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Chapter Four Problems

1. Define Work:

 

 

Explain why forces that are perpindicular to motion do not do any work on the object?

 

 

If it took a certain amount of work to move an object a certain distance, how much more work would it take to move the same object with the same force three times the distance?

 

 

 

If it took a certain amount of work to move an object a certain distance, how much more work would it take to move the same object with twice the force over the same distance?

 

 

 

What relationship does work have with distance?

 

  With Force?

 

  If it took a certain amount of work to move an object a certain distance, how much more work would it take to move the same object with twice the force over three times the distance? (6 times the work)

 

 

 

If you wanted to maintain the same amount of work in stopping a car over a certain distance, but use half the force to do so, how would your distance have to change?

 

 

 

If your work quadrupled from a certain amount in moving an object, list three ways this could be accomplished.

 

 

 

 

 

2. A sled 5-kg sled is carrying a 45-kg box, and is being pulled with a force of 250 N at a 45 degree angle. If sled is pulled with a distance of 15 meters, and the coefficient of kinetic friction is .5, find the work done by the applied force. (2652 J)

 

 

 

How much of the applied work went into overcoming frictional work? (-2349 J)

 

 

 

What is the total work done on the object? (303 J)

 

 

 

A 50-kg sled is pulled acrossed the floor for a distance of 15 meters with a force of 250 N. If the coefficient of friction is .5, find the work done by the applied force. (3750 J)

 

 

 

How much of the applied work was done in overcoming frictional work? (-3675 J)

 

 

 

Find the total work done on the object. (75 J)

 

 

 

Use the following questions to discover the three keys to total work on an object on your lecture sheet:

1. If the net force on the object is zero, what is the total work done?

 

2. If The applied force is larger than the frictional force, the net force is positive, and the object is speeding up (accelerating). Would the total work be positive or negative?

 

3. If The frictional force is larger than the Applied force, the net force is negative, and the object is slowing down (accelerating). Would the total work be positive or negative?

 

 

Ten thousand Joules of total work was done on a car. If the work done by the engine equaled 13,000 J, how much work was done by air-resistance? (3000 J).

 

 

  What must be true about the work done by the engine and the air-resistance, so that the car travels at a constant velocity?

 

 

 

In suming up the three keys of total work done, answer the following:

What happens to a car's acceleration if the work done by the car is greater than the frictional force's work?

 

What happens to the car's acceleration if the work done by the car is less than the frictional force's work?

 

What happens to the car's acceleration is the work done by the car is equal to the work done by the frictional force's work?

 

 

3. A 35-kg crate is being pulled up an incline with an angle of 40 degrees. The coefficient of kinetic friction is .40. If the crate is pulled a distance of 10.0 meters, and the force used is equal to 400 N, draw in all of the forces in the picture below.

Find the work done by the applied force. (4000 J)

 

 

Find the work done by the frictional force. (- 1050 J)

 

 

Find the work done by the parallel force. (- 2200 J)

 

 

What was the total work done on the crate? (750 J)

 

 

How do you know that the crate went up the incline instead of down from the last answer?

 

 

 

 

Why is the work done by the parallel force negative in this problem?

 

 

What must the force equal so that the total work done on the crate is zero? (325 N)

 

 

Would the crate be accelerating or moving a constant speed? Explain.

 

 

4. What is the relationship between the work done on an object and the velocity it attains?

 

 

What does that mean in terms of: does it take a lot of work, or a little work to get a small change in velocity?

 

 

It takes a certain amount of work to get a car from 0 to 20 mph. How much more work would it take to get the car from 0 to 40 mph? (Answer this with 2 times or 3 times, not an actual amount of work).

 

 

How much more work would it take to get the car from 0 to 60 mph?

 

 

 

Keep in mind W = Fx = 1/2mVf^2 - 1/2mVo^2. Answer the following questions based on a car's engine doing a certain amount of work (from rest) over a certain amount of distance (which means the engine accelerates the car to a certain speed and in doing so, had to travel a distance).

If you wanted to do 36 times the work, but do it over the same original distance, how much more force must the engine supply?

 

 

If you wanted to do 36 times the work, how could you change the distance with which you did the work so that you would only need to increase the force by four times? (In other words, make the engine use a force that is only four times bigger than the original).

 

 

If you wanted to do 36 times the work, how could you change the distance with which you did the work so that you would only need to increase the force by six times? (In other words, make the engine use a force that is only six times bigger than the original).

 

 

What happens to the force needed by the engine as the distance over which the car does the work increases?

