1. Jane the shot putter has a mass of 50kg. g = 9.8 m/s^2 G = 6.67*10-11 Nm^2/kg

Question

1. Jane the shot putter has a mass of 50kg.

g = 9.8 m/s^2

G = 6.67*10-11 Nm^2/kg^2

a. What is her weight on earth?

b. A neutron star has a mass of 3.0*1030 kg and a diameter of 20km. What is her weight on the surface of a neutron star?

c. She also throws the hammer. How fast will she have to throw the hammer for it to orbit just above the surface of the neutron star?

d. How long will it take for the hammer to complete one trip around the neutron star?

e. Neutron stars have the shape of a ball. The moment of inertia of a ball is I = 2/5*M*R2. Jane is actually the super hero Super Woman, also know as mom. The neutron starts is at rest. She applies a tangential force to the surface of the neutron star for one second and gets it to a rotation speed of 700 times a second. What force did she apply? (how much force)

f. After the neutron star is rotating, what is the velocity of a point on its equator?

Explanation / Answer

a) W = m g = 50*9.81= 490.5 N
b) W = G M m/r^2 = 6.67E-11*3.0E30*50/(10.0E3)^2=1.0E14 N

c) if orbiting

G M m/r^2 = mv^2/r

G M/r = v^2

v = sqrt(6.67E-11*3.0E30/10.0E3)= 1.41E8 m/s

d)

v = 2 pi r/T

T = 2*pi*10.0E3/1.41E8= 4.46E-4 s

e)

torque = dL/dt

L = I w

torque = r F

so

10.0E3*F = 2/5*3.0E30*10.0E3^2*(2*pi*700)

F=5.28E37 N

f) v = w r = (2*pi*700)*20.0E3= 8.80E7 m/s

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