ball of mass 0.5 kg is rolling across a table top with a speed of 5 m/s. when the ball reaches the edge it rolls down a incline plane onto the floor 1.0 meters below. what is the speed of the ball when it reaches the floor?

Answer 1

Use the law of conservation of energy:\[KE_i+U_i=KE_f+U_f\]

Answer 2

yeah I know that. but how exactly do I do the problem?

Answer 3

By defining the kinetic and potential energies at the beginning and end and solving the equation for the final velocity. Try defining each quantity separately first.

Answer 4

???

Answer 5

What is the formula for the kinetic energy of an object?

Answer 6

KE=1/2mv^2

Answer 7

And for the potential energy of an object?

Answer 8

PE=mgh

Answer 9

Ok, so use the law of conservation of energy by replacing those terms with those equations.

Answer 10

I'm sure you think I'm stupid but I haven't slept in days and a friend of mine commited suicide a few days ago. so really physics is the last thing on my mind but it has to be done

Answer 11

Still, this isn't a place to bring homework for someone to do for you. If you are willing to accept help and hints, that's okay. But I (and many others) won't do your homework for you.

Answer 12

didn't ask for you to

Answer 13

actually I've done half of it myself but am stuck on this one question so lay off

Answer 14

Then provide what you've done so far and what you are stuck on, and I'm happy to help.

Answer 15

PE= mgh> 0.5 (9.8)(1.0)= PE=4.9

Answer 16

Ok. So that's the initial potential energy of the ball. What about the initial kinetic energy?

Answer 17

I don't know. I'm confused

Answer 18

6.25

Answer 19

I think

Answer 20

Ok. The kinetic energy is this:

\[KE=\frac{1}{2}mv^2=\frac{1}{2}(0.5kg)(5\frac{m}{s})^2=6.25J\]Yep! Good job.

Now try and find the potential energy after the ball has rolled down the slope.

Answer 21

wtf is that!?!?

Answer 22

What do you mean?!

Answer 23

I'm trying to read the big long jumble

Answer 24

It's just finding the kinetic energy of the object.

Go ahead and try to find the potential energy after the ball rolls down the slope.

Answer 25

oh wait.. never mind. I get it

Answer 26

the whole fraction bracket thing threw me off

Answer 27

won't it just be the same as the original?

Answer 28

Well, the mass and gravity will be the same, but the height will have changed.

If the initial height was at 1 meter, and it falls down 1 meter, then it will be at some new height. You'll have to calculate the potential energy using that height.

Answer 29

it says the ball rolls down an incline onto the floor 1.0 meter below without bouncing and I am to calculate the speed of the ball when it reaches the floor

Answer 30

Yes. You can calculate the speed by knowing the potential/kinetic energy before and after the fall, using:\[KE_i+U_i=KE_f+U_f\]You've found the initial energies, now you just need to find the final potential energy. Then you will be able to use that formula to find the velocity.

Answer 31

but how do I know what the other height is??

Answer 32

You used 1 meter to calculate your first potential energy, right?

And since the ball dropped 1 meter off of the able, the new height will be 0 meters.

Answer 33

please don't judge me. I usually catch on quickly but I'm exhausted

Answer 34

That's fine. Here, let me draw a picture. One sec.

Answer 35

so it's 0?

Answer 36

Yes. When you're using gravitational potential energy, you can set any height to be your 0 height. In this case, by saying that the initial potential energy was from 1 meter, that means that 1 meter below that would be 0 meters.

Answer 37

but when you multiply the mass+gravity by 0 it just comes out to be 0

Answer 38

That's right. It is 0. Now let's look back at the conservation of energy equation:\[KE_i+U_i=KE_f+U_f\]\[6.25J+4.91J=\frac{1}{2}mv_f^2\]Do you see where to go from here?

Answer 39

what is this i+u?

Answer 40

Ah. Is the LaTeX not rendering correctly for you? The above should look like this:

Answer 41

we don't use anything with an i

Answer 42

It just means:

initial kinetic energy + initial potential energy = final kinetic energy + final potential energy

It's only to be able to differentiate between the two.

Answer 43

so I basically add 4.9 and 6.25

Answer 44

You have to solve that equation for the velocity. Adding 4.9 and 6.25 will only tell you the kinetic energy when the ball gets to the floor, not the velocity.

Answer 45

well yeah I knew that. I meant that would be my next step

Answer 46

Yep. That's right. And then you just have to solve that equation to get your final answer.

Answer 47

11.15=1/2(0.5)v^2 > v=sqrt of 2(9.8)(0.5)

Answer 48

that's wrong.

Answer 49

\[11.15J=\frac{1}{2}mv^2\]\[\sqrt{\frac{(2)11.15J}{0.5kg}}=6.68\frac{m}{s^2}\]That's what I get.

Answer 50

I've got 2 more to do and no clue how to do them

Answer 51

I'd be glad to help you, but I have to get off for the night. Good luck!

Answer 52

well it has to be done tonight