Work and Power

When a force acts upon an object to cause a displacement of the object, it is said that work was done upon the object. There are three key ingredients to work - force, distance, and cause. In order for a force to qualify as having done work on an object, there must be a distance and the force must cause the displacement. There are several good examples of work that can be observed in everyday life - a horse pulling a plow through the field, a father pushing a grocery cart down the aisle of a grocery store, a freshman lifting a backpack full of books upon her shoulder, a weightlifter lifting a barbell above his head, an Olympian launching the shot-put, etc. In each case described here there is a force exerted upon an object to cause that object to be displaced.

Work is done on an object if a force is applied and the object moves in the direction in which force is applied.

 

 

Mathematically, work can be expressed by the following equation.

W=F*d

where

W is work

F is the force,

d is the distance

Units of Work

Whenever a new quantity is introduced in physics, the standard metric units associated with that quantity are discussed. In the case of work (and also energy), the standard metric unit is the Joule (abbreviated J). One Joule is equivalent to one Newton of force causing a displacement of one meter. In other words,

The Joule is the unit of work.

1 Joule = 1 Newton * 1 meter

1 J = 1 N * m

 

Power

Sometimes, the work is done very quickly and other times the work is done rather slowly. For example, a rock climber takes an abnormally long time to elevate her body up a few meters along the side of a cliff. On the other hand, a trail hiker (who selects the easier path up the mountain) might elevate her body a few meters in a short amount of time. The two people might do the same amount of work, yet the hiker does the work in considerably less time than the rock climber. The quantity that has to do with the rate at which a certain amount of work is done is known as the power. The hiker has a greater power rating than the rock climber.

Power is the rate at which work is done. It is the work/time ratio. Mathematically, it is computed using the following equation.

P=W/t

where

P is power

W is watt

t is time

The standard metric unit of power is the Watt. As is implied by the equation for power, a unit of power is equivalent to a unit of work divided by a unit of time. Thus, a Watt is equivalent to a Joule/second. 

Solve the following problems. REMEMBER YOU MUST SHOW ALL YOUR WORK

1. How much work is done by a crane that lowers 1,000 newtons of material a distance of 150 meters?

2. How much work is done when a 1 kilogram mass is raised a vertical distance of 1 meter?

3. A 49 newton rock is lifted 2 meters in 5 seconds.

a. How much work is done?

b. What power is used?

4. A student who weighs 500 newtons climbed the stairs from the first floor to the third floor, 15 meters above, in 20 seconds.

a. How much work did she do?

b. What was her power?


5. A box is pushed across the floor for a distance of 5 meters with a force of 50 newtons in 5 seconds.

a. How much work is done?


b. What is the power?

6. A woman lifts a 300 newton child a distance of 1.5 meters in 0.75 seconds. What is her power output in lifting the child?

7. Calculate the work done by a 47 N force pushing a pencil 0.26 m.

8.  Calculate the work done by a 47 N force pushing a 0.025 kg pencil 0.25 m against a force of 23 N.

9. Calculate the work done by a 2.4 N force pushing a 400. g sandwich across a table 0.75 m wide.

10. How much work is it to lift a 20. kg sack of potatoes vertically 6.5 m? Acceleration 9.8m/s²

11.  If a small motor does 520 J of work to move a toy car 260 m, what force does it exert?

12.  A girl pushes her little brother on his sled with a force of 300 N for 750 m.  How much work is done?

a. How much power does it take to lift 30.0 N 10.0 m high in 5.00 s?

13.  How much power does it take to lift 30.0 kg 10.0 m high in 5.00 s?

14. Indicate whether or not the following represent examples of work. Explain your answer.

	Work done
A teacher applies a force to a wall and becomes exhausted. Explanation:	Yes or No?
b. A weightlifter lifts a barbell above her head. Explanation:	Yes or No?
c. A waiter carries a tray full of meals across a dining room at a constant speed. Explanation:	Yes or No?
d. A rolling marble hits a note card and moves it across a table. Explanation:	Yes or No?
e. A shot-putter launches the shot. Explanation:	Yes or No?

15. You must exert a force of 4.5 N on a book to slide it across a table. If you do 2.7 J of work in the process, how far have you moved the book?

16. A child pulls a sled up a snow-covered hill. The child does 405 J of work on the sled. If the child walks 15 m up the hill, how large of a force must the child exert?

17. How much work is done on a small car if a 3150 N force is exerted to move it 75.5 m to the side of the road?

18. A crate is being lifted into a truck. If it is moved with a 2470 N force and 3650 J of work is done, then how far is the crate being lifted?

