# Work energy and power.

1. May 27, 2016

### alijan kk

1. The problem statement, all variables and given/known data
Ima Scaarred (m=56.2 kg) is traveling at a speed of 12.8 m/s at the top of a 19.5-m high roller coaster loop.

a. Determine Ima's kinetic energy at the top of the loop.
b. Determine Ima's potential energy at the top of the loop.
c. Assuming negligible losses of energy due to friction and air resistance, determine Ima's total mechanical energy at the bottom of the loop (h=0 m).
d. Determine Ima's speed at the bottom of the loop.

2. Relevant equations
PE=MGH
KE=0.5*MV^2

3. The attempt at a solution
i tried to find b

pe=0.5*56.2*12.8

=14,027.52

help me understanding the question.

a. 4.60 x 103 J
b. 1.07 x 104 J
c. 1.53 x 104 J
d. 23.4 m/s

2. May 27, 2016

### billy_joule

Looks like you've mixed your two relevant equations together.

your relevant equation says pe = mgh, but that's not what you've done, what is m? g? h?
First identify all your variables so you know where they'll go in your equations.

Also, your arithmetic is wrong, 0.5*56.2*12.8 does not equal 14,027.52
Show your units with your working, and be specific on exactly where you're stuck/ what you don't understand, it makes it easier to help.

3. May 27, 2016

### alijan kk

PE= mass*gravity*height

i want to imagine the picture of that question so that it would be easy for me , i want to understand the question

4. May 27, 2016

### alijan kk

is 359.68
but it is also wrong....

is there any role of friction?
or use of this formula
Pi+Ki=Pf+Pi

5. May 27, 2016

### alijan kk

All the ANswers i have got!! thank you bilijoule i was making big mistake,,,,

6. May 27, 2016

### billy_joule

Great, good work.

7. May 28, 2016

### alijan kk

thankyou\
but i m still trying to find the speed at the bottom of the loop .

KE=KE
4600=0.5*56.2*v^2
4600=28.1*v^2
4600/28.1=v^2
v^2=163.7
square root both sides
v=12.8

so this way i got the initial velocity but how to get the speed at the bottom?

8. May 28, 2016

### billy_joule

When Ima gets to the bottom, the potential energy she had at the top has been converted to kinetic energy via Conservation of Energy.
This should be somewhat intuitive, ever ridden your bike down a hill? You don't even need to pedal to gain kinetic energy..it's coming from somewhere else..
The higher the hill the faster you'll be going at the bottom...
The relevant equation:
EKi + EPi = EKf + EPf

(which is what I think your earlier equation in post #4 was supposed to be?
)

Solving for EKf is the answer to c), then solving EKf = 1/2 mv2 for v will give the answer to d)

9. May 28, 2016

### alijan kk

v=23 m/s !! thanks for the equation .
KEf=1/2mv^