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Chapter Three Problems

1. Explain Aristotle's concept of the "Natural State of Motion."

 

 

 

 

Why do you suppose Aristotle thought this way about motion? (Think about their experience with everyday life).

 

 

 

 

Explain Galileo's logic to refute Aristotle's idea of motion including the diagrams:

 

 

 

 

In order for Galileo's logical argument to work, what did he have to neglect?

 

 

 

 

How does this contrast with Aristotle's view point?

 

 

 

 

2. Define the term inertia:

 

 

 

 

Which quantity is more fundamental: mass or weight? Explain why.

 

 

 

 

Is it possible for an object to have mass but no weight? Give an example if possible.

 

 

Is it possible for an object to have weight but no mass? Give an example if possible.

 

 

Which object has more mass: a one cubic meter piece of steel, or a one cubic meter piece of wood? Explain why.

 

 

Which object has more mass: a one pound piece of iron, or one pound of feathers? (Careful with this answer!) Explain why.

 

 

Explain the last two levels in terms of density: which object out of each pair is more dense?

 

 

Can an object have a small density but large inertia? Give an example if possible.

 

 

3. State Newton's First Law of Motion:

 

 

 

 

Which part of Newton's First Law did Aristotle not consider and why?

 

 

 

 

Come up with your own example of the first part of the First Law:

 

 

 

 

Come up with your own example of the second part of the First Law:

 

 

 

 

Why is the First Law often referred to as the Law of Inertia?

 

 

 

 

In the movie True Lies, Arnold Schwarzenneger tries to get a horse to jump from one building top to another, but the horse stops at the edge and Arnold flies over the top of the horse. Which part of Newton's First Law explains why that happened?

 

 

 

 

A friend is pulling you in a wagon from rest, but pulls too hard and you fall backwards onto the ground. Which part of Newton's First Law explains why that happened?

 

 

 

 

4. Define Force:

 

 

 

 

What does Net Force mean?

 

 

 

 

The net force on a box is zero. Does that mean there are no forces acting on the box? Explain.

 

 

 

 

If the net force on an object is zero, does that mean the object is not moving? Explain.

 

 

 

 

What must the acceleration be for an object if Newton's First Law applies to its motion?

 

 

 

What is the net force on an object if Newton's First Law applies to its motion?

 

 

 

What can you conclude about acceleration and net force?

 

 

 

 

5. What is the relationship between Force and Acceleration?

 

 

 

 

If you were to double the force on an object, what would happen to its acceleration?

 

 

 

 

If you wanted your acceleration to drop by one fourth, how would you have to change the force?

 

 

 

 

A .045-kg golf ball at rest on a tee is struck by a driver and flies off with a speed of 40 m/s. If the impact time was .00010 seconds, find the force on the ball. (F = 18,000 N = 4050 pounds).

 

 

 

 

A .149-kg baseball traveling at 90 mph is struck by a bat and flies off in the opposite direction with a speed of 100 mph. If the impact time was .00050 seconds, find the force on the ball. (convert the mph to m/s!) (F = -25,000 N = -5,700 pounds).

 

 

 

 

In the last two problems, how is it possible for the force to be so large and yet the golf-club and baseball bat do not break?

 

 

 

 

6. A 100-kg motorcycle carrying a 70-kg rider comes to a stop in 40 m from a speed of 50 km/h (14 m/s) when its brakes are applied. Find the force exerted by the brakes in pounds. (F = -416.5 N = -94 pounds)

 

 

 

 

Find the force exerted on only the rider in pounds. (F = -172 N = -39 pounds)

 

 

 

 

An empty truck whose mass is 2000-kg has a maximum acceleration of 1.0 m/s^2. What is its maximum acceleration when it is carrying a 1000-kg load? (.67 m/s^2)

 

 

 

 

A bicycle and its rider together have a mass of 80-kg. If the bicycle's speed is 6.0 m/s, how much force is needed to bring it to a stop in 4.0 seconds? (F = -120 N = -27 pounds)

 

 

 

 

A force of 3000 Newtons is applied to a 1000-kg car when the driver steps on the gas. If the acceleration of the car is 2.0 m/s^2, what must be the force exerted on the car by the air resistance? (1000 N)

 

 

 

 

We know that acceleration does not have to point in the direction of motion. If the acceleration points in the opposite direction, the object will be slowing down. However, does net force always point in the direction of acceleration? Defend your answer.

 

 

 

 

7. A 120.0-kg person is hanging from a rope that has a maximum tension of 1500.0 N. Draw the force diagram.

 

 

 

 

Write the net force equation:

 

 

What is the tension in the rope if the person is just hanging there? (T = 1176 N)

 

 

If the person pulls up with an acceleratio of 2.5 m/s^2, will the rope break? You must show your work to prove your answer.

