- #1

- 89

- 0

We get through F = ma that

F*s = ma*s = ma*v*dt

We also know that when a is constant (which it is due to the constant force) we got:

a*dt = 2v

which gives us that the work, F*s, equals

2mv^2 instead of (1/2)mv^2

What is wrong?

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter Hymne
- Start date

- #1

- 89

- 0

We get through F = ma that

F*s = ma*s = ma*v*dt

We also know that when a is constant (which it is due to the constant force) we got:

a*dt = 2v

which gives us that the work, F*s, equals

2mv^2 instead of (1/2)mv^2

What is wrong?

- #2

- 2,411

- 710

F*ds = m*a*v*dt

Try taking it from here.

- #3

- 89

- 0

F*s = m*a*v*(t_2 - t_1) = m*v*2v = 2mv^2

I assume that over our given time and with our constant force we have a * (t_2 - t_1) = 2*v.

- #4

- 2,411

- 710

Did you know that

a=dv/dt?

a=dv/dt?

- #5

- 12,134

- 161

We get through F = ma that

F*s = ma*s = ma*v*dt

We also know that when a is constant (which it is due to the constant force) we got:

a*dt = 2v

which gives us that the work, F*s, equals

2mv^2 instead of (1/2)mv^2

What is wrong?

You're using "v" to mean the average velocity (= s/dt)

When we say that work = (1/2) m v^2, "v" is the final velocity.

The final velocity is twice the average velocity, they are not equal.

- #6

Doc Al

Mentor

- 45,250

- 1,601

You here assume that s = v*Δt, but that should be s = vOkey, lets say we got an object with no start velocity (V_i = 0) which is being pushed by a constant force F, under a certain distance s (during a time intervall dt).

We get through F = ma that

F*s = ma*s = ma*v*dt

F*Δs = ma*Δs = ma*(v/2)*Δt

No, for constant acceleration, starting from rest: a*Δt = v.We also know that when a is constant (which it is due to the constant force) we got:

a*dt = 2v

Nope, you get:which gives us that the work, F*s, equals

2mv^2 instead of (1/2)mv^2

F*Δs = ma*Δs = ma*(v/2)*Δt = m*(v/2)*a*Δt = 1/2mv^2.

As expected.

Share: