AP Physics Chapter 4 Study Guide

Weight

The weight of an object is the downward force exerted on it by the Earth (or any other celestial object large enough and near enough to produce a substantial gravitational interaction).

Load–force exerted perpendicularly on a supporting surface.

Example 11

The fire alarm goes off, and a 97 kg fireman slides 3.0 m down a pole to the ground floor in 1.2 s. What was the upward force exerted by the pole on the fireman?

Example 12

A passenger of mass m= 72.2 kg stands on a bathroom scale in an elevator. We are concerned with the scale readings when the cab is stationary, and when it is moving up or down.
(a) Find the general solution for the scale reading, whatever the vertical motion of the cab.
(b) What does the scale read if the cab is stationary or moving upward at a constant 0.50 m/s?
(c) What does the scale read if the cab accelerates upward at and downward at ?

Example 13

A 5.0 kg salmon is weighed by hanging it from a fish scale attached to the ceiling of an elevator. What is the apparent weight of the salmon, , if the elevator (a) is at rest, (b) moves with an upward acceleration of , or (c) moves with a downward acceleration of ?

Inclined Planes

When an object is on an inclined plane the normal force is only equal to part of the gravitational force . This is usually done with the use of sine and cosine.

Inclined Planes

Example 14

A trained sea lion slides from rest with constant acceleration down a 3.0 m long ramp into a pool of water. If the ramp is inclined at an angle of above the horizontal. (a) Find the acceleration the sea lion has down the plane. (b) Find how long the sea lion takes to make a splash in the pond.

Coupled Motions

When two masses are connected by an unstretchable rope they are coupled and will move together. Here are some different combinations for coupled motions. If you are not sure which way they move make a guess and the only difference will be the sign of the motion.

Atwood Machine

Example 15

A block of mass slides on a frictionless tabletop. It is connected to a string that passes over a pulley and suspends a mass . Find the acceleration of the masses and the tension in the string.

Example 16

Atwood's Machine

The figure shows two blocks connected by a cord that passes over a massless, frictionless pulley. The lighter block has a mass m = 1.3 kg and the heavier block has a m = 2.8 kg. Find the magnitudes of the accelerations of the two blocks and the magnitude T of the force on each block from the cord.

Friction

There are three different types of friction that we will study in this class. Static friction is when there is no movement between the surfaces; Kinetic (or sliding) friction is when the two surfaces are sliding along each other; and Rolling friction when one surface is rolling along another surface.

Static Friction:

There are three insights about static friction that need to be looked at in the study of friction.

(1) is proportional to the normal force. Remember the normal force, , is always perpendicular to the surface.

(2) The same block sitting on a different surface will have a different .

(3) is independent of the apparent size of the contact area between the two solid surfaces.

Static friction is calculated by finding the Normal force and a proportionality constant, , called the coefficient of static friction. The coefficient of friction depends on the two materials in contact.

Approximate Friction Coefficients
Material
Steel on ice	0.1	0.05
Steel on steel-dry	0.6	0.4
Steel on steel-greased	0.1	0.05
Rope on wood	0.5	0.3
Teflon on Steel	0.04	0.04
Shoes on ice	0.1	0.05
Climbing boots on rock	1.0	0.8
Leather-soled shoes on carpet	0.6	0.5
Leather-soled shoes on wood	0.3	0.2
Rubber-soled shoes on wood	0.9	0.7
Auto tires on dry concrete	1.0	0.7-0.8
Auto tires on wet concrete	0.7	0.5
Auto tires on icy concrete	0.3	0.02
Rubber on asphalt	0.60	0.40
Teflon on Teflon	0.04	0.04
Wood on wood	0.5	0.3
Ice on ice	0.05-0.15	0.02
Glass on glass	0.9	0.4

Kinetic Friction:

When two surfaces are in motion with respect to each other there is Kinetic friction. Once two objects are in motion it is easier to keep them in motion. To calculate Kinetic friction you need the normal force and the coefficient of kinetic friction.

Rolling Friction:

When one surface is rolling over another surface there is rolling friction. To calculate rolling friction you need the normal force and the coefficient of rolling friction.

Friction Examples

Example 17

The figure shows a coin of mass m at rest on a book that has been tilted at an angle with the horizontal. By experimenting, you find that when is increased to , the coin is on the verge of sliding down the book, whicch means that even a slight increase beyond produces sliding. What is the coefficient of static friction between the coin and the book?

