Science Quiz Thread

[steve_bnk]

A 10 kg mass changes velocity by 10m/s. How much does the energy change in the mass?


A 10 kg mass changes velocity by thefunction v(t) = sin(t) over t = 0 to 6.2831853 . What is the change in energy?

Kinetic Energy = (1/2)*(Mass)*(Velocity^2)

 

[Underseer]

Why didn't you just say 2*pi for the second one?

 

[steve_bnk]

Why didn't you just say 2*pi for the second one?

Why not then answer the question, it is a sh0rt leap from 2pi.

 

[Bomb#20]

A 10 kg mass changes velocity by 10m/s. How much does the energy change in the mass?

Insufficient data. What's the initial velocity?

A 10 kg mass changes velocity by thefunction v(t) = sin(t) over t = 0 to 6.2831853 . What is the change in energy?

Kinetic Energy = (1/2)*(Mass)*(Velocity^2)

Kinetic energy at t=0 is the same as at t=2pi. If you want the change in energy moment by moment, as a function of t, insufficient data. What's the initial velocity?

 

[bigfield]

A 10 kg mass changes velocity by 10m/s. How much does the energy change in the mass?

You didn't specify whether velocity increases or decreases my 10m/s, so I assume you are asking for a solution that works for both.

ΔE = energy at final velocity - energy at initial velocity

ΔE = 1/2m(v±10)² - 1/2mv²

ΔE = 1/2m((v ± 10)² - v²)

ΔE = 1/2m(v² ± 20v + 100 - v²)

ΔE = 1/2m(±20v + 100)

If m = 10kg

ΔE = 1/2(10)(±20v + 100)

ΔE = 5(±20v + 100)

ΔE = ±100v + 500 Joules

 

[bigfield]

A 10 kg mass changes velocity by thefunction v(t) = sin(t) over t = 0 to 6.2831853 . What is the change in energy?

Kinetic Energy = (1/2)*(Mass)*(Velocity^2)

ΔE = energy at final velocity - energy at initial velocity

6.2831853 ≈ 2*Pi

initial velocity = sin(0) = 0
final velocity = sin(6.2831853) ≈ 0

Therefore energy at final velocity ≈ energy at initial velocity

Therefore ΔE ≈ 0.

 

[steve_bnk]

ΔE = energy at final velocity - energy at initial velocity

6.2831853 ≈ 2*Pi

initial velocity = sin(0) = 0
final velocity = sin(6.2831853) ≈ 0

Therefore energy at final velocity ≈ energy at initial velocity

Therefore ΔE ≈ 0.

Yes. if you saw that the average valueof a sine or cos as the derivative in multiples of 2pi is zero thenthe net change in velocity is zero and the net change in energy iszero regardless of how much energy was expended in the path..

E= 1/2 m*v^2
dE/dv = 2*(1/2) * m * v
dE = m*v

Which leadsto Newtonian conservation of momentum, mv1 = mv2.


Velocity is a vector having magnitudeand direction, so velocity can be be signed. Numerically works eitherway.


One an learn a lot from apparentlysimple problems.