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**Physics Final---Multiple Problems---Help**

Hey everyone, I have my physics final on Monday and I'm working through a practice test right now that is giving me a ton of trouble. If you can help with any/all of the problems i'd appreciate it.

1)

## Homework Statement

1)A 74 kg bungee jumper is tied to a 39 m cord (unstretched). She leaps (from rest) off a

tall bridge (much taller than 39 m), so that she falls freely for 39 m before the cord begins

to stretch. The stretched cord stops her briefly above the water before yanking her back

upward. What is the magnitude of the impulse exerted on the bungee jumper while the

cord stretches during the downward motion?

Answer: 2046 kg m^2

2)

## Homework Statement

10)A weight of Mg = 50 N is attached to the free end of a light string wrapped around a

pulley of radius R = 0.25 m and mass m = 3 kg. The pulley is free to rotate frictionlessly

in a vertical plane about the horizontal axis passing through its center, but remember that

the pulley is a solid disk and is not massless. The weight is released from rest 5 m above

the floor. The speed of the weight when it reaches the floor is:

Answer 8.7 m/s

I tried using the formula T = F

_{perp}d = (I)(alpha) I wanted to find alpha, change it to linear acceleration and then plug that acceleration into a standard kinematic to find V

_{final}. No such luck.

3)

## Homework Statement

11) A car of mass 1000 kg moves on a circular track of radius 100 m with a speed of 50

m/s. What is the magnitude of its angular momentum (in kg m2/s) relative to the center of the race track?

Answer: 5 x 10^6

I tried using the formula Angular Momentum = (I)(angular velcoity) and manipulating some of the variables around. I couldn't make it work.

4)

## Homework Statement

12) Two 1 kg particles are connected by a string 1 m long. They are set spinning about

their center of mass with an angular velocity of 2 rad/s in outer space, where external

forces are negligible. The tension in the string is:

Answer: 2N

5)

## Homework Statement

13) A disk of radius R and mass M has a moment of inertia given by I = ½ MR2 for

rotations about an axis through the center of the disk. If a second disk of twice the mass

and half the radius is added as shown in the figure, what is the new moment of inertia of

the combined disks?

Answer: 3/4 MR^2

6)

## Homework Statement

A spherical asteroid of mass Mast = 1016kg and radius Rast = 10 km (moment of inertia

Iast = 4×1023kg m2) is slowly rotating in free space at an angular velocity of ωi =

+6.28×10−4rad/s (one revolution every 10,000 seconds) around an axis through its center

of mass. A small comet of mass mc = 1011kg and traveling at vi = 100,000 m/s hits the

asteroid at a glancing blow, in a direction directly opposing the motion of that part of the

asteroid, as described in the figure. If the comet sticks to the edge of the asteroid (embeds

itself in it), what is the final angular velocity of the composite object?

Answer: +3.78 × 10−4 rad/s (same rotation direction)

7)

## Homework Statement

A mass m = 0.1 kg is attached to a massless spring of constant k = 10 kg/s2. The other

end of the spring is attached to a pivot point about which the spring is free to rotate

frictionlessly on a tabletop. The mass also moves frictionlessly on the tabletop. The

unstretched spring length is r = 20 cm. The mass is set to rotate at a constant angular

velocity, which stretches the spring to a new length R = 25 cm, but the spring does not

oscillate. What is the angular momentum of the mass about the pivot point?

Answer: 0.028 kg m2/s

8)

## Homework Statement

A 3 kg air-track frictionless glider is attached to each end of the track by two coil

springs. It takes a horizontal force of 0.9 N to displace the glider to a new equilibrium

position, x = 0.3 m. What is the period of oscillations about the equilibrium point?

Answer: 6.28 s

9)

## Homework Statement

The Earth has a mass mE = 6×1024 kg, and orbits around the Sun (mass mS=2×1030kg)

along an approximately circular orbit of radius R=1.5×1011m. What is the total

mechanical energy (K+U) of the Earth, in reference to the Sun? Take U=0 at infinity.

(Remember: 1 year = 3.16×107s, G = 6.67×10-11 N m2/kg2; Hint: the circumference of a

circle is 2πR)

Answer: −2.7×1033 J

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