3 questions on power and energy

[jinkyfishies]

Homework Statement

1. a light pingpong ball and a heavier baseball bat are thrown vertically upwards. compare their initial kinetic energies and initial velocities if both balls reach the same maximum height.

2. a rollercoaster is designed with its first hill of height 75m. at the bottom of the hill the velocity is 33m/s. does the speed at the bottom make sense? explain using a calculation if needed

3. compare the performance of a fast sports car (porsche) to a slower fuel efficient toyota corolla using the concept of power.

Homework Equations

ek=1/2mv^2
eg=mgh
p=w/t

The Attempt at a Solution

1. i think the heavier one will have a greater kinetic energy and a higher velocity

2. i think it doesn't make sense because mgh=1/2mv^2
9.81×75=0.5(33^2)
735.75=544.5
since theyre not equal it wouldn't make sense

3. i just have no idea

 

[phinds]

You might want to rethink the velocity part of #1

 

[jinkyfishies]

You might want to rethink the velocity part of #1

but if they reach the same heigh, wouldn't that mean you would need more force/a greater velocity on the heavier object? if you gave the same velocity to both id think that would make the heavier one go lower than the light one

 

[phinds]

if you gave the same velocity to both id think that would make the heavier one go lower than the light one

Why? If you DROP them both they start out with the same velocity. Do you think the heavier one will travel faster?

 

[NascentOxygen]

2. a rollercoaster is designed with its first hill of height 75m. at the bottom of the hill the velocity is 33m/s. does the speed at the bottom make sense? explain using a calculation if needed

I'm not sure about this, but possibly what is intended here is that before climbing the hill the speed is 33m/s. Will that be sufficient to see the car clear the hill?

On the other hand, if it's correct as you interpreted it to be and that 33m/s is the speed after descending the hill, then having less than expected speed could easily be explained by friction losses on the track.

 

[Brian T]

For 3, consider the formula for power and what work represents.

For 2, you are right. The only minor justification would be friction, but even then a well-designed roller coaster would not have that much friction.