19. If 16,700 J of work is done to shoot the human cannonball down a 3.05 m barrel, then how much force is applied to the person to fire them out the cannon?

20. An elephant pushes with 2000 N on a load of trees. It then pushes these trees for 150 m. How much work did the elephant do?

21.  An 190,000 W engine can accelerate from rest to a top speed in 9 s. How much work did the engine do?

22. Another engine reaches its top speed from rest in 7.5 s. It is able to perform 250,000 J of wok in that time. How much power does this engine have in that time?

23. If a runner exerts 350 J of work to make 125 W of power, then how long did it take the runner to do the work?

Momentum

Friction

For better or for worse, friction is an inescapable force we encounter every moment of our lives. We depend on friction in order to walk, we take advantage of friction in order to light a match, we try to reduce friction in our car engines and door hinges, and friction is generated as the muscle fibers of our hearts contract and relax with each heart beat. Usually physicists and engineers invest a lot of time and energy into trying to reduce or eliminate friction within the moving parts of machinery, but others sometimes look for ways to increase friction. Whether an engineer is trying to design a better set of automobile brakes or a more efficient wind turbine, a thorough understanding of friction is a vital prerequisite.  

Friction occurs whenever two surfaces are in contact with each other, and in general, it is the roughness of the surfaces that determines the amount of friction that results. Even surfaces that look and feel smooth may contain thousands of irregular bumps, pits, ridges, and valleys, although a microscope may be required to actually see them. When two such surfaces slide past one another, the tiny bumps and ridges on one surface can get hung up briefly in the pits and ridges on the other surface. It is the brief locking together of the surface irregularities that creates friction and impedes their motion.

Static friction is the force that must be overcome in order to set a body in motion. Kinetic friction is the force that must be overcome in order to keep a body in motion. Kinetic friction is usually less than static friction, but both types occur mainly because of the surface macro- and microscopic imperfections.

When an object such as a coffee cup is at rest on a table top, some of its surface imperfections are pressed up against the similar imperfections of the table, with the tiny peaks of one surface nestled into the tiny valleys of the other. To set the cup in motion and make it slide across the table, enough force must be applied to get the peaks and valleys on the upper surface up and out of the valleys and peaks on the stationary surface below. Static friction is the force that must be overcome to disengage these peaks and valleys in order for the cup to begin sliding across the table.

https://www.schooltube.com/video/19192f02dc78fcccaf82/

While friction is primarily caused by surface roughness, there are many modern synthetic materials that have exceptionally smooth surfaces. For these materials, the friction that results from surface roughness can be very, very small.

Another way to reduce friction is issuing lubricants. A lubricant is a substance introduced between two surfaces to lessen the friction between them. Common lubricants include:

Oils

Waxes

Grease

Ice

Friction also can be harmful or helpful. For example all brake systems are based in increase the friction between the wheel and the brake, reducing the force on the wheel and its acceleration. The friction between your foot and the floor allow you to walk and do not felt.

Examples of harmful friction would be an abrasion to the skin from a person sliding on a rug 

Questions

I. What is friction?

II. Friction is an important force in nature. It can be harmful or helpful. Describe some ways it is harmful and some ways it is helpful.

III. Describe a situation in which using wheels would reduce friction between a moving object and the surface over which it travels.

IV. Hypothesize what your life would be like if there were no friction. Which actions would be more difficult? Which would be easier?

V. How lubricants affect friction between two objects?

VI. Give three daily life examples of lubricants reducing friction between two objects.

Newton´s Laws of Motion

After Newton established the three Newton’s laws of motion; the way people saw the motion of the objects was change.

Let start knowing a little about Sir Isaac Newton.

There was this fellow in England named Sir Isaac Newton, one of the greatest scientists and mathematicians that ever lived. A little bit stuffy, bad hair, but quite an intelligent guy. He worked on developing calculus and physics at the same time.

Sir He was born in England on December 25, 1643. He was born the same year that Galileo died. He lived for 85 years.

Isaac Newton was raised by his grandmother. He attended Free Grammar School and then went on to Trinity College Cambridge. Newton worked his way through college. While at college he became interested in math, physics, and astronomy. Newton received both a bachelors and masters degree. While Newton was in college he was writing his ideas in a journal. Newton had new ideas about motion, gravity, the diffraction of light, and forces. Newton's ideas were so good that Queen Anne knighted him in 1705. His accomplishments laid the foundations for modern science and revolutionized the world. Sir Isaac Newton died in 1727.

