Question

The spring shown in the figure is compressed 58 cm and used to launch a 100 kg physics student. The track is frictionless until it starts up the incline. The student's coefficient of kinetic friction on the 30∘ incline is 0.15 . Spring constant is 80,000 N/m. The student is on a hill 10m high. How far up the incline does the student go?

Answer 1

can you post the figure just for clarity?

Answer 2

great...now where are you having problems?

Answer 3

idk what formula to use or how to start

Answer 4

ok lets not worry about formulas yet...in your own words how would you describe what is happening?

Answer 5

well there pushing the kid with a spring

Answer 6

ok now lets use some physics vocabulary...the spring stores what type of energy?

Answer 7

The spring stores potential energy. Do you know the equation for the stored potential energy in the spring?

Answer 8

you still there?

Answer 9

KE = PE + Wf

Answer 10

be right back in ten mniutes

Answer 11

I am back,,,the potential energy in the spring when released imparts kinetic energy to the student agreed?

Answer 12

yes

Answer 13

ok now what happens to the energy of the student as he starts sliding down the hill then up the other stop before stopping?

Answer 14

it increases?

Answer 15

Yes as he slides down the hill the total energy increases because of an increase in gravitational potential energy. Now when he is at the bottom and starts sliding up the other side,what happens to his energy?

Answer 16

it decreases and makes him slide back?

Answer 17

yes it does but since we want to calculate how far up the hill he goes we wont let him slide back down.

Answer 18

So what we have to use the the work-energy theorem which for this problem looks like:
Total energy inital = Total energy final
PE (spring) + PE (coming down hill) = Work done against friction up hill + PE (how high he stops up hill)

Does this make sense to you?

Answer 19

sort of

Answer 20

ok fair enough....lets start plugging in some formulas

PE spring = 1/2kx^2 k is spring stiffness, x is spring displacement
PE coming down hill = mgh (here h=10m)

Now you will have to label a distance along the hill that he slide up lets call if "s"

Work against friction = coeff of kinetc friction * Normal force *s
PE (how high he stops on hill) = mg(s*sin 30)

To get the normal force correct, you need to draw the student going up the hill and draw a FBD of him to see what the normal equals in terms of g

Answer 21

once you get the normal force correct, there is only one unknown to solve for "s" which is what the problem is asking for

Answer 22

let me what you get for the work done against friction and I will check it for you and we can continue

Answer 23

im confused

Answer 24

Lets do it a piece at a time...
First calculate PE for the spring = 1/2 kx^2
both k and x (the spring displacement are given in the problem)
k must be in N/m and x must be in meters.
Calculate PE of the spring please.

Answer 25

13456

Answer 26

Units that go with that....

Answer 27

Units are very important in physics

Answer 28

J

Answer 29

Good Joules...ok
lets get the increase in PE as he slides down the hill 10 m
PE(down hill) = mgh
Calculate that for me

Answer 30

9800

Answer 31

Units....

Answer 32

Now a FBD of the student on the 30 degree incline

Answer 33

J

Answer 34

ok so now draw the FBD of the student on the i30 degree incline please...use the draw tool

Answer 35

im not really good at drawing FBD

Answer 36

Try that is the only way to learn... I will help

Answer 37

Give me a few minutes please

Answer 38

Take a look at my diagram and see if makes sense

Answer 39

I got to run now but send me your questions and we can continue