Work and Conservation of Energy
I just pushed an initially stationary 86 kg box 5 m across the floor by exerting a 42 N force on
the box in the direction of the motion. The coefficient of static and kinetic friction between the
floor and the box are both 0.04. How much work did I do
210 J
A 6 kg shopping cart is moving toward you (50kg) at 8 m/s. From a standing start you jump
straight up into the air and land in the cart. What is the velocity of the cart after you jump in?
0.857 m/s
Find the net torque on the wheel shown to the right about the
axle through π, taking π = 12.00 cm and π = 27.0 cm. Note: By convention, a positive torque acts to rotate an object counter-clockwise, and a negative torque act to rotate an object clockwise
-3.88 N*m
A merry-go-round, whose radius is 3 m, initially rotates at 10 rpm. It is decelerating at a rate of
0.05 rad/s2 due to friction.
(a) What is its initial angular velocity (in radians/second)?
b) How long will it take for the merry-go-round to stop rotating?
a) 1.047 rad/s
b) 20.9 s
What is the force pushing in on a completely empty 20 cm diameter metal sphere? By
βcompletelyβ empty I mean there is little to no air or anything else on the inside of the sphere.
12,700 N
A 0.3 kg hockey puck is initially moving at 8 m/s. It is then struck by a hockey stick and given 126
J of energy. What is its final velocity?
plus/minus 30.1 m/s
A golf club hits a golf ball of mass 40g from a tee. The
speed of the golf ball leaving the tee is 80 m/s.
(a) What is the impulse experienced
by the golf ball?
(b) If the time of contact between the club and the golf ball is 15 ms, what is the average force exerted by the club on the ball during the contact?
(a) 3.2 N*S
(b) 213 N
Two tiny masses of mass π1 = 1.60 kg and π2 = 2.40 kg are at locations of π₯1 = 0.8 m and
π₯2 = 1.2 m on a very long massless lever. At what location do you need to put a fulcrum so that
the weights are balanced and the lever does not rotate (i.e. so that the net torque is zero)? What
does this location represent?
1.04 m
Model a merry-go-round as a 2.8 m diameter disk with mass 250 kg. You are exerting a 50 N
force on the merry-go-round parallel to and at its edge causing it to start from rest and start rotating
in the clockwise direction.
What is the angular acceleration of the merry-go-round?
0.286 rad/s
How far will an oxygen molecule travel, on average, in 5 minutes?
10.4 cm
Your 1300 kg car is behind a truck traveling at a steady speed of 20 m/s on a long, flat road.
To pass it, you speed up to 27 m/s over the course of 4.0 s. Neglecting dissipative forces like
friction and air resistance, what engine power is required to accomplish this?
53,500 W
Cart A is travelling to the right at 4.2 m/s runs into Cart B moving at 3.1 m/s to the left. They
collide elastically and after the collision Cart A is moving left at 1.0 m/s. What is the velocity of
Cart B?
6.3 m/s to the right
The masses of the Earth and Moon are 5.97 Γ 1024 kg and 7.35 Γ 1022 kg, respectively, and
their centers are separated by 3.84 Γ 108 m. Where is the center of mass of this system located?
Hint: Take the location of the Earth to be x = 0
4.67 β 10^6 π
A winch of radius 15 cm and mass 5 kg is attached to a 3 kg box which is hanging off the side of a
cliff. It accelerates at 3.68 m/s^2. What is its angular acceleration?
24.5 rad/s^2
Water is held up behind a 50 m tall dam. If water is allowed to flow out from the bottom of the
dam, how fast will it be moving?
31.3 m/s
A 70 g rock is moving 8 π/π toward a spring whose spring constant is 780 N/m. Shortly before the
rock hits the spring you apply a force of 80 N to the rock over a distance of 20 cm in an attempt
to speed it up. How far does the spring compress before the rock comes to a complete stop?
You may assume there is no friction
0.216 m
A carβs bumper is designed to withstand a 4.0-km/h (1.12-m/s) collision with an immovable
object without damage to the body of the car. The bumper cushions the shock by absorbing the
force over a distance. Calculate the magnitude of the average force on a bumper that collapses
0.200 m while bringing a 900-kg car to rest from an initial speed of 1.12 m/s.
-2820 N
Mass of the sign, M = 20 kg. The mass of the bar is
m = 4 kg.
a) Find the tension in the string.
b) Find the force the wall applies to the rod
a) 480 N
b) 463 N @ 2.43 degrees
Model a merry-go-round as a 2.8 m diameter disk with mass 250 kg. It is initially rotation at
3 πππ/π . You jump onto the edge of the merry-go-round while it is spinning. If your mass is 85
kg what is your speed after jumping onto the merry-go-round?
1.79 rad/s
A cube of wood (density = 875 kg/m3) has sides of 10 cm. How much force (in addition to its own weight) would be needed to immerse this cube in a tub of mercury (density = 13,600 kg/m^3)?
125 N downwards
A 3 kg box is moving at 15 m/s along a surface with no friction. It then encounters a surface with
which it has a coefficient of kinetic friction of 0.2. How far does the box slide before coming to a
complete stop?
57.4 m
A 17.0 g bullet traveling 260 m/s embeds itself in a 3.50 kg block sitting on a table, which
makes the block move backward along the table. If the coefficient of kinetic friction between
the table and the block is 0.15 how far will the block move before coming to a complete stop?
0.537 m
The mass in the hand is 6 kg. The forearm can be
assumed to be uniform with a mass of 1 kg.
a) What is the force πΉβπ?
b) What is the force at the joint? (the joint is labeled as O)
a) 562 N upward
b) 493 N downward
A winch of radius 15 cm and mass 5 kg is attached to a 3 kg box which is hanging off the side of a
cliff.
a) What is the velocity of the box when it has fallen 5 m?
b) What is the angular velocity of the winch?
a) -7.31 m/s
b) 48.7 πππ/π
The last meter of a 4 cm diameter pipe is 50 m below the surface of a freshwater lake. Water is
being sucked into the pipe such that it moves at 15 m/s in the pipe. What is the difference in
force being exerted on the walls of the pipe due to the water inside the pipe and the water
outside the pipe?
14,100 N