Water pressure on the bottom surface is the total weight of the water above it Plus the atmospheric pressure weighing down from above on the whole thing!

However this pressure is not just directed DOWNWARD P atm But outward as well

3.0 meters Swimming along the 10-foot bottom of the pool your back supports a ~3 meter column of water. With cross-sectional area A  0.75 m 2 That’s a 3  0.75 = 2.25 m 3 volume of water with a weight of  Vg = 22,050 Newtons  5000 pounds!

Water pressure at any level is P atm + the additional weight of the water above it

Simple evidence of pressure increasing with depth:

Water flows through the upper horizontal section of pipe with a speed v It must flow through this lower section of pipe with A. a speed greater than v. B. a speed equal to v. C. a speed less than v.

Water flows through the upper horizontal section of pipe with a speed v The pressure experienced by the water in the lower section of pipe must be ___ the pressure in the top section. A. greater than B. equal to C. less than

Water flows continuously through the point where two sections of pipe join. The pipe at left has diameter D. The pipe at right diameter d = D/2. If water flows through the left pipe with a speed V it travels in the right pipe with a speed of A. B. C. V D. 2V E. 4V

Water flows continuously through the point where two sections of pipe join. The pipe at left has diameter D. The pipe at right diameter d = D/2. The pressure experienced by water in the right pipe must be ___ the water pressure in the left pipe. A. less than B. equal to C. greater than

Bernoulli’s Equation P +  v 2 +  gh = constant 1212 When a stream of water either speeds up or flows uphill the pressure it exerts drops! When a stream of water slows or flows downhill the pressure it exerts drops! Speeding up or rising uses up energy!

A B C D Low pressure water from reservoir Pumping station/purification plant Water storage at low pressure Low pressure water from reservoir air at atmospheric pressure

Force Displacement,  x F  xF  x Also means: F = k  x “spring constant” in units of N/m The restoring force grows so many Newtons for every meter stretched.

Look up any catalog of springs. Their “strength” or “spring rate” is given as “the load per unit deflection” lbs/inor lbs/ft or N/mm or N/cm or N/m 9.5 lbs/in 32 lbs/in 45 lbs/in 96 lbs/in Springs of increasing strength or stiffness

Force Displacement,  x Work done against an elastic force starting with force  0 ending with force = k  x W = F avg d =  x F max 2 = k(  x)

Dropped with potential energy mg(h 1 ) …equal to the kinetic energy it strikes ground with Golf Ball h1h1 rebounding with a slightly smaller kinetic energy equal to the potential energy mg(h 2 ) it will climb up to. h2h2 outgoing kinetic energy incoming kinetic energy This is a ratio of energy after energy before

Golf balls (and many industrial materials) are rated on their “coefficient of restitution” outgoing speed incoming speed Since our ratio: outgoing speed incoming speed

An elastic ball wastes 30% of the collision energy as heat each time it bounces on a hard floor. This ball will rebound with ___  the kinetic energy it strikes the floor with. A C. E. (0.70) 2 = 0.49 B D. F. (0.30) 2 = 0.09 This ball will rebound with ___  the speed it strikes the floor with.

Liveliness of bouncing objects can be described by either ratio: ratios of heights ratios of speeds Although they are related, they are not the same number! coefficient of restitution

Turning right on level ground relies entirely on friction A banked curve let’s the car’s own weight help negotiate the turn Note: the normal force is greater. Note: the frictional forces are smaller. Why? Curves are usually banked so that you still make the turn even if friction vanishes!

N f The total surface forces are not off-centered at all so produce no net torque of their own!

f N

At the bottom of the swing, the bucket must be supported by a force A. less than its weight. B. equal to its weight. C. greater than its weight.

This wheel is rolling away from you (into the screen): Its angular momentum points in what direction? A. right.B. left. C. down.D. up. E. into the screen. F. out of the screen.

Torques as well as angular momenta are both assigned directions by the “right-hand rule.”

The approximately circular orbits of planets and moons lead Newton to G is a universal constant measured to be 6.67  N·m 2 /kg N·m 2 /kg 2

and for any moon orbiting any planet: For any planet (or star or asteroid) the acceleration down toward its center is which means:

p = 0 p gas p rocket p i = 0 = p f p gas = – p rocket = p gas + p rocket p i = 0 = p f = p rifle + p bullet p rifle = – p bullet

The 90-kg fullback runs up the middle at 8 m/sec straight into the waiting arms of the 110-kg defensive tackle. The tackle wraps his arms about the fullback and the two are carried along together by the fullback’s momentum with what speed?