 

 

 

 

What is the maximum acceleration the person can have without breaking the roge? (2.7 m/s^2).

 

 

 

 

If the person pulled up with a force of 300 Newtons, would the rope break? You must show your work to prove your answer.

 

 

 

 

What is the maximum force the person can use to pull himself up without breaking the rope? (324 N).

 

 

 

 

Why does the tension in the rope increase when the person pulls himself up?

 

 

 

 

What would happen to the tension in the rope if the person were to slide down the rope? Explain!

 

 

 

 

8. A 70-kg person stands on a scale in an elevator. How many Newtons does the scale read when the elevator is at rest? (686 N)

 

 

What will the scale read when the elevator is accelerating up at 2.0 m/s^2? (826 N)

 

 

What will the scale read when the elevator is accelerating down at 2.0 m/s^2? (546 N)

 

 

When it is moving up at a constant speed of 3.0 m/s? (686 N)

 

 

When it is moving down at a constant speed of 4.0 m/s? (686 N)

 

 

Why are the last two answers the same as the first answer? Which of Newton's Laws explains this?

 

 

A 150-kg man is standing on a scale in an elevator. The scale reads 1470 Newtons. Is the elevator moving or standing still? Show why by seeing if that reading is greater than, less than, or the same as his weight.

 

 

Suddenly the scale reads 1570 N. Is the elevator moving up or down?

 

 

What is the acceleration? (a = + .67 m/s^2)

 

 

If the scale read suddenly reads 1270 N, is the elevator moving up or down?

 

 

What is the acceleration? (a = - 1.3 m/s^2)

 

 

If the elevator cable’s maximum tension is 15,000 N, and the elevator weighs 8530 N, what is the maximum acceleration possible? Assume the man is still inside. (a = 4.9 m/s^2)

 

 

Why must the scale read more than the person's weight when the elevator is accelerating up?

 

 

Why must the scale read less then the person's weight when the elevator is accelerating down?

 

 

We know if the elevator's acceleration is -9.8 m/s^2 (meaning it is falling at the same rate of gravity), the scale would read zero, and the person would feel weightless. What happens if the elevator's acceleration is greater than -9.8 m/s^2? In other words, what would the person feel and where would that person be?

 

 

 

 

9. A 5.0-kg block is suspended from a rope attached to the ceiling. A 10.0-kg mass is attached to Another rope, which is attached to the bottom of the 5.0-kg block. Find the tension in the rope that is attached to the ceiling. (147 N)

 

 

Find the tension in the rope that is attached to the bottom of the 5.0-kg block. (98 N)

 

 

If the blocks now accelerate up at 2.0 m/s^2, find the tension in both ropes. (177 N and 118 N)

 

 

Why do you suppose the tension in the top string is larger than the bottom string?

 

 

How much net force must one supply to give a 1.0-kg object an upward acceleration of 2g. This means the acceleration is 2 times 9.8. (F = 19.6 N)

 

 

How much is this force compared to the weight of the object? (2 times)

 

 

How much force is actually exerted by the hand on the object? (29.4 N or 3 times the weight)

 

 

Explain why the total force exerted by the hand is 3 times the weight.

 

 

How much net force must one supply to give the same object a downward acceleration of 2g? (19.6 N)

 

 

How much force is actually exerted by the hand on the object this time? (9.8 N or one times the weight)

 

 

Why is this force so much less than the force required for the upward acceleration?

 

 

10. Find the acceleration equation for the following diagram below:

Step One: Draw the force diagram for each mass.

 

 

 

 

Step Two: Determine which forces are positive and negative.

 

 

 

 

Step Three: Write the net force Equations

 

 

 

 

Step Four: Solve for a

 

 

 

 

Consider the three following scenarios:

a. If the mass on the table is larger than the hanging mass, how does the acceleration compare to the acceleration when the two masses are equal?

 

 

b. When the two masses are equal, explain why a = g/2.

 

 

c. If the mass on the table is smaller than the hanging mass, how does the acceleration compare to the acceleration when the two masses are equal?

 

 

Consider the picture below when following the steps to deriving the acceleration equation. (Hint: the string that connects the hanging mass (mass 3) and the first mass (mass 1), is tension one. The string that connects mass 1 to mass 2 is tension 2)

Step One: Draw the Force Diagram:

 

 

 

 

 

 

Step Two: +/- Forces for each mass

 

 

 

 

 

 

Step Three: Net force equation for each mass:

 

 

 

 

 

 

Click here for the answer!

  For Honors Physics only:

 

Step Four: Solve the system of equations for acceleration.

 

 

 

 

 

 

Click here for the answer!

  What would the acceleration equal if all the masses were equal? (a = g/3)