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Find the speed of an object using work and energy

  • #1

Homework Statement


An object with mass 100 kg moved in outer space. When it was at location < 9,-24,-4 > its speed was 3.5 m/s. A single constant force < 250,400,-170 > N acted on the object while the object moved from location < 9,-24,-4 > m to location < 15,-17,-8 > m. Then a different single constant force < 140,250,150 > N acted on the object while the object moved from location < 15,-17,-8 > m to location < 19,-24,-3 > m. What is the speed of the object at this final location?

Homework Equations


Kf = Ki + W1 + W2
W = F*displacement

The Attempt at a Solution


W1 = <250, 400,-170>*<6,7,-4> = 4980J
W2 = <140,250,150>*<4,7,5> = 3060J

Kf = Ki + W1 + W2
1/2(100)vf^2 = 1/2(100)(vi)^2 + W1 + W2
1/2(100)vf^2 = 1/2(100)(3.5)^2 + 4980 + 3060
50vf^2 = 612.5 + 8040
vf^2 = 173.05
vf = 13.2 m/s

(the answer's supposed to be 10.2 m/s) Thanks in advance!
 

Answers and Replies

  • #2
ehild
Homework Helper
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Homework Statement


An object with mass 100 kg moved in outer space. When it was at location < 9,-24,-4 > its speed was 3.5 m/s. A single constant force < 250,400,-170 > N acted on the object while the object moved from location < 9,-24,-4 > m to location < 15,-17,-8 > m. Then a different single constant force < 140,250,150 > N acted on the object while the object moved from location < 15,-17,-8 > m to location < 19,-24,-3 > m. What is the speed of the object at this final location?

Homework Equations


Kf = Ki + W1 + W2
W = F*displacement

The Attempt at a Solution


W1 = <250, 400,-170>*<6,7,-4> = 4980J
W2 = <140,250,150>*<4,7,5> = 3060J

Kf = Ki + W1 + W2
1/2(100)vf^2 = 1/2(100)(vi)^2 + W1 + W2
1/2(100)vf^2 = 1/2(100)(3.5)^2 + 4980 + 3060
50vf^2 = 612.5 + 8040
vf^2 = 173.05
vf = 13.2 m/s

(the answer's supposed to be 10.2 m/s) Thanks in advance!
Check the sign of the red number in W2 = <140,250,150>*<4,7,5>
 
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