Constant Force Motion and the Free Body Diagram

Teacher Excellence WorkshopJune 19, 2009

Mass versus Weight

Mass is inertia, or resistance to acceleration.Weight and mass are not equivalent!Weight is gravitational force, which is equal to mg near the earth’s surface.

Apparent weight

Apparent weight is a force that acts in opposition to gravitational force in order to prevent a body from going into freefall.When you stand on the floor, the floor pushes up on your feet with a force equal to your apparent weight.

Elevator rides

When you are in an elevator, your actual weight (mg) never changes.You feel lighter or heavier during the ride because your apparent weight increases when you are accelerating up, decreases when you are accelerating down, and is equal to your weight when you are not accelerating at all.

Going Up?

W

Wapp

Groundfloor

Normal feeling

v = 0a = 0

W

Wapp

Juststarting up

Heavy feeling

v > 0a > 0

W

Wapp

Betweenfloors

Normal feeling

v > 0a = 0

W

Wapp

Arriving attop floor

Light feeling

v > 0a < 0

W

Wapp

Topfloor

Normal feeling

v = 0a = 0

W

Wapp

Arriving atGround floor

Heavy feeling

v < 0a > 0

W

Wapp

Betweenfloors

Normal feeling

v < 0a = 0

W

Wapp

Beginningdescent

Light feeling

v < 0a < 0

Going Down?

Sample problem: An 85-kg person is standing on a bathroom scale in an elevator. What is the person’s apparent weighta) when the elevator accelerates upward at 2.0 m/s2?

b) when the elevator is moving at constant velocity between floors?

c) when the elevator begins to slow at the top floor at 2.0 m/s2?

Normal force

The normal force is a force that keeps one object from penetrating into another object.The normal force is always perpendicular a surface.The normal exactly cancels out the components of all applied forces that are perpendicular to a surface.

Problem: derive an expression for the normal force of a box on a flat table.

Problem: Derive an expression for the normal force of a box sitting on a ramp.

Problem: derive an expression for the normal force an eraser being pushed up against a whiteboard by a force F.

Problem: derive an expression for the normal force an eraser being pushed up against a whiteboard by a force F.

Problem: Derive the normal force for the box in the picture below. The box is sitting on the floor, but is being pulled by the force shown. Ignore friction.

6.0 kg

F = 20 N

40o

Problem: A 10-kg box rests on a ramp that is laying flat. The coefficient of static friction is 0.50, and the coefficient of kinetic friction is 0.30.a) What is the maximum horizontal force that can be applied to the box before it begins to slide?

b) What force is necessary to keep the box sliding at constant velocity?

Tension

Tension is a pulling force that arises when a rope, string, or other long thin material resists being pulled apart without stretching significantly.Tension always pulls away from a body attached to a rope or string and toward the center of the rope or string.

A physical picture of tension

Imagine tension to be the internal force preventing a rope or string from being pulled apart. Tension as such arises from the center of the rope or string. It creates an equal and opposite force on objects attached to opposite ends of the rope or string.

Tension examples

Note that the pulleys shown are magic! They affect the tension in any way, and serve only to bend the line of action of the force.

Sample problem: A 1,500 kg crate hangs from a crane cable. What is the tension in the cable when the crate is motionless? Ignore the mass of the cable.

Suppose the crane accelerates the crate upward at 1.2 m/s2. What is the tension in the cable now?

Sample problem: A 1,500 kg crate hangs from a crane cable. What is the tension in the cable when the crate is motionless? Ignore the mass of the cable.

Suppose the crane accelerates the crate upward at 1.2 m/s2. What is the tension in the cable now?

Gravity

A very common accelerating force is gravity. Here is gravity in action. The acceleration is g.

The pulley lets us use gravity as our accelerating force… but a lot slower than free fall. Acceleration here is a lot lower than g.

Slowing gravity down

Pulleys

Pulleys bend the line of action of the force of gravity without affecting tension.The pulley is “magic” – no mass, no friction, and no effect on the tension.The pulley simply bends the line of action of the force.

m1

m2

Sample problem: Derive an expression for the acceleration due to gravity of the system below, and for the tension in the string.

Frictionless table

m1

m2

Sample problem: Derive an expression for the acceleration due to gravity of the system below, and for the tension in the string.

Frictionless table

m1

m2

Problem: Derive the acceleration, assuming a frictionless surface. Determine the tension in the string.

35o

3.0 kg5.0 kg

Problem: Derive the acceleration, assuming a coefficient of friction of 0.20 between the table and the 3.0 kg block. Determine the tension in the string.

35o

3.0 kg5.0 kg