# Kinetic Energy and Momentum

## Homework Statement

A Vulcan spaceship has a mass of 65,000 kg and a Romulan spaceship is twice as massive. Both have engines that generate the same total force of 9.5 x 10^6 N. Neglecting any changes in mass due to whatever is expelled by the engines, calculate the kinetic energy and momentum of each spaceship if each spaceship fires its engines for 100s, starting from rest.

K=1/2mv^2
p (momentum)=mv

## The Attempt at a Solution

First I dealt with the Vulcan:
F=ma--> F/m=a 9.5 x 10^6 N/ 6.5 x 10^4 kg= 146 m/s^2
Vf-Vi=a(delta-t) Vf=146m/s^2(100s)=14600 m/s^2
K=1/2mv^2=1/2(6.5 x 10^4kg)(14600 m/s)^2= 6.93 x 10^12 J

p=mv=(6.5 x 10^4kg)(14600m/s)=9.49x10^8 kg m/s

I just need to know... Am I on the right track? Are there factors I'm not taking into account?

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Hootenanny
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## Homework Statement

A Vulcan spaceship has a mass of 65,000 kg and a Romulan spaceship is twice as massive. Both have engines that generate the same total force of 9.5 x 10^6 N. Neglecting any changes in mass due to whatever is expelled by the engines, calculate the kinetic energy and momentum of each spaceship if each spaceship fires its engines for 100s, starting from rest.

K=1/2mv^2
p (momentum)=mv

## The Attempt at a Solution

First I dealt with the Vulcan:
F=ma--> F/m=a 9.5 x 10^6 N/ 6.5 x 10^4 kg= 146 m/s^2
Vf-Vi=a(delta-t) Vf=146m/s^2(100s)=14600 m/s^2
K=1/2mv^2=1/2(6.5 x 10^4kg)(14600 m/s)^2= 6.93 x 10^12 J

p=mv=(6.5 x 10^4kg)(14600m/s)=9.49x10^8 kg m/s

I just need to know... Am I on the right track? Are there factors I'm not taking into account?
I'm not checking your arithmetic, but your method seems good to me .

Thanks!

touche yellowgators!
I only have 1 reproche; the method that you used makes the percent of error higher than it schoul really be. In addition your method is time consuming. Try using this method next time:
1)P=F*t=(m*v1)-(m*v2) ****v1 is initial velocity and v2 is final velocity*******
The impulse P = 9.5 x 10^6 N * 100s
P=9.5 x 10^8 N*s

2) v2 is found by:
P=(m*v2)-(m*v1) *******v1 equals to 0 *******
P=m*v2
v2=9.5 x 10^8 N*s/6.5 x 10^4 kg = 14615.38m/s

3)Potential energy(PE) = F*d
PE=9.5 x 10^6 N* (14615.38m/s/2) *100s ****d=average velocity*time********
PE=6.94*10^12J

A difference of 0.01*10^12 might not seem much but look at it again :10000000000. Wow, that is a big number!!!!!!!!!. that number schould really be larger because i aslo rounded.
well, here you go

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the method that you used makes the percent of error higher than it schoul really be. In addition your method is time consuming. Try using this method next time
I looked over that method. Thanks! Using the law of conservation of energy is more straightforward than how I approached the problem. That will be helpful for future problems.