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Exam 2 (Total 88 Points)

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P1. (6 pts) A 5.972 × 1024 kg planet makes a circular orbit of a radius of 93 million miles around its sun at a constant

velocity of 30 km/s. What is the radial acceleration experienced by the planet.

P2. (10 pts) Draw the velocity-time and acceleration-time graph from the given position-time graph

P4. (10 pts) A 100 kg projectile is launched vertically upwards and its velocity at an elevation of 100 m is 10 m/s and it

still seems to be gaining height. Calculate the initial velocity of the projectile and the maximum height reached. If the

100 kg projectile is now replaced by a 1 kg projectile calculate its initial velocity for the same scenario. Ignore air friction.

Solve using work-energy only.

P5. (10 pts) A 2000 lb car traveling at a speed of 50 ft/s bumps into another car heading the same direction at 70 ft/s.

The final velocity of the car after the collision is 10 ft/s. The total time for the collision is 0.5 seconds. What is the

average force experienced by the driver in this car? Now imagine that air bags deploy right after the collision and it takes

an additional .3 seconds for the driver’s head to come to a complete rest. Calculate the average force experienced by

the driver in this case.

P3. (15 pts) A target is located is at a 100 m elevation and 100 m horizontal distance. Calculate the velocity and angle of

launch of a projectile that must hit the target at the point where it just starts to fall back to the ground. The time it takes

for the projectile to reach the target is 2 seconds. Ignore air friction.

P6. (22 pts) You decide to pull a couple of trolleys tied to each other by a rope and initially at rest across a flat surface.

The pull force is also applied at 30 degrees to the ground. One trolley weights 10 kg and the other weights 200 kg. The

coefficient of kinetic friction between the ground and the 10 Kg trolley is .03. the heavier trolley is on wheels and the

coefficient of kinetic friction between the ground and the 200 kg trolley is .003. You wish to cover a distance of 100 m in

3 minutes. What force must you apply?

P7. (15 pts) You decide to pull a couple of trolleys tied to each other by a rope and initially at rest across a flat surface.

The pull force is also applied at 30 degrees to the ground. One trolley weights 10 kg and the other weights 200 kg. The

coefficient of kinetic friction between the ground and the 10 Kg trolley is .03. the heavier trolley is on wheels and the

coefficient of kinetic friction between the ground and the 200 kg trolley is .003. The final speed of the trolleys after 3

minutes is 5 m/s. What force must you apply? Hint: Use impulse momentum.

𝑣 = 𝑣0 + 𝑎𝑐 𝑡

𝑣 2 = 𝑣02 + 2𝑎𝑐 (𝑠 − 𝑠0 )

1

𝑠 = 𝑠0 + 𝑣0 𝑡 + 𝑎𝑐 𝑡 2

2

𝑠 = (𝑣0 + 𝑣)

𝑡

2

F = ma

an = v2/r

FK = kN

W=F*d

PE = mgh

KE = mv2/2

mv1 + Fave t = mv2

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