Sponge - A 200 kg hockey player pushes a 150 kg official after receiving a penalty. If he pushes with a force of 500 N, what is the acceleration of each person?

Newton’s Law of Universal Gravitation - every particle in the universe exerts a force on every other particle by the following equation:

F = G m1m2 /r2

G = 6.67259 x 10-11 N•m2/kg2

G is the universal gravitational constant. It was first measured by Henry Cavendish (1731-1810) over 100 years after Newton wrote the law.

The forces between two particles are an action-reaction pair, as in Newton’s third law.

Ex. 5 - What is the magnitude of the gravitational force that acts on each particle, assuming m1 = 12 kg, m2 = 25 kg,

and r = 1.2 m?

The value “r” must be measured from the centers of the objects if they are not particles.

The weight of an object is the gravitational force that the Earth exerts on the object.

If “W” is weight, Newton’s law of gravitation becomes:

W = G MEm2 /r2

Ex. 6 - The mass of the Hubble space telescope is 11 600 kg. Determine the weight of the telescope (a) when it was resting on the Earth and (b) as it is in its orbit 569 km above the Earth’s surface.

Relation Between Mass and Weight -

W = G ME m2 /r2 W = m g

g is determined by G, ME, and r.

The normal force FN is one component of the force that a surface exerts on an object with which it is in contact, namely, the component that is perpendicular to the surface.

The forces on the block are balanced. Adding another downward force causes FN to increase. Adding an upward force, subtracts from W and FN decreases; possibly to zero.

Ex. 8 - In a circus balancing act, a woman performs a headstand on top of a man’s head. The woman weighs 490 N, and the man’s head and neck weigh 50 N. It is primarily the seventh cervical vertebra in the spine that supports all the weight above the shoulders. What is the normal force that this vertebra exerts on the neck and head of the man (a) before the act and (b) during the act?

When a person is accelerated upward or downward, the apparent weight is greater or less than the true weight.

FN = mg + ma“a” is + if upward, - if downward

If a person is in free fall, a = -g and by FN = mg + ma, FN = zero. The apparent weight in free fall is zero.

Friction is a parallel force to the direction of intended motion.

Friction before an object starts to move is static friction. The maximum static frictional force, fSMAX, is the maximum frictional force that can be applied before motion and acceleration occur.

The ratio of fSMAX to FN is called the coefficient of static friction. It is represented by µS.

fSMAX = µS FN

fSMAX = µS FN

This equation relates only the magnitudes of the vectors, not the directions.

Ex. 8 - A sled is resting on a horizontal patch of snow, and the coefficient of static friction is µS = 0.350. The sled and its rider have a total mass of 38.0 kg. Determine the horizontal force needed to start the sled barely moving.

When two surfaces are moving across each other, the friction is called kinetic friction fK. It is usually less than static friction. µK is the coefficient of kinetic friction.

fK = µK FN

Ex. 10 - A sled is traveling at 4.00 m/s along a horizontal stretch of snow. The coefficient of kinetic friction is mK = 0.0500. How far does the sled go before stopping?