Download Homework #3 - University of St. Thomas

Homework #3
Chapter 6: Work, Energy and Power
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#1: Give two examples of situations in which you might think you’re doing work but in which, in
the technical sense, you do no work.
#2: If the scalar product of two nonzero vectors is zero, what can you conclude about their
relative directions?
#6: Does the gravitational force of the Sun do work on a planet in a circular orbit? On a comet in
an elliptical orbit? Explain.
#12: IF the coefficient of kinetic friction is 0.21, how much work do you do when you slide a
50kg box at a constant speed across a 4.8m wide room?
⃗⃗ ∙ 𝐶⃗) = 𝐴⃗ ∙ 𝐵
⃗⃗ + 𝐴⃗ ∙ 𝐶⃗
#17: Show that the scalar product obeys the distributive law: 𝐴⃗ ∙ (𝐵
#24: Spider silk is a remarkable elastic material. A particular strand has a spring constant
70mN/m, and it stretches 9.6cm when a fly hits it. How much work did the fly’s impact to on the silk
strand?
#29: After a tornado, a 0.50g drinking straw was found embedded 4.5cm in a tree. Subsequent
measurements showed that the tree exerted a stopping force of 70N on the straw. What was the
straw’s speed?
#31: A typical human diet is “2000 calories” per day, where the “Calorie” describing food is
actually 1 kilocalorie. Express 2000kCal/day in Watts.
#37: Estimate your power output as you do deep knee bends at the rate of one per second.
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#42: Two people push a stalled car at its front doors, each applying a 280N force at 25° to the
forward direction (i.e. relative to the body of the car). How much work does each person do in pushing
the car 5.6m?
#43: You’re at the gym, doing arm raises. With each rep, you lift a 20N weight 55cm. (a) How
many raises must you do before you’ve expended 200kcal of work? (b) If your workout takes 1.0min,
what is your average power output?
#64: A 1400kg car ascends a mountain road at a steady 60km/h, against 450N force of air
resistance. If the engine supplies energy to the drive wheels at a rate of 38kW, what’s the slope angle of
the road?
Chapter 7: Conservation of Energy
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#2: Is the conservation of energy principle related to Newton’s laws, or is it an entirely separate
physical principle? Discuss.
#6: If the force is zero at a given point, must the potential energy also be zero at that point?
Give an example.
#14: You fly from Boston’s Logan Airport, at sea level, to Denver, altitude 1.6km. Taking your
mass to be 65kg and the zero of potential energy at Boston, what’s your gravitational potential energy
(a) at the plane’s 11km cruising altitude, and b) in Denver?
#18: A biophysicist grabs the ends of a DNA strand with optical tweezers and stretches it 26μm.
How much energy is stored in the stretched molecule if its spring constant is 0.046pN/μm?
#19: A skier starts down a frictionless 32° slope. After a vertical drop of 25m, the slope
temporarily levels out and then slopes down at 28°, dropping an additional 38m vertically before
leveling out again. Find the skier’s speed on the two level stretches.
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#27: A particle is trapped in a potential well described by 𝑈(𝑥) = 16𝑥 2 − 𝑏, with U in Joules, x
in meters, and b = 4.0J. Find the force on the particle when it’s at (a) x =2.1m, (b) x=0m, and (c) x=-1.4m.
#32: A carbon dioxide molecule can be modeled as a carbon atom and an oxygen atom
connected by a spring. If a displacement of the carbon by 1.6x10-12m from its equilibrium position
relative to the oxygen increases the molecule’s potential energy by 0.015eV, what’s the spring constant?
#37: A particle moves along the x-axis under the influence of a force 𝐹⃗ = 𝑎𝑥 2 + 𝑏, where a and
b are constants. Find its potential energy as a function of position, taking U = 0 at x=0.
#40: A child on a swing whose 3.2m long chains make a maximum angle of 50° with the vertical.
What’s the child’s maximum speed?
Chapter 8: Gravity
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#2: Explain the difference between G and g.
#6: Can you put a satellite in an orbit that keeps it stationary over the south pole? Explain.
#14: Calculate the gravitational acceleration at the surface of (a) Mercury and (b) Saturn’s moon
Titan. (See Appendix E for relevant information.)
#15: Two identical lead spheres with their centers 14m apart attract each other with a 0.25μN
force. Find their mass.
#21: Calculate the orbital period for Jupiter’s moon Io, which orbits 4.22x105km from the
planet’s center. (See Appendix E for relevant information.)
#26: A rocket is launched vertically upward from Earth’s surface at 5.1km/s. What’s it’s
maximum altitude?
#29: What’s the total mechanical energy associated with Earth’s orbital motion?
#34: One of the largest-standing athletic records is Cuban Javier Sotomayor’s 2.45m high jump.
How high could Sototmayor jump on (a) Mars and (b) Earth’s moon? (See Appendix E for relevant
information.)
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#44: Satellites A and B are in circular orbits, with A twice as far from Earth’s center as B. How do
their orbital periods compare?