Momentum and Impulse on a Toy Car: How to Find Velocity and Momentum?

AI Thread Summary
The discussion focuses on calculating the momentum and velocity of a toy car subjected to a varying force. The car, with a mass of 7.0 kg, starts from rest, and participants are trying to determine its momentum at specific times and its velocity at t = 9.0 s. The equations of motion, including momentum (p = mv) and impulse (J = Ft), are referenced, but confusion arises regarding the requirement for unit vector notation and the non-constant nature of the force. Participants express frustration over the lack of a visible diagram, which is crucial for understanding the force's impact over time. The conversation highlights the importance of visual aids in solving physics problems involving variable forces.
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Homework Statement


A 7.0 kg toy car can move along an x axis; Figure gives Fx of the force acting on the car, which begins at rest at time t=0. The scale on the Fx axis is set by Fxs = 6.0 N. In unit-vector notation, what is p at (a)t = 1.0 s and (b)t = 6.0 s,(c) what is v at t = 9.0 s?

http://edugen.wiley.com/edugen/courses/crs1650/art/qb/qu/c09/q30.jpg

Homework Equations


p = mv
F = ma
J = Ft
V2 = v1 + at


The Attempt at a Solution



I tried solving for V2 using F = ma
f = m(v2-v1/t)
6 = 7 (v2 - 0/1)

then i plugged this value into p = mv but then i realized they want unit vector notation and I got really confused! =S
 
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Difficult to tell what is going on without the diagram.
 
You are dealing with a force that is not constant. The easiest way to deal with this is to remember the change in momentum is equal the the integral of the force with respect to time. I.e. the area under your force curve.
 
Delphi51 said:
Difficult to tell what is going on without the diagram.

I see a diagram. Sometimes. It does seem to come and go. When I first open the page it's there. If I refresh the page it disappears. I'm using Firefox on Ubuntu. Hmm. Now it seems to be gone completely. Too bad. It was a nice diagram.
 
Last edited:
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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