Momentum-Work: Confused about KE = 1/2mv2?

[Zula110100100]

I am confused about the KE = 1/2mv²

I was able to get v²=2as from it, by removing mass from each side you get as = 1/2v² then rearrange, but I was trying to relate momentum and work in my head, and since p = mv than KE = 1/2 p * v

but starting with Work = F * s

and since s = vt

Work = F*vt

then solve for time t = W/Fv

and p = mv
v = at
so p = mat

so p = Ft(assuming no original momentum)

substitute for t and

p = FW/Fv

p = W/v

W = pv

W = mv²

So what am I doing wrong? becuase mv² does not equals 1/2mv²

I was thinking maybe because I am not using t₀ and v₀, but it doesn't seem like that's it, it seems the only way is with the 2as but it should tie back in somewhere...

and even working backwards from KE = 1/2mv²
Fvt = 1/2pv
devide by V and multiply by 2
and p = 2 F*t
p = 2 m*a*t
p = 2 mv

 

[Doc Al]

and since s = vt

Since the speed is not constant, you need to use the average velocity when calculating distance. In the KE formula, the v is the final speed.

 

[Zula110100100]

Oh, okay, so it kinda has to do with not using v_{0[\SUB]...and the like}

 

[Doc Al]

Oh, okay, so it kinda has to do with not using v_{0[\SUB]...and the like}

_{Right. For the simple case of a constant force applied to an object initially at rest (v0 = 0), we'll have vave = v/2. So:
W = F*s = F*v/2*t = (F*t)*v/2 = (mv)*v/2 = 1/2mv². As expected.}

 

[PJC01]

Hello, it seems like you are on the right track in trying to relate momentum and work. However, there are a few things that need to be clarified. First, the equation KE = 1/2mv2 is the equation for kinetic energy, not momentum. Momentum is calculated as p = mv, as you correctly stated. Kinetic energy is the energy an object possesses due to its motion, while momentum is a measure of an object's motion and mass combined.

In order to relate momentum and work, we need to use the equation W = F * d, where d is the distance an object moves due to the applied force. We can also use the equation W = ΔKE, which means the work done on an object is equal to the change in its kinetic energy.

Now, let's look at your calculation of momentum and work. You correctly stated that p = F * t, but this only applies if the force is constant. In your case, you are using the equation p = mv, where v is the final velocity. However, in the equation W = F * d, the distance d is the distance an object moves while the force is acting on it. So, in order to use this equation, we need to find the distance an object moves while the force is acting on it, which is given by d = 1/2at2 (assuming the initial velocity is 0).

Substituting this into the equation W = F * d, we get W = F * 1/2at2. Now, we can also use the equation W = ΔKE, which means W = KEf - KEi. If we assume the initial kinetic energy is 0, then W = KEf. Substituting this into the equation W = F * 1/2at2, we get KEf = F * 1/2at2. We can also substitute p = mv into this equation, which gives us KEf = p * 1/2at2.

Now, we can rearrange this equation to get p = KEf * 2/at2. This is the equation that relates momentum and work. As you can see, it is different from the equation you were using (p = 2 F * t). This is because we need to take into account the distance an object moves while the force is acting on it.

In summary, momentum and work are related through the equation p =