A tennis ball rebounds straight up from the ground with speed 4.8 m/sec. How high will it climb? It will climb until its speed drops to zero! final speed = 0 g =  9.8 m/sec 2 and in that much time it will rise a distance or since time up = time down the distance it falls from rest in 0.49 sec:

A tennis ball rebounds straight up from the ground with speed 4.8 m/sec. How high will it climb? It will climb until all its kinetic energy has transformed into gravitational potential energy! = = meter

A skier starts from rest down a slope with a 33.33% grade (it drops a foot for every 3 horizontally). h 3h3h The icy surface is nearly frictionless. How fast is he traveling by the bottom of the 15-meter horizontal drop? W The long way: The accelerating force down along the slope is in the same proportion to the weight W as the horizontal drop h is to the hypotenuse he rides: F The slope is long So it takes him During which he builds to a final speed:

A skier starts from rest down a slope with a 33.33% grade (it drops a foot for every 3 horizontally). h 3h3h The icy surface is nearly frictionless. How fast is he traveling by the bottom of the 15-meter horizontal drop? W The short way: The gravitational potential energy he has at the top of the slope will convert entirely to kinetic energy by the time he reaches the bottom. F = m/sec

h 3h3h3h3h 2h2h ½h½h 1.5h h The bottom of the run faces a slope with twice the grade (steepness). Neglecting friction, the skier has just enough energy to coast how high? A B C D

We know rubber tires are easily deformed by the enormous weight of the car they support…but not permanently. They regain their round shape when removed. This “spring-like” resiliency explains the rebound of all sorts of balls.

Racquetball rebounding from concrete. Tennis ball rebounding from concrete.

Airtrack bumper carts:

Notice that if the spring bumbers reverberate (ring) this would have to represent some energy that did not get returned to forward motion! This represents a fractional loss in kinetic energy! A purely ELASTIC COLLISION is defined as one which conserve kinetic energy. Unlike the stored potential of the compressed bumpers, this is not a “potential” energy that can ever be recovered as kinetic energy.

Look how a racquetball still undulates after leaving the