Example 18

If a car's wheels are "locked" during emergency braking, the car slides along the road. Ripped-off bits of tire and small melted sections of road form the "skid marks" that reveal that cold-welding occurred during the slide. The record for the longest skid marks on a public road was reportedly set in 1960 by a Jaguar on the M1 highway in England–the marks were 290 m long! Assuming that = 0.60 and the car's acceleration was constant during the braking, how fast was the car going when the wheels became locked?

Example 19

Sea Lion Friction

A trained sea lion slides from rest with constant acceleration down a 3.0 m long ramp into a pool of water. If the ramp is inclined at an angle of above the horizontal. (a) Find the acceleration the sea lion has down the plane. (b) Find how long the sea lion takes to make a splash in the pond.

Example 20

In the figure a crate of dilled pickles with mass moves along a plane that makes an angle of with the horizontal. The crate is connected to a crate of pickled dills with mass by a taut, massless cord that runs over a frictionless, massless pulley. The dills descend with constant velocity. (a) What are the magnitude and direction of the frictional force on the pickles from the plane? (b) What is ?

The Drag Force and Terminal Speed

Air behaves like a fluid when an object is moving through it. Since, the object and fluid are moving relative to each other and there is friction between the object and the fluid. This friction force is called the drag force. The drag force is calculated using:

where C is the drag coefficient, is the air density, A is the effective cross-sectional area of the object, and v is the velocity.

Terminal velocity is when a falling object will not go any faster. If you look at this from a Physics perspective the velocity is constant, therefore the acceleration is zero. Which means that by Newton's Second Law

Then solving for the velocity:

Example 21

If a falling cat reaches a first terminal speed of 97 km/h while it is tucked in and then stretches out, doubling A, how fast is it falling when it reaches a new terminal speed?

Example 22

A raindrop with a radius r = 1.5 mm falls from a cloud that is at height h = 1200 m above the ground. The drag coefficient C for the drop is 0.60. Assume that the drop is spherical throughout its fall. The density of water is , and the density of air is . (a)What is the terminal speed of the drop? (b)What would be the drop's speed just before impact if there were no drag force?

Example 22a

Calculate the drag force on a missile 53 cm in diameter cruising with a speed of 250 m/s at low altitude, where the density of air is . Assume C = 0.75.

Static Equilibrium

When external forces act on a body resulting in no change of motion then the body is in equilibrium. Under Newton's Second Law if there is no change in motion the acceleration is zero. Which also means the sum of all the forces is zero. The First Condition of Equilibrium is:

and if we resolve the vectors into perpendicular component vectors:

Parallel Force Systems

When a mass is attached to a rope so that it hangs there is tension on the rope. If there is only one rope the weight of the mass is equal to the tension in the rope.

If there is more than one rope supporting the mass then we can use the idea of a force-multiplier. As the figure show the weight is distributed among the ropes.

Static Equilibrium Examples

Example 23

A person hoists a bucket of water from a well and holds the rope, keeping the bucket at rest, as at left. A short time later, the person ties the rope to the bucket so that the rope holds the bucket in place, as at right. In this case, is the tension in the rope (a) greater than, (b) less than, or (c) equal to the tension in the first case?

Example 24

To hang a 6.20 kg pot of flowers, a gardener uses two wires–one attached horizontally to a wall, the other sloping upward at an angle of and attached to the ceiling. Find the tension in each wire.

Example 25

A 1.84 kg bag of clothespins hangs in the middle of a clothesline, causing it to sag by an angle . Find the tension, T, in the clothesline.

Example 26

A traction device employing three pulleys is applied to a broken leg, as shown in the figure. The middle pulley is attached to the sole of the foot, and a mass m supplies the tension in the ropes. Find the value of the mass m if the force exerted on the sole of the foot by the middle pulley is to be 165 N.

Example 27

A 10 kg monkey climbs up a massless rope that runs over a frictionless tree limb and back down to a 15 kg package on the ground. (a) What is the magnitude of the least accleration the monkey must have if it is to lift the package off the ground? If, after the package has been lifted, the monkey stops its climb and holds onto the rope, what are (b) the magnitude and (c) the direction of the monkey's acceleration, and (d) what is the tension in the rope?

The End