Concept #1: Work Done by Gravity

Practice: You push on 3 kg box against a wall for a distance of 2 m with a 100-N force that makes 53° with the horizontal, as shown. The box-wall coefficient of friction is 0.3. Calculate the work done by:

(a) you,

(b) friction,

(c) gravity.

Practice: A 70 kg person hikes from the bottom to the top of a 1,000 m hill with varying speeds. The path you take is very irregular, with varying inclinations. How much total work does gravity do on you during the entire hike?

Concept #2: Work on Inclined Planes

Practice: You push a 2-kg box from the bottom of an inclined plane with 50 N for 10 m. The incline makes 37° with the horizontal, and the box-incline coefficient of friction is 0.6. Find the work done by:

(a) you,

(b) friction, and

(c) gravity.

Example #1: Work on Inclined Planes

A 50 g mass is lifted upwards 20 cm. How much work is done by the gravitational force?

A 360-kg piano slides 3.6 m down a 26 incline and is kept from accelerating by a man who is pushing back on it parallel to the incline.Determine the force exerted by the man.Determine the work done by the man on the piano.Determine the work done by the force of gravity.Determine the net work done on the piano. Ignore friction.

A grocery cart with mass of 14 kg is being pushed at constant speed up a flat 15 ramp by a force FP which acts at an angle of 17 below the horizontal.Find the work done by each of the forces ( mg, FN , FP ) on the cart if the ramp is 16 m long.

A physics professor is pushed up a ramp inclined upward at an angle 31.0 above the horizontal as he sits in his desk chair that slides on frictionless rollers. The combined mass of the professor and chair is 86.0 kg . He is pushed a distance 2.55 m along the incline by a group of students who together exert a constant horizontal force of 601 N . The professors speed at the bottom of the ramp is 2.05 m/s .Use the work-energy theorem to find his speed at the top of the ramp.

You need to raise a heavy block by pulling it with a massless rope. You can either (a) pull the block straight up height h, or (b) pull it up a long, frictionless plane inclined at a 15
angle until its height has increased by h. Assume you will move the block at constant speed either way.Will you do more work in case a or case b? Or is the work the same in both cases?

A 20.0-kg crate sits at rest at the bottom of a 15.1 m -long ramp that is inclined at 36 above the horizontal. A constant horizontal force of 290 N is applied to the crate to push it up the ramp. While the crate is moving, the ramp exerts a constant frictional force on it that has magnitude 65.0 N.What is the total work done on the crate during its motion from the bottom to the top of the ramp?How much time does it take the crate to travel to the top of the ramp?

An
14.0-kg
package in a mail-sorting room slides
4.00 m
down a chute that is inclined at
56.0
below the horizontal. The coefficient of kinetic friction between the package and the chutes surface is
0.60.Calculate the work done on the package by friction.Calculate the work done on the package by gravity.Calculate the work done on the package by the normal force.What is the net work done on the package?

A
7.00-kg
package slides
2.80 m
down a long ramp that is
inclined at
26.0
below the horizontal. The coefficient of kinetic
friction between the package and the ramp is
exttip{mu _{
m k}}{mu_k} = 0.360.Calculate the work done on the package by friction.Calculate the work done on the package by gravity.Calculate the work done on the package by the normal force.Calculate the total work done on the package.If the package has a speed of
2.60 m/s
at the top of the ramp, what is its speed after it has slid
2.80 m
down the ramp?

A boxed 13.0 kg computer monitor is dragged by friction 6.50 m up along the moving surface of a conveyor belt inclined at an angle of 36.1 above the horizontal. If the monitors speed is a constant 2.60 cm/s , how much work is done on the monitor by friction, gravity, and the normal force of the conveyor belt?

How much work is done by the gravitational force when a 260-kg pile driver falls 2.60 m ?

A hammerhead with a mass of 2.3 kg is allowed to fall onto a nail from a height of 0.45 m .What is the maximum amount of work it could do on the nail?

A gondola can carry 20 skiers, with a total mass of up to 1960 kg . The gondola ascends at a constant speed from the base of a mountain, at 2060 m , to the summit at 3555 m .How much work does the motor do in moving a full gondola up the mountain?How much work does gravity do on the gondola?If the motor is capable of generating 10 % more work than found in A, what is the acceleration of the gondola?

Determine the work a hiker must
do on a 13.1 kg backpack to carry it up a hill of height exttip{h}{h} = 12.0 m . The hill is not an even slope but rather an irregular curve as in the figure.Does the work done by gravity depend only on the height of the hill and not on its shape or the path taken?Determine also the work done by gravity on the backpack.

