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• An object at rest remains at rest, and an object in motion continues in motion with constant velocity (that is, constant speed in a straight line) unless the object experiences a net external force.
• In other words, when the net external force on an object is zero, the object’s acceleration (or the change in the object’s velocity) is zero.
• Newton's first law refers to the net force on an object.The net force is the vector sum of all forces acting on an object.
• The net force on an object can be found by using the methods for finding resultant vectors.
Section 2 Newton’s First Law
Although several forces are acting on this car, the vector sum of the forces is zero. Thus, the net force is zero, and the car moves at a constant velocity.
2. Select a coordinate system, and apply it to the free-body diagram.
Tip: To simplify the problem, always choose the coordinate system in which as many forces as possible lie on the x- and y-axes.
Choose the x-axis parallel to and the y-axis perpendicular to the incline of the table, as shown in (a). This coordinate system is the most convenient because only one force needs to be resolved into x and y components.
• Inertia is the tendency of an object to resist being moved or, if the object is moving, to resist a change in speed or direction.
• Newton’s first law is often referred to as the law of inertia because it states that in the absence of a net force, a body will preserve its state of motion.
• Equilibrium is the state in which the net force on an object is zero.
• Objects that are either at rest or moving with constant velocity are said to be in equilibrium.
• Newton’s first law describes objects in equilibrium.
Tip: To determine whether a body is in equilibrium, find the net force. If the net force is zero, the body is in equilibrium. If there is a net force, a second force equal and opposite to this net force will put the body in equilibrium.
• If two objects interact, the magnitude of the force exerted on object 1 by object 2 is equal to the magnitude of the force simultaneously exerted on object 2 by object 1, and these two forces are opposite in direction.
• In other words, for every action, there is an equal and opposite reaction.
• Because the forces coexist, either force can be called the action or the reaction.
• Action-reaction pairs do not imply that the net force on either object is zero.
• The action-reaction forces are equal and opposite, but either object may still have a net force on it.
Section 3 Newton’s Second and Third Laws
Consider driving a nail into wood with a hammer. The force that the nail exerts on the hammer is equal and opposite to the force that the hammer exerts on the nail. But there is a net force acting on the nail, which drives the nail into the wood.
• The normal force acts on a surface in a direction perpendicular to the surface.
• The normal force is not always opposite in direction to the force due to gravity.
– In the absence of other forces, the normal force is equal and opposite to the component of gravitational force that is perpendicular to the contact surface.
• In free-body diagrams, the force of friction is always parallel to the surface of contact.
• The force of kinetic friction is always opposite the direction of motion.
• To determine the direction of the force of static friction, use the principle of equilibrium. For an object in equilibrium, the frictional force must point in the direction that results in a net force of zero.
Overcoming Friction A student attaches a rope to a 20.0 kg box of
books.He pulls with a force of 90.0 N at an angle of 30.0° with the horizontal. The coefficient of kinetic friction between the box and the sidewalk is 0.500. Find the acceleration of the box.
4. Evaluate The box accelerates in the direction of the net force, in accordance with Newton’s second law. The normal force is not equal in magnitude to the weight because the y component of the student’s pull on the rope helps support the box.
• Air resistance is a form of friction. Whenever an object moves through a fluid medium, such as air or water, the fluid provides a resistance to the object’s motion.
• For a falling object, when the upward force of air resistance balances the downward gravitational force, the net force on the object is zero. The object continues to move downward with a constant maximum speed, called the terminal speed.
Use the passage below to answer questions 1–2. Two blocks of masses m1 and m2 are placed in contact with each other on a smooth, horizontal surface. Block m1 is on the left of block m2. A constant horizontal force F to the right is applied to m1.
Use the passage below to answer questions 1–2. Two blocks of masses m1 and m2 are placed in contact with each other on a smooth, horizontal surface. Block m1 is on the left of block m2. A constant horizontal force F to the right is applied to m1.
Multiple Choice, continued Use the passage below to answer questions 1–2.
