Inelastic Collision Calculate the Percent Change in KE

[arizona1379]

Homework Statement

An archer fires a 20g bolt with a speed of105 m/s through a 400 g apple initially at rest.
The bolt exits the apple with a speed of 45 m/s. What is the percent change in kinetic energy of the apple/bullet system?

m1= 20g
Vi1= 105 m/s
Vf2= 45 m/s
m2= 400g
Vi2= 0 m/s
Vf2= ?

Homework Equations

(m1v2+m2v2)i=(m1v2+m2v2)f

ΔKE= ((.5)(m1)(Vi1)²+(.5)(m2)(Vi2)²)i -((.5)(m1)(Vf1)²+(.5)(m2)(Vf2)²)f

%ΔKE= 100(F-I/I)

The Attempt at a Solution

(20g)(105 m/s)+(400g)(0 m/s)=(20g)(45 m/s)+ (400g)(vf)
2100(g)(m/s)=900(g)(m/s)+(400g)(vf)
1200g(g)(m/s)=400g(vf)
3 m/s = vf

ΔKE= ((.5)(20g)(105m/s)²+(.5)(400g)(0)²)i -((.5)(20g)(45m/s)²+(.5)(400g)(3 m/s)²)f

22050J-110250J=-88200J

100x(-88200)/110250J= -80%

Figured it out myself. :)

:::::Lashawnda:::::

 

[hjelmgart]

You did 2100 = 900 + 400 vf and isolated it wrong at the next step.

 

[arizona1379]

2100-900=1200
1200/400= 3

 

[arizona1379]

you did 2100 = 900 + 400 vf and isolated it wrong at the next step.

2100-900=1200
1200/400= 3

 

[Nickie]

Great job on solving the problem and showing your work! It's important for scientists to show their thought process and calculations in order to support their conclusions. In this case, the percent change in kinetic energy is negative, which means that there was a decrease in kinetic energy after the collision. This makes sense, since the apple slowed down and the bolt lost some of its initial speed as it passed through the apple. Keep up the good work!