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Classical Mechanics: Momentum and Velocity

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A 4.0 kg toy race car can move along an x axis. The figure below gives Fx of the force acting on the car, which begins at rest at time t = 0. (The vertical axis is marked in increments of 2 N.)

See the attached document for the necessary graph.

(a) What is the momentum of the car at t = 6.0 s

(b) What is the momentum of the car at t = 9.0 s

(c) What is the car's velocity at t = 7.0 s?

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Momentum and velocity are calculated for a 4.0 kg toy car.

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A partially inelastic collision

3.) A car of mass 1148 kg has kinetic energy of 117 kJ. The driver sees a stalled SUV of mass 2700 kg blocking the intersection. Because he is having a bad hair day, the driver plows into the SUV without braking. The two vehicles stick together (a perfectly inelastic collision) and slide to a stop.

a) How much work is done against the force of friction, during the time when the vehicles are sliding? [Hint: Find the kinetic energy of the resulting two-car mess just after the collision.] Find your answer in kJ.

b) The answer to a) above is less than the original kinetic energy. Assume that the energy was transformed to work done by crushing the cars and that the cars were crushed a total of 77 cm. What, then, was the magnitude of the average force during the collision? (in N)

Assume that the wheels of both cars are locked and do not roll. Also assume that the pavement is dry and that the coefficient of friction between the cars and the road is µ = 1.003. [HINT: To answer the following three questions, you may find it useful to find an expression for the distance traveled on an abitrary slope and then simply plug in angles for the specific cases.]

c) If the pavement was level, how far did the two vehicles slide? in m)

d) Suppose that the pavement was not level, that the car was heading up a hill whose slope was 12.0°. Then the distance the two "shmooshed" vehicles slid uphill was how many m?

e) Suppose this time that the car had been heading down the 12.0° grade when it hit the SUV. The distance of slide would then be how many m?

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