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Phys 270 Midterm Chapter 1-5
Time limit: 75 minutes
Each question worths 10 points.
Constants: g = 9.8m/s2 , G = 6.67 × 10−11 N m2 kg −2 .
1. A sky diver of mass 80.0kg (including parachute) jumps off a plane and begins her descent. (a) At
some point during her free fall, the sky diver reaches her terminal speed. What is the magnitude of
the drag force Fdrag due to air resistance that acts on the sky diver when she has reached terminal
speed? (b) For an object falling through air at a high speed v, the drag force acting on it due to
air resistance can be expressed as F = Kv 2 , where the coefficient K depends on the shape and
size of the falling object and on the density of air. For a human body, the numerical value for
K is about K1 = 0.250kg/m. Using this value for K, what is the terminal speed vterminal of the
sky diver? (c) When the parachute is fully open, the effective drag coefficient of the sky diver
plus parachute increases to K2 = 60.0kg/m. What is the drag force Fdrag acting on the sky diver
immediately after she has opened the parachute? (d) What is the terminal speed vterminal of the
sky diver when the parachute is opened?
2. Figure 1 shows a bob of mass m is suspended from a fixed point with a massless string of length
L (i.e., it is a pendulum). You are to investigate the motion in which the string moves in a cone
with half-angle θ. Express your answers below in terms of some or all of the variables m, L, and θ,
as well as the acceleration due to gravity g. (a) What tangential speed, v, must the bob have so
that it moves in a horizontal circle with the string always making an angle θ from the vertical? (b)
How long does it take the bob to make one full revolution (one complete trip around the circle)?
Figure 1: Question 2
3. (a) A skier of mass 65.0kg is pulled up a snow-covered slope at constant speed by a tow rope
that is parallel to the ground. The ground slopes upward at a constant angle of 26.0◦ above the
horizontal and you can ignore friction. Draw a force diagram and calculate the tension in the tow
rope. (b) A .22 rifle bullet, traveling at 350m/s , strikes a block of soft wood, which it penetrates
to a depth of 0.130m. The block of wood is clamped in place and doesn’t move. The mass of the
bullet is 1.80g. Calculate the magnitude of the retarding force the wood exerts on the bullet.
4. Two blocks with masses M1 and M2 hang one under the other as shown in Figure 2. The blocks
are accelerating upward with acceleration of magnitude a. (a) Draw the two force diagrams for
the blocks. (b) Find the tensions T1 and T2 in terms of the masses, a and g. [Note that you are
NOT asked to find a.]
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Figure 2: Question 4
5. A ball is launched up a semicircular chute (Figure 3) in such a way that at the top of the chute,
just before it goes into free fall, the ball has a centripetal acceleration of magnitude 3g (where g
is the acceleration due to gravity). How far from the bottom of the chute does the ball land?
Figure 3: Question 5
6. A flea jumps straight up to a maximum height of 0.470m. (a) What is its initial velocity as it
leaves the ground? (b) How long is the flea in the air from the time it jumps to the time it hits
the ground?
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