A 0.050-kg rock moves from the origin to the point (3.0 m, 5.0 m) in a coordinate system in which the positive y-direction is upward.The rock first moves horizontally from the origin to the point (3.0 m, 0). Then it moves vertically from (3.0 m, 0) to (3.0 m, 5.0 m). How much work is done on the rock by gravity during the displacement?Instead of the path in part (a), let the rock first move vertically from the origin to (0, 5.0 m) and then horizontally from (0, 5.0 m) to (3.0 m, 5.0 m). How much work is done on the rock by gravity during the displacement?

The cable of a crane is lifting a
750 kg
girder. The girder
increases its speed from 0.25 m/s
to 1.25 m/s
in a distance of
4.1
m.How much work is done by gravity?How much work is done by tension?

A 75-kg roofer climbs a vertical 7.0-m ladder to the flat roof of a house. He then walks 12 m on the roof, climbs down another vertical 7.0-m ladder, and finally walks on the ground back to his starting point.How much work is done on him by gravity as he climbs up?How much work is done on him by gravity as he climbs down?How much work is done on him by gravity as he walks on the roof?What is the total work done on him by gravity during this round trip?On the basis of your answer to part E, would you say that gravity is a conservative or nonconservative force? Explain.How much work is done on him by gravity as he walks on the ground?

Eight books, each 7.5 cm thick with mass 1.6 kg , lie flat on a table.How much work is required to stack them one on top of another?

What magnitude force is required to give a helicopter of mass M an acceleration of 0.10g upward?What work is done by this force as the helicopter moves a distance h upward?

A sack of flour of mass 5.50-kg is lifted vertically at a constant speed of 3.10 m/s through a height of 16.0 m . Use exttip{g}{g} = 9.80 m/s2 .How great a force is required?How much work is done on the sack by the lifting force?What becomes of this work?

In a certain library the first shelf is 15.5 cm off the ground, and the remaining 4 shelves are each spaced 33.5 cm above the previous one.If the average book has a mass of 1.40 kg with a height of 22.2 cm , and an average shelf holds 28 books (standing vertically), how much work is required to fill all the shelves, assuming the books are all laying flat on the floor to start?

The two ropes seen in the figure are used to lower a 255 kg piano 5.70 m from a second-story window to the ground.
You may want to review (Pages 214 - 218).How much work is done by each of the three forces?

A sack of flour of mass exttip{m}{m} is lifted vertically at a constant speed of exttip{v}{v} through a height of exttip{h}{h}.How great a force is required?How much work is done on the sack by the lifting force?What becomes of this work?

A 66.5 kg hiker starts at an elevation of 1320 m and climbs to the top of a 2710 m peak.What is the hikers change in potential energy?What is the minimum work required of the hiker?Can the actual work done be greater than this?Explain.

A cyclist intends to cycle up a 8.50 hill whose vertical height is 130 m . The pedals turn in a circle of diameter 36.0 cm .Assuming the mass of bicycle plus person is 75.0 kg , calculate how much work must be done against gravity.If each complete revolution of the pedals moves the bike 5.60 m along its path, calculate the average force that must be exerted on the pedals tangent to their circular path. Neglect work done by friction and other losses.

A 76.0-kg firefighter climbs a flight of stairs 21.0 m high. How much work is required?

A 5 kg mass is pushed across a floor with a coefficient of kinetic friction of 0.35. If the force pushing the mass is 70 N, how much work is done after 5 s by:(a) the pushing force(b) friction after(c) the normal force(d) gravity

An object released from rest at the top of a 30.0° incline slides down the incline to the bottom of the incline. During this motion the work done on the block by the friction force on the block isA) positiveB) negativeC) zero

A box is pulled by a force F up a ramp that is inclined at 37° above the horizontal. The direction of this force is 60.0° above the horizontal. The force has magnitude 60.0 N. The box travels a distance of 5.00 m along the surface of the ramp. How much work does the force F do during this displacement of the box?A) 300 JB) 150 JC) 240 JD) 276 JE) None of the above answers

A block of mass 10.0 kg slides 16.0 m down a 36.9° incline, from point A at the top of the incline to point B at the bottom. As the block moves from point A to point B, the surface of the incline exerts a constant friction force that has magnitude 42.0 N.As the block moves from A to B, how much work is done on it by the friction force? (Be sure to indicate whether the work is positive or negative).

A block of mass 10.0 kg slides 16.0 m down a 36.9° incline, from point A at the top of the incline to point B at the bottom. As the block moves from point A to point B, the surface of the incline exerts a constant friction force that has magnitude 42.0 N.As the block moves from A to B, how much work is done on it by the gravity force? (Be sure to indicate whether the work is positive or negative).

A 1.75 m tall person lifts a 1.65 kg book off the ground so it is 2.15 m above the ground.(a) What is the potential energy of the book relative to the ground?(b) What is the potential energy of the book relative to the top of the persons head(c) How is the work done by the
person related to the answers in parts A and B?

