Physics 141: Homework 6
Due for upload by May 21st at 11:59pm
Instructor Nick Stair
Score:
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Physics 141 (Instructor Nick Stair ): Homework 6
Problem 1
For all problems in this homework set, assume objects are on earth at sea level unless otherwise specified.
IMPORTANT: If a problem asks to find a force (F⃗ ), it means find the force vector, which must be reported
in component or column format. Any problem that just want a number, will ask that your find the magnitude
of a force, meaning |F⃗ |.
Problem 1
A helicopter lifts a m = 72 kg astroknot (yes astroknot) a height h = 15 m vertically from the ocean by a
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wench with a massless cable. The acceleration of the astroknot is 10
g ĵ. The helicopter does not move, only
the astroknot. [4 points each]
a) How much work is done on the astroknot by the tension T⃗ in the cable?
b) How much work is done on the astroknot by the force of gravity F⃗g ?
c) What is the net work done on the astroknot?
d) What is the velocity of the astroknot when they reach the helicopter?
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Physics 141 (Instructor Nick Stair ): Homework 6
Problem 2
Problem 2
A skier with m = 80 kg slides from rest a distance d = 40 m down a slope that makes a θ = 25 degree angle
the horizontal. Assume the skier is moving to the right with respect to the page. The coefficient of kinetic
friction between the skier is µk = 0.2. [4 points each]
a) Find the magnitude of the kinetic force of friction acting on the skier.
b) Find the work done by gravity on the skier.
c) Find the work done by friction on the skier.
d) Find the velocity of the skier at the 40 m mark.
e) The kinetic energy of an object is defined as K = 21 mv 2 , using this fact, what do you notice about the
net work and the kinetic energy?
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Physics 141 (Instructor Nick Stair ): Homework 6
Problem 3
Problem 3
Consider a bullet with m fired from a barrel with length ℓ. The pushing force F⃗p of the expanding gas behind
the bullet is given as a function of x by:
F⃗p (x) = α + βx − γx2 î
where α, β, γ are constants and x is the distance the bullet has traveled in the chamber. [4 points each]
a) If F⃗p is expressed in newtons, and x is expressed in meters, what are the units of α, β, and γ?
b) Find an expression for the work done by the pushing force of the gas (F⃗p ) over the distance ℓ of the entire
barrel (DO NOT use the numbers from below).
Now assume that α = 15, 000, β = 10, 000, and γ = 25, 000 (each with the appropriate units you found
above).
c) What is the Work done by the pushing force of the gas if ℓ = 0.6 m.
d) What is the Work done by the pushing force of the gas if ℓ = 1.0 m, based on your conclusion from
Problem 2 part e), of the two barrel lengths which should you use if you want a faster bullet?
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Physics 141 (Instructor Nick Stair ): Homework 6
Problem 4
Problem 4
A spring with an equilibrium length ℓo = 10 cm is attached to a roof. When a ball with mass m = 2.0 kg is
hung from the spring, the spring stretches to a length of ℓ = 15 cm. [4 points each]
a) Find the value of the spring constant k in SI units.
b) How long is the spring when a M = 3.0 kg mass is hung from it?
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