PHYSICS 8A, Section 2 – Fall 2011
Midterm 2, C. Bordel
Thursday, November 3rd, 2011
6:30pm-8pm
Reminder
θ
τ
sinrF=;
θ
sinrpL =; 2
/12
1MLI centerrod =; 2
/5
2MRI diameterspheresolid =;
2
/2
1MRI axiscylindersolid =; 2
/3
2MRI diameterspherehollow =;
2
/MRI axiscylinderhollow =
Problem 1 – Spacecraft around Earth (25 pts)
A spacecraft of mass m is in circular orbit above the equator at distance d above Earth’s surface.
Earth has mass M and radius R, and air resistance neglected.
a- Determine the moment of inertia of the spacecraft about the Earth’s South-North axis while it is in
orbit if the spacecraft can be approximated as a solid sphere with a radius rsc. Show that the
spacecraft can actually be considered as a point particle.
b- How much work needs to be done against the gravitational force to bring the spacecraft from its
original distance to infinity?
c- What is the minimum speed ve that the spacecraft needs to reach from its original altitude in order
to escape the gravitational field of the Earth?
d- What is the sign of the mechanical energy of the spacecraft when v> ve? Explain why.
Figure 1
Problem 2 – Ballistic pendulum (25 pts)
An apple of mass M suspended from a massless string is used as a ballistic pendulum to determine
the speed vi of an arrow of mass m that hits it, as shown in Figure 2. Air resistance is neglected, and
we’ll assume that the arrow hits the apple horizontally, the apple being initially at rest.
a- From the height h of the swing, determine the speed vf of the combined system right after the
collision. What is the direction of
f
v
v?
b- Calculate the speed vi of the arrow immediately before it strikes the apple.
c- Name what type of collision this is; you will need to show a proof to justify your claim.
d- Afterwards, an experiment is performed where air resistance reduces the maximum height
reached by the apple and arrow to H. Calculate the work done by the drag force on the ballistic
pendulum from the collision until the arrow and apple reaches this new maximum height H.
Figure 2