During his work, he came up with the three basic ideas that are applied to the physics of most motion (NOT modern physics). 

The ideas have been tested and verified so many times over the years, that scientists now call them Newton's Three Laws of Motion. 

Newton´s 1^st law of motion

¨An object at rest will remain at rest unless unbalanced forces acted on it, and an object in motion will continuous moving with a constant velocity and in a straight line unless unbalanced forces acted on it¨

Motion (or lack of motion) cannot change without unbalanced force acting. If nothing is happening to you, and nothing does happen, you will never go anywhere. If you're going in a specific direction, unless something happens to you, you will always go in that direction. Forever. 

This law sometimes is called law of Inertia. Inertia is the capacity of all the objects to resist any changes in motion. In other words:

This law is the same reason why you should always wear your seatbelt.

Newton´s 2^nd law of motion

¨"The acceleration of an object depends on the mass of the object an the amount of force applied"

Everyone unconsciously knows the Second Law. Everyone knows that heavier objects require more force to move the same distance as lighter objects.

This law permits us to calculate the force required moving objects, or the acceleration of an object after a force acted on it.

This law can be written as:

a=F/m

a is acceleration in m/s²

F is net force in N

m is mass in kg

We can use this equation to calculate Force or mass, using the triangle to clearway the unknown. Remember for use the triangle you just have to cover the unknown and you will obtain the formula that you need.

Newton´s 3^rd law of motion

¨Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first. For every action there is an equal and opposite reaction¨

This means that for every force there is a reaction force that is equal in size, but opposite in direction. That is to say that whenever an object pushes another object it gets pushed back in the opposite direction equally hard. Forces are found in pairs.

Think about the time you sit in a chair. Your body exerts a force downward and that chair needs to exert an equal force upward or the chair will collapse. It's an issue of symmetry. Acting forces encounter other forces in the opposite direction. There's also the example of shooting a cannonball. When the cannonball is fired through the air (by the explosion), the cannon is pushed backward. The force pushing the ball out was equal to the force pushing the cannon back, but the effect on the cannon is less noticeable because it has a much larger mass. That example is similar to the kick when a gun fires a bullet forward. 

This law is exemplified by what happens if we step off a boat onto the bank of a lake: as we move in the direction of the shore, the boat tends to move in the opposite direction (leaving us facedown in the water, if we aren't careful!).

I. Solve the following problems

1. What net force is required to accelerate a car at a rate of 2 m/s² if the car has a mass of 3,000 kg?

 2. A10 kg bowling ball would require what force to accelerate down an alleyway at a rate of 3 m/s²?

3. Sally has a car that accelerates at 5 m/s². If the car has a mass of 1000 kg, how much force does the car produce?

4. What is the mass of a falling rock if it produces a force of 147 N?

5. What is the mass of a truck if it produces a force of 14,000 N while accelerating at a rate of 5 m/s² ?

6. What is the acceleration of softball if it has a mass of 0.5 kg and hits the catcher's glove with a force of 25 N?

7. Your own car has a mass of 2000 kg. If your car produces a force of 5000 N, how fast will it accelerate?

8. Sally wants to accelerate even faster than in problem #3, so she removes 500 kg of mass from her car. How fast will her 1500 kg car accelerate if it produces 5000 N of force?

9. Sally challenges you to a race. On the first turn you run off the course and your car strikes a large bale of hay. Your car still produces 5000 N of force, but now it accelerates at only 2 m/s². What is the mass of your car now that the bale of hay is stuck to it?

10. Even tough she is way ahead of you, Sally switches her car to run on nitrous oxide fuel. The nitrous oxide allows her car to develop 10,000 N of force. What is Sally's acceleration if her car has a mass of 500 kg?

II. Write the term that matches each description in items 1 through 6 below on the spaces provided.

Unscramble the boxed letters to spell the term that answers question 7.

			1
					2
3
							4
				5
		6

1. A measure of an object’s tendency to remain at rest or continue at constant speed

2. How far something travels

3. How far something ends up from its starting place

4. A push or a pull

5. Forces that result in no change in an object’s motion

6. The force that resists motion

7. An object will remain at rest or move in a straight line with constant speed unless it is acted upon by a force. This is the definition of Newton’s first law of

III. Give three daily examples for daily applications for each one of the three Newton´s laws of motion.

IV. Use Newton´s 3^rd law of motion to explain why your foot hurt after you kick a rock

V. What is inertia?      

VI. Rockets make use of Newton’s third law of motion. What is that law?

VII. A spacecraft traveling through space can travel at a constant speed and in a straight path without using engines. Why?