physics: how does this question incorporate f=mv-mu/t?

Question

a car of mass 600 kg accelerates from rest to 8m/s in 40s.
i find that resultant force on car in 120N

so: if car is fitted with trailer mass 100kg, find time taken to accelerate to 8m/s.

assuming that F is 120N,
the textbook answer is:
F=ma
F=m x (v-u)/t

t=(mv-mu)/F
=(700x8)/120
= 46.7seconds.
what i need to understand is how F=ma got into that if the car is with a trailer. and why is there a momentum equation?

thanks T^T

Answer 1

Newton's first law says that if something accelerates, there has to be a force.

His second law tells us that the acceleration and force are related by the mass (in this case, the weight) of the object.

Adding the trailer made the whole thing more massive (in the technical sense!), i.e. more resistant to acceleration, so the same force (produced by the engine) sped it up slower than before.

What does the textbook do here? Well, essentially it finds the force and then applies it to the new weight.
F=ma
120=700a
a = 6/35

Now, to find the time, we use v=u+at
8=0+(6/35)t
t=280/6=46.7s

I don't like the textbook's method, because it uses some algebraic manipulation which is neat for an experienced person, but sucks when you're trying to figure it out. I hope this helps.

Answer 2

Good question...here's the physics.

Change in momentum over time dp/dt = m dv/dt; where dv/dt is the change in velocity over time, commonly called acceleration a = dv/dt = (v1 - v0)/(t1 - t0); where v1 is the velocity at t1 time and v0 is at t0. dp/dt = (p1 - p0)/(t1 - t0) where the 0 and 1 mean initial and later momenta and time like we used the notation for velocity.

Now, here's the cool part, we call dp/dt force. That is, a change in momentum over time is force. So look at this, F = dp/dt, by definition, that's what we call it...force F. Then F = dp/dt = m dv/dt = ma. And there we have it, good old F = ma, which is just the change in momentum over time.

In your case v1 = v = 8 mps and v0 = u = 0 mps. Further t1 - t0 = 40 seconds. So F = dp/dt and dt = elapsed time = m(v - u)/F = 600(8 - 0)/120 = time to get to 8 mps from zero with a push of 120 Newtons.

So, to answer your question explicitly, your problem is not about momentum so much as it is about change in momentum. And that change comes about because there is a force accelerating the mass and changing the velocity. Bottom line, when there is a net force acting on a mass, there will be a change in momentum. And that's Newton's F = ma.

Answer 3

The car and trailer form a system whose mass is 700 kg.

Force is equal to rate of change of momentum with time

Force (F) =mass (m) *acceleration(a)

acceleration(a)=(v-u) / t

F=ma=m(v-u)/t= (mv - mu ) /t