You are pushing a wooden crate across the floor at constant speed. You decide to turn the crate on end, reducing by half the surface area in contact with the floor. In the new orientation, to push the same crate across the same floor with the same speed, the force that you apply must be about

1. four times as great2. twice as great3. equally great4. half as great5. one-fourth as great

as the force required before you changed the crate’s orientation.

The frictional force does not depend on surface contact area!

An object is held in place by friction on an inclined surface. The angle of inclination is increased until the object starts moving. If the surface is kept at this angle, the object

1. slows down.2. moves at uniform speed.3. speeds up.4. none of the above

Net force is no longer zero.

Example: A truck drags a car with locked wheels up a 30o concrete incline. The car has a mass of 1000 kg, the truck pulls with a force of 15 kN and the coefficient of kinetic friction between rubber and concrete is 0.8.

a) What is the frictional force acting on the car?b) What is the acceleration of the car?

30oW

NF

fk

b)

xx amF

yy amF

xx amF

xk ammgfF

sin

Nf kk cosmgk

yy amF

a)

yammgN

cos0

cosmgN

N6790

m

mgmgFa kkx

sincos

2

3.3s

m

Circular Motion:

We know that a an object traveling in a circular path has a centripetal (center seeking) acceleration directed towards the center of curvature.

Where does this acceleration come from?If there is an acceleration it must be due to a net force in the same direction as the acceleration.

This net force that causes a centripetal acceleration is called a centripetal force.The centripetal force is not a specific force, it is any force that causes an object to accelerate towards the center of curvature.

Examples:

The planets move in (roughly) circular orbits, what is the centripetal force keeping the planets in orbit?

Gravitational force directed towards the large central mass.

A mass attached to a string is swung in a circle over a person’s head. What is the centripetal force keeping the mass in its circular path?The tension in the string pulls the mass towards the center.

A car driving around a curve is traveling in part of a circular path. What keeps the car in this circular path?Friction between the tires and the road directed towards the center of the curve.

Example: What is the max speed a car can go around a 20o banked curve without sliding? The curve has a radius of 10 m and the static coefficient of friction between the tires and the road is 0.8.

20o

z

r

N

W

fs

rr amF

zz amF

rs amfN

cossin max

zs amfWN

sincos max

0

0sincos NmgN s

sincos s

mgN

rs

s

s

ammgmg

sincos

cos

sincos

sin

rs amNN

cossin

sincos

cossin

s

sr ga

R

v2

2

1

max sincos

cossin

s

sRgvs

m7.12 mph4.28

The max velocity depends on the incline angle and the radius of curvature.