Chapter 4: Forces and Newton's Laws of Motion Quick Check

Q1. The net force on an object points to the left. Two of three forces are shown. Which is the missing third force?

Background

Topic: Vector Addition of Forces

This question tests your understanding of how multiple forces combine to produce a net force, specifically using vector addition and Newton's Second Law.

Key Terms and Formulas

• Force (): A vector quantity that causes acceleration.

• Net Force (): The vector sum of all forces acting on an object.

• Newton's Second Law:

• Vector Addition:

Step-by-Step Guidance

1. Identify the direction of the net force (to the left) and the directions of the two given forces ( and ).

2. Draw or visualize the vector addition of and ; consider their vertical and horizontal components.

3. Determine what vector must be added to and so that the sum points to the left.

4. Check if the vertical components cancel, leaving only a horizontal component pointing left.

Try solving on your own before revealing the answer!

Q2. A ball rolls down an incline and off a horizontal ramp. Ignoring air resistance, what force or forces act on the ball as it moves through the air just after leaving the horizontal ramp?

Background

Topic: Forces on a Projectile

This question tests your understanding of projectile motion and the forces acting on an object in free flight.

Key Terms and Formulas

• Projectile: An object moving through the air under the influence of gravity only.

• Gravity (): The force acting downward on the ball.

• Newton's First Law: An object in motion remains in motion unless acted upon by a net force.

Step-by-Step Guidance

1. After the ball leaves the ramp, consider what forces are acting on it (no contact with ramp).

2. Ignore air resistance as stated in the question.

3. Identify the long-range force acting on the ball (gravity).

4. Recognize that no horizontal force acts on the ball after it leaves the ramp; its horizontal motion is due to inertia.

Try solving on your own before revealing the answer!

Q3. A cart is pulled to the right with a constant, steady force. How will its acceleration graph look?

Background

Topic: Newton's Second Law and Acceleration Graphs

This question tests your ability to relate a constant force to the resulting acceleration of an object.

Key Terms and Formulas

• Acceleration (): The rate of change of velocity.

• Newton's Second Law:

• Constant Force: Implies constant acceleration if mass is constant.

Step-by-Step Guidance

1. Recall that a constant force applied to a mass produces a constant acceleration.

2. Examine the three acceleration graphs and identify which one represents constant acceleration.

3. Match the graph to the physical scenario described (cart pulled with steady force).

4. Consider the relationship: , where is constant.

Try solving on your own before revealing the answer!

Q4. An elevator, lifted by a cable, is moving upward and slowing. Which is the correct free-body diagram?

Background

Topic: Free-Body Diagrams and Newton's Second Law

This question tests your ability to analyze forces acting on an object in motion, specifically when the object is slowing down.

Key Terms and Formulas

• Free-Body Diagram: A visual representation of all forces acting on an object.

• Tension (): The force exerted by the cable.

• Weight (): The force of gravity acting downward.

• Net Force (): Determines the direction of acceleration.

Step-by-Step Guidance

1. Identify the forces acting on the elevator: tension upward and weight downward.

2. Since the elevator is moving upward but slowing, its acceleration is downward.

3. Determine which diagram shows a net force pointing downward (tension less than weight).

4. Compare the length of the arrows representing tension and weight in each diagram.

Try solving on your own before revealing the answer!

Q5. A ball has been tossed straight up. Which is the correct free-body diagram just after the ball has left the hand? Ignore air resistance.

Background

Topic: Free-Body Diagrams for Projectile Motion

This question tests your understanding of the forces acting on a projectile immediately after it leaves contact with the thrower.

Key Terms and Formulas

• Gravity (): The only force acting on the ball after it leaves the hand.

• Projectile: An object in free flight under gravity.

Step-by-Step Guidance

1. After the ball leaves the hand, it is no longer in contact with any other object.

2. Ignore air resistance as stated in the question.

3. Draw the free-body diagram showing only the force of gravity acting downward.

4. Check that no other forces (such as upward push) are present.

Try solving on your own before revealing the answer!