 

 

In the end, it doesn't matter how the car does the work (either large force over a small distance, or small force over a large distanct), the same work will be done on the car, which means the car will reach a new velocity. If the work is 36 times more than the original, how much does the velocity increase?

 

 

 

 

5. A quarterback throws a 40-mph pass down the field. With what force does he do so if the football’s mass is .65-kg and the distance with which he throws the ball is .90 m? (115 N = 26 lb).

 

 

 

How much work was done on the football? ( 104 J)

 

 

 

How much kinetic energy was given to the football? Show by using the KE equation too. (104 J).

 

 

 

How much work will a receiver have to do in order to bring the football to a stop? ( 104 J)

 

 

 

With what force does the football hit the receiver in the chest if the impact distance is 2.0 cm? (5200 N = 1200 lb).

 

 

 

Why do you suppose such a big force does not knock the receiver down? (hint: we've answered this type of question before).

 

 

 

How can the receiver use his hands to make the force of impact less?

 

 

 

A 1.0-kg trout is hooked by a fisherman and swims off at 2.5 m/s. The fisherman stops the trout in .50 meters by braking his reel. How much tension (force) in pounds is exerted on the line? (6.25 N = 1.41 pounds)

 

 

 

If the fisherman in problem six wanted to have less force exerted on the line, but still stop the same fish that had the same speed, would he have to stop the fish with a bigger distance or smaller distance? Explain.

 

 

 

We have determined in class that there is no avoiding the following truth (Fill in the blanks with the appropriate words:

However, we can control the amount of force needed to either make the object move or stop by adjusting what variable? Explain using logic.

 

 

 

6. In the picture below, fill in the correct amount of work, and explain why the force used to stop the car is very large!

If the mass of the car were 800-kg, how fast was the car traveling before it hit the wall? ( 20 m/s = 45 mph).

 

 

If the impact distance were .50 meters, with what force did the car hit the wall? (320,000 N = 72,000 pounds).

 

 

If your mass was 60-kg (you are traveling the same speed as the car) and you weren't wearing a seatbelt, with what force would you hit the dashboard if your impact distance was .25 meters? (48,000 N = 11,000 pounds)

 

 

What would have to be the impact distance in this situation, so that the force stopping the car would be 11,000 N, which is approximately 30 times smaller than the force above. (15 meters).

 

 

Why do you suppose cars are built so that they crumple on impact? What does the crumpling accomplish? Explain.

 

 

A car is traveling 70 mph and is approaching another car traveling at 80 mph. If they were to have a head on collision, how much more damage would occur to both cars as compared to if one car were to hit a tree head on at 25 mph?

 

 

If work had a direct straight line relationship with velocity, how would the damage due to a wreck increase as the velocity increased?

 

 

How has your perception of driving too fast and the dangers involved with a crash changed knowing what you know now?

 

 

 

 

7. Explain why two ramps of the same height but with different slopes will result in the same speed.

 

 

Explain why the work to raise an object up a certin height is equal to mgh:

 

 

Define the Conservation of Energy:

 

 

Fill in the blanks in the picture below that summarizes energy conservation:

How much work could the ball do on on something (or how much work would it require to stop

 

 

The Conservation of Energy Law says energy is neither created nor destroyed. What does happen to energy throughout a situation such as that in the picture above?

 

 

Now consider energy lost due to friction in the picture below:


Does the fact heat is lost due to friction violate the Conservation of Energy? Explain.

 

 

Now explain Galileo's argument about the ball stopping when it reaches its original height (On a double ramp) in terms of energy.

 

 

8. A 3.0-kg rock is dropped from a height of 100 meters. Find the its kinetic energy and potential energies when it is 50 meters from the ground. (PE = 1470 J, KE = 1470 J)

 

How fast is it going at that point? (31 m/s)

 

How fast is the ball going when it hits the ground? (44 m/s)

 

 

A ball has a potential energy of 196 J. If its mass is 2.0 kg, how high is it in the air? (10 meters)

 

 

A falling stone gains kinetic energy as it loses potential energy thereby keeping the total energy constant. However, when the stone hits the ground, it loses all of its kinetic energy, but it is not restored to potential energy. Where does the energy go to ensure energy conservation?

 

 

For Honors Physics only:

A 5.0-kg ball is dropped from a height of 60 meters. How high above the ground will it be when one-third of the total energy is kinetic energy? (40 meters)

 

 

A woman skis down a slope 100 meters high. Her speed at the foot of the slope is 20 m/s. What percentage of her initial potential energy was lost due to friction? (80 percent)