1
Duration: 10 mins
NAME:
PHY 121 - Quiz 4 Solution
Q1: Two workhorses tow a barge along a straight canal. Each horse exerts a constant force of magnitude F , and
the tow ropes make an angle θ with the direction of motion of the horses and the barge. Each horse is traveling at a
constant speed. v a.)How much work W is done by each horse in a time t? b) How much power P does each horse
provide? Express the work in terms of the quantities given in the problem introduction (2 points).
FIG. 1: Workhorses towing a barge.
SOLUTION:
Work done by each horse
W = F~H · ~s
W = F cos(θ) v t
(1)
(2)
Power provided by each horse
P =
W
= F cos(θ) v
t
(3)
2
Q2:
In this problem, you will calculate work done on an object moving in a straight line. Find the work done by
the 18-newton force W18 , 30-newton force W30 , 12-newton force W12 , and 15-newton force W15 (2 points).
FIG. 2: Work concept.
SOLUTION:
W
W18
W30
W12
W15
=
=
=
=
=
F~ · ~s
18 × 160 × cos(0) = 2880.00 Joules
30 × 160 × cos(30) = 4156.92 Joules
12 × 160 × cos(180) = −1920.00 Joules
15 × 160 × cos(220) = −1838.50 Joules
(4)
(5)
(6)
(7)
(8)
Q3: You are a member of an alpine rescue team and must project a box of supplies, with mass m up an incline of
constant slope angle α so that it reaches a stranded skier who is a vertical distance h above the bottom of the incline.
The incline is slippery, but there is some friction present, with kinetic friction coefficient µk . Use the work-energy
theorem to calculate the minimum speed v that you must give the box at the bottom of the incline so that it will
reach the skier. Express your answer in terms of some or all of the variables m, g, h, µ k , &α (2 points).
SOLUTION:
Potential energy of the system WP E ,
WP E = −m g h
(9)
WF = −µk dN cos(α)
(10)
Work done by the friction is given as WF ,
Where d is the horizontal distance up the slope d = h/sin(α). From conservation of energy we can write
Change in Kinetic energy = Change in potential energy
(Kf − Ki ) = (Pf − Pi )
1
h
0 − mv 2 = −m g h − µk mgcos(α)
2
sin(α)
(11)
(12)
Which gives
v=
s
2gh 1 + µk cot(α)
(13)