Two blocks of masses m1 and m2 are placed in contact with each other on a smooth, horizontal surface. Block m1 is on the left of block m2. A constant horizontal force F to the right is applied to m1.
2. What is the horizontal force acting on m2? F. m1a G. m2a H. (m1 + m2)a J. m1m2a
Multiple Choice, continued Use the passage below to answer questions 1–2.
Two blocks of masses m1 and m2 are placed in contact with each other on a smooth, horizontal surface. Block m1 is on the left of block m2. A constant horizontal force F to the right is applied to m1.
2. What is the horizontal force acting on m2? F. m1a G. m2a H. (m1 + m2)a J. m1m2a
3. A crate is pulled to the right with a force of 82.0 N, to the left with a force of 115 N, upward with a force of 565 N, and downward with a force of 236 N. Find the magnitude and direction of the net force on the crate.
A. 3.30 N at 96° counterclockwise from the positive x-axis B. 3.30 N at 6° counterclockwise from the positive x-axis C. 3.30 x 102 at 96° counterclockwise from the positive x-axis D. 3.30 x 102 at 6° counterclockwise from the positive x-axis
3. A crate is pulled to the right with a force of 82.0 N, to the left with a force of 115 N, upward with a force of 565 N, and downward with a force of 236 N. Find the magnitude and direction of the net force on the crate.
A. 3.30 N at 96° counterclockwise from the positive x-axis B. 3.30 N at 6° counterclockwise from the positive x-axis C. 3.30 x 102 at 96° counterclockwise from the positive x-axis D. 3.30 x 102 at 6° counterclockwise from the positive x-axis
5. A freight train has a mass of 1.5 x 107 kg. If the locomotive can exert a constant pull of 7.5 x 105 N, how long would it take to increase the speed of the train from rest to 85 km/h? (Disregard friction.)
A. 4.7 x 102s B. 4.7s C. 5.0 x 10-2s D. 5.0 x 104s
5. A freight train has a mass of 1.5 x 107 kg. If the locomotive can exert a constant pull of 7.5 x 105 N, how long would it take to increase the speed of the train from rest to 85 km/h? (Disregard friction.)
A. 4.7 x 102s B. 4.7s C. 5.0 x 10-2s D. 5.0 x 104s
Use the passage below to answer questions 6–7. A truck driver slams on the brakes and skids to a stop through a displacement Δx.
Standardized Test Prep Chapter 4
6. If the truck’s mass doubles, find the truck’s skidding distance in terms of Δx. (Hint: Increasing the mass increases the normal force.) A. Δx/4 B. Δx C. 2Δx D. 4Δx
Use the passage below to answer questions 6–7. A truck driver slams on the brakes and skids to a stop through a displacement Δx.
Standardized Test Prep Chapter 4
6. If the truck’s mass doubles, find the truck’s skidding distance in terms of Δx. (Hint: Increasing the mass increases the normal force.) A. Δx/4 B. Δx C. 2Δx D. 4Δx
Base your answers to questions 10–12 on the information below. A 3.00 kg ball is dropped from rest from the roof of a building 176.4 m high.While the ball is falling, a horizontal wind exerts a constant force of 12.0 N on the ball.
10. How long does the ball take to hit the ground?
Base your answers to questions 10–12 on the information below. A 3.00 kg ball is dropped from rest from the roof of a building 176.4 m high.While the ball is falling, a horizontal wind exerts a constant force of 12.0 N on the ball.
10. How long does the ball take to hit the ground? Answer: 6.00 s
Base your answers to questions 10–12 on the information below. A 3.00 kg ball is dropped from rest from the roof of a building 176.4 m high.While the ball is falling, a horizontal wind exerts a constant force of 12.0 N on the ball.
11. How far from the building does the ball hit the ground?
Base your answers to questions 10–12 on the information below. A 3.00 kg ball is dropped from rest from the roof of a building 176.4 m high.While the ball is falling, a horizontal wind exerts a constant force of 12.0 N on the ball.
11. How far from the building does the ball hit the ground? Answer: 72.0 m
Base your answers to questions 10–12 on the information below. A 3.00 kg ball is dropped from rest from the roof of a building 176.4 m high.While the ball is falling, a horizontal wind exerts a constant force of 12.0 N on the ball.
12. When the ball hits the ground, what is its speed?
Base your answers to questions 10–12 on the information below. A 3.00 kg ball is dropped from rest from the roof of a building 176.4 m high.While the ball is falling, a horizontal wind exerts a constant force of 12.0 N on the ball.
12. When the ball hits the ground, what is its speed? Answer: 63.6 m/s
Base your answers to questions 13–15 on the passage.
A crate rests on the horizontal bed of a pickup truck. For each situation described below, indicate the motion of the crate relative to the ground, the motion of the crate relative to the truck, and whether the crate will hit the front wall of the truck bed, the back wall, or neither. Disregard friction.
13. Starting at rest, the truck accelerates to the right.
Base your answers to questions 13–15 on the passage.
A crate rests on the horizontal bed of a pickup truck. For each situation described below, indicate the motion of the crate relative to the ground, the motion of the crate relative to the truck, and whether the crate will hit the front wall of the truck bed, the back wall, or neither. Disregard friction.
13. Starting at rest, the truck accelerates to the right. Answer: at rest, moves to the left, hits back wall
Base your answers to questions 13–15 on the passage.
A crate rests on the horizontal bed of a pickup truck. For each situation described below, indicate the motion of the crate relative to the ground, the motion of the crate relative to the truck, and whether the crate will hit the front wall of the truck bed, the back wall, or neither. Disregard friction.
14. The crate is at rest relative to the truck while the truck moves with a constant velocity to the right.
Base your answers to questions 13–15 on the passage.
A crate rests on the horizontal bed of a pickup truck. For each situation described below, indicate the motion of the crate relative to the ground, the motion of the crate relative to the truck, and whether the crate will hit the front wall of the truck bed, the back wall, or neither. Disregard friction.
14. The crate is at rest relative to the truck while the truck moves with a constant velocity to the right. Answer: moves to the right, at rest, neither
Base your answers to questions 13–15 on the passage.
A crate rests on the horizontal bed of a pickup truck. For each situation described below, indicate the motion of the crate relative to the ground, the motion of the crate relative to the truck, and whether the crate will hit the front wall of the truck bed, the back wall, or neither. Disregard friction.
Base your answers to questions 13–15 on the passage.
A crate rests on the horizontal bed of a pickup truck. For each situation described below, indicate the motion of the crate relative to the ground, the motion of the crate relative to the truck, and whether the crate will hit the front wall of the truck bed, the back wall, or neither. Disregard friction.
15. The truck in item 14 slows down. Answer: moves to the right, moves to the right,
16. A student pulls a rope attached to a 10.0 kg wooden sled and moves the sled across dry snow. The student pulls with a force of 15.0 N at an angle of 45.0º. If µk between the sled and the snow is 0.040, what is the sled’s acceleration? Show your work.
16. A student pulls a rope attached to a 10.0 kg wooden sled and moves the sled across dry snow. The student pulls with a force of 15.0 N at an angle of 45.0º. If µk between the sled and the snow is 0.040, what is the sled’s acceleration? Show your work.
Extended Response, continued 17. You can keep a 3 kg book from dropping by pushing
it horizontally against a wall. Draw force diagrams, and identify all the forces involved. How do they combine to result in a zero net force? Will the force you must supply to hold the book up be different for different types of walls? Design a series of experiments to test your answer. Identify exactly which measurements will be necessary and what equipment you will need.
17. You can keep a 3 kg book from dropping by pushing it horizontally against a wall. Draw force diagrams, and identify all the forces involved. How do they combine to result in a zero net force? Will the force you must supply to hold the book up be different for different types of walls? Design a series of experiments to test your answer. Identify exactly which measurements will be necessary and what equipment you will need.
Answer: Plans should involve measuring forces such as weight, applied force, normal force, and friction.