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2) Using your amazing telescope, you just found a star with a planet orbiting it at a distance
of 850,000,000 km. You measured the orbital period to be 4.5 years.
a. Find the centripetal acceleration of the planet.
b. You don't know the mass of the planet m, but you can solve for the mass of the
star M. Find the magnitude of the force of gravity acting on the planet, in terms
of m, using both Newton's second law and the law of universal gravitation. Solve
for the star's mass M by setting these results equal to each other.
3) While ice skating, you are trying to coast as far as you can on a frozen lake. The
coefficient of kinetic friction between your skates and the ice is /k = 0.05. You acquire a
speed of 10 m/s before coasting.
a. What is the force of kinetic friction acting on you, in terms of your mass m (You
can leave this answer in variables; you will not be able to get a number.)?
b. What is the magnitude and direction of your acceleration?
c. How far will you coast?
4) Hellings 6.11
5) A block of unknown mass m sits on a ramp with an adjustable tilt. You slowly increase
its angle above the horizontal, until it begins to slide, which happens at 34.
a. Make a useful diagram with a coordinate system.
b. Using Newton's second law of motion, find the coefficient of static friction.
(Hint: Start by just writing the x and y components from Newton's second law.
Consider the moment just before static friction is overcome, when the acceleration
is still zero.)
c. As you were slowly raising the ramp, what was happening to the magnitude of the
static friction force? Was is increasing, decreasing, or remaining constant?
d. Now go back and review your work in part b. Make sure you have used correct
notation for vectors, magnitudes, and components of vectors throughout. If you
are unsure, ask for help.

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6) You are given a spring and asked to find the spring constant.
a. What simple experiment could you do to find the spring constant? What things
would you measure?
b. Pretend you did your proposed experiment, and make up realistic measurements.
c. Given your made-up measurements, what is the spring constant?

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