Download HW6.1 – This is a lot of work!

HW6.1 – This is a lot of work!
WORK (make FBDs with the displacement vector shown clearly in order to calculate work)
1. A student holds her 1.5-kg psychology textbook out of a second floor classroom window until her arm is
tired; then she releases it.
a) How much work is done on the book by the student in simply holding it out the window?
b) How much work is done by the force of gravity during the time it falls 3.0 m?
2. Joe horizontally pushes a 10-kg box at constant velocity of 3.0 m/s. The coefficient of kinetic friction
between the box and floor is 0.50.
a) How much work does Joe do if he pushes the box for 15 meters?
b) How much work does friction do as Joe pushes the box?
3. Jane uses a vine wrapped around a pulley to lift a 70-kg Tarzan (with minimal effort) to a tree house 9.0
meters above the ground.
a) How much work does Jane do when she lifts Tarzan?
b) How much work does gravity do when Jane lifts Tarzan?
4. A father pulls his child in a little red wagon with constant speed. If the father pulls with a force of 16 N for
10.0 m, and the handle of the wagon is inclined at an angle of 60o above the horizontal, how much work
does the father do on the wagon? How much work does friction do on the wagon? How much work does
the normal force do on the wagon? How much work does gravity do on the wagon?
5. A bicycle rider pushes a bicycle that has a mass of 13 kg up a
steep hill. The incline is 250 and the road is 275 m long. The
rider pushes the bike parallel to the road with a force of 58 N.
(Do not assume that the rider is pushing at a constant speed)
a) How much work does the rider do on the bicycle?
b) How much work is done by the force of gravity on the bike?
c) How much work is done by the normal force on the bike?
d) What is the net work on the bike?
FN
Fpush
275m
250
Fg
20
The velocity-time graph of a particle of mass 2 kg moving in a
straight line is as shown in the graph at left. Find the work done
by all the forces acting on the particle (Wnet). (Don’t forget
how to analyze motion graphs!)
v (m/s)
6.
0
0
t (s)
2
KINETIC ENERGY AND THE WORK ENERGY THEOREM
7. A 10.0 g bullet has a speed of 1200 m/s.
a) What is the kinetic energy of the bullet?
b) How much work was done on the bullet to make it reach this speed if it started from rest?
c) What is the bullet’s kinetic energy if the speed is halved?
d) What is the bullet’s kinetic energy if the speed is tripled?
8. Two people, of equal weight, are running at 4 m/s and 5 m/s respectively. Both increase their speed by 1
m/s in a time span of 10 s.
a) Who does more work?
b) Who develops more power?
c) How fast would each person have to go to double their kinetic energy? (How is v related to K?)
d) By what factor does the runners’ kinetic energy increase if their speed is doubled?
9. A 1200-kg automobile travels at 25 m/s.
a. What is its kinetic energy?
b. What net work would be required to bring it to a stop?
10. A 2.5 –g bullet traveling at 350 m/s hits a tree and slows uniformly to a stop while penetrating a distance
of 12 cm into the tree’s trunk. What force was exerted on the bullet in bringing it to rest?
11. a) How much work is done by the force shown at right when it
acts on an object and pushes it from x = 0.25 m to x = 0.75 m?
b) Determine the final speed of a 1 kg object subjected to this
force over this displacement if the initial speed of the object at
0.25 m was 0.3 m/s.
12. How much work is done by the force shown below when it acts
on an object and pushes it from x = 1.0 m to x = 4.0 m?
Fx (N)
1.5
1
0.5
0
1
2
x (m)
13. A 2.0 kg stone moves along an x axis on a
horizontal frictionless surface, accelerated
by a force Fx(x) that varies with the stone’s
position as shown below
a) How much work is done on the stone by
the force as the stone moves from its
initial point at x1 = 0 to x2 = 8 m?
b) The stone starts from rest at x = 0.
What is its speed at x = 8 m?
3
Fx (N)
0
4
5
4
3
2
1
0
-1 0
-2
-3
-4
1
2
3
4
5
6
7
Answers
1a) 0 b) 44.1J
2a) 735 J
b) -735 J
3a) 6174 J
b) -6174 J
4) Wpull = 80 J, Wf = -80J, WN = Wg = 0
5a) 15,950 J b) -14,806 J c) 0 N d) 1144J
6. -400J
7a) 7200 J
b) 7200 J
c) 7200/4 = 1800 J
d) 7200(9) = 64,800 J
8a) and b) 5m/s runner
c) 1.41 xs
d) 4xs
9a) 375,000J b) -375,000J
10. 1276N
11a) 0.3 J
b) 0.83 m/s
12) 2.5 J
13a) 9.5 J b) 3.1 m/s
8
x (m)