A box with mass 5.00 kg is pulled up a 36.9° incline by a constant force F that has magnitude 75.0 N and that is parallel to the incline. The distance along the incline from the bottom to the top is 6.00 m. During the motion of the box, the surface of the incline exerts a constant friction force fk = 18.0 N on the box, in a direction opposite to the motion.
For the motion from the bottom of the incline to the top, how much work is done by each of the following forces? In addition to giving the magnitude of the work, be sure to indicate whether the work done is positive or negative.
(i) the force F that pulls the box
(ii) the friction force fk
(iii) the gravity force
(iv) the normal force

A ramp is inclined at 36.9° above the horizontal. A block with mass 0.500 kg is pulled up the ramp by a force F. The block starts at point A at the bottom of the ramp and ends up at point B at the top of the ramp. The distance from A to B, measured along the ramp is 5.00 m. The work done on the block by gravity as the block moves from point A to point B is
A) +24.5 J
B) -24.5 J
C) +19.6 J
D) -19.6 J
E) +14.7 J
F) -14.7 J
G) None of the above answers

A block with mass 5.0 kg slides a distance of 6.0 m from point A at the top of a ramp to point B at the bottom of the ramp. The ramp is inclined at 53° above the horizontal. For the displacement of the block from A to B the work done on the block by gravity is
A) 177 J
B) -177 J
C) 235 J
D) -235 J
E) 294 J
F) -294 J
G) zero
H) None of the above answers

When an object is moved from rest at point A to rest at point B in a gravitational field, the net work done by the field depends on the mass of the object and
1. the nature of the external force moving the object from A to B.
2. the velocity of the object as it moves between A and B.
3. both the positions of A and B and the path taken between them.
4. the path taken between A and B only.
5. the positions of A and B only.

What is the minimum work needed to push a 950-kg car 360 m up along a 8.0 incline? Ignore friction.

A 125.2 N carton is pulled up a frictionless baggage ramp inclined at 31.0 degrees above the horizontal by a rope exerting a 75.2 N pull parallel to the ramps surface. The carton travels 6.05 m along the surface of the ramp.(a) Calculate the work done on the carton by the rope.(b) Calculate the work done on the carton by the gravity.(c) Calculate the work done on the carton by the normal force of the ramp.(d) What is the net work done on the carton?(e) Suppose that the rope is angled at 45.2 degrees above the horizontal, instead of being parallel to the ramps surface. How much work does the rope do on the carton in this case?

A boy in a wheelchair (total mass 47.0 kg) has speed 1.40 m/s at the crest of a slope 2.60 m high and 12.4 m long. At the bottom of the slope his speed is 6.20 m/s. Assume air resistance and rolling resistance can be modeled as a constant friction force of 41.0 N. Find the work he did in pushing forward on his wheels during the downhill ride.

A luggage handler pulls a 19.0-kg suitcase up a ramp inclined at 34.0 degrees above the horizontal by a force vec{F} of magnitude 167 N that acts parallel to the ramp. The coefficient of kinetic friction between the ramp and the incline is 0.310. The suitcase travels 3.90 m along the ramp. Calculate the work done on the suitcase by:vec{F(a) the gravitational force(b) the normal force(c) the friction force(d) Calculate the total work done on the suitcase.(e) If the speed of the suitcase is zero at the bottom of the ramp, what is its speed after it has traveled 3.90 m along the ramp?

A 1.6 kg book is lying on a 0.76-m-high table. You pick it up and place it on a bookshelf 2.21 m above the floor.(a) How much work does gravity do on the book?(b) How much work does your hand do on the book?

Spiderman, whose mass is 80.0 kg, is dangling on the free end of a 12.0-m-long rope, the other end of which is fixed to a tree limb above. By repeatedly bending at the waist, he is able to get the rope in motion, eventually getting it to swing enough that he can reach a ledge when the rope makes a 60.08 angle with the vertical. How much work was done by the gravitational force on Spiderman in this maneuver?

A 76.0-kg painter climbs a ladder that is 2.75 m long leaning against a vertical wall. The ladder makes an 31.0° angle with the wall. How much work does gravity do on the painter?

In 1990, Walter Arfeuille of Belgium lifted a 281.5-kg object through a distance of 17.1 cm using only his teeth. (a) How much work was done on the object by Arfeuille in this lift, assuming the object was lifted at constant speed? (b) What total force was exerted on Arfeuille’s teeth during the lift?

The record number of boat lifts, including the boat and its ten crew members, was achieved by Sami Heinonen and Juha Räsänen of Sweden in 2000. They lifted a total mass of 653.2 kg approximately 4 in. off the ground a total of 24 times. Estimate the total work done by the two men on the boat in this record lift, ignoring the negative work done by the men when they lowered the boat back to the ground.