Newton’s second law

an object of mass m

Free-body diagram

Applying Newton’s second law

1. Draw a picture of the situation.

2. Identify the “object” that you will analyze.

3. Identify forces on the object (think of what interacts with the object; for tips, see next slide).

4. Draw a force diagram, showing all forces acting on the object.

5. Write Newton’s second law in component form.

6. Substitute forces from your force diagram into your equations.

7. Identify known forces and the acceleration (if it is known). Identify the unknown variable.

8. Do the math.

9. Check your work.

Identifying forces

To identify all forces acting on an object, ask yourself the following:

1. What objects are “touching” the given object? These are contact forces.

2. What objects exert a force through “action at a distance” such as a gravitational, electrostatic, or magnetic force? These are action-at-a-distance forces.

Gravitational force of Earth on a body is called weight.

Poll

What objects exert a force on box B?

1. Earth, table, box A

2. Earth, table, box A, hand

3. table, box A, hand

4. Earth, floor, hand

5. box A

Contact Forces - Surface Interactions

The component of a contact force perpendicular to the surface(s) is called the normal component of the contact force.

The component of a contact force parallel to the surface(s) is called the frictional component of the contact force.

Example

A refrigerator magnet “sticks” to a refrigerator and is at rest. What are the forces acting on it?

Example in 1-D -- equilibrium

Suppose that the gymnast in the picture has a mass of 70 kg and is at rest. If each ring exerts the same force on the gymnast, what is the force on the gymnast by each ring? (Assume the ropes/straps are vertical.)

Poll

A gymnast on the rings at a certain instant of time has a downward acceleration. Which force is larger in magnitude?

1. The force on the gymnast by the rings (together).

2. The gravitational force on the gymnast by Earth (i.e. the weight of the gymnast).

3. Neither, these forces are equal.

Poll

A gymnast on the rings at a certain instant of time has an upward acceleration. Which force is larger in magnitude?

1. The force on the gymnast by the rings (together).

2. The gravitational force on the gymnast by Earth (i.e. the weight of the gymnast).

3. Neither, these forces are equal.

Poll

You stand on a bathroom scale in an elevator on the first floor. When the elevator first starts moving upward, you speed up. As it is speeding up, which is larger in magnitude, the force on you by the scale or your weight?

1. The force on me by the scale.

2. My weight

3. Neither, because they are equal.

Poll

You stand on a bathroom scale in an elevator on the first floor. After initially speeding up, the elevator will reach a constant velocity. As it moves upward with a constant velocity, which is larger in magnitude, the force on you by the scale or your weight?

1. The force on me by the scale.

2. My weight

3. Neither, because they are equal.

Poll

You stand on a bathroom scale in an elevator on the first floor. When the elevator gets to the top floor, it slows down. As it is slowing down, which is larger in magnitude, the force on you by the scale or your weight?

1. The force on me by the scale.

2. My weight

3. Neither, because they are equal.

Example 1-D -- constant acceleration

Analyze the forces on the girl with the yellow backpack in the picture below. If she is speeding up, what force is larger? (neglect friction)

Poll

Analyze the forces on the girl with the yellow backpack in the picture below. If she is slowing down, what force is larger? (neglect friction)

1. The force on the girl by the guy on the bike.

2. The force on the girl by the guy with the cool hat.

3. Neither, because these forces are equal.

Poll

Analyze the forces on the girl with the yellow backpack in the picture below. If she is speeding up, what force is larger? (neglect friction)

1. The force on the girl by the guy on the bike.

2. The force on the girl by the guy with the cool hat.

3. Neither, because these forces are equal.

Example 1-D -- constant acceleration

http://bobsled.teamusa.org/news/article/6595

A 120-kg bobsled is pushed during a training run over a distance of 40 m in 5.0 s. (a) What is the net force on the bobsled? (b) If there is a constant frictional force by the track on the sled of 100 N, what is the force on the sled by the man?

Example 1-D -- constant acceleration

Suppose that Dr. Titus, starting at rest, has a vertical leap of 24 in. If his mass is 80 kg and if his feet are in contact with the floor for 0.5 s, what is the (average) force by the floor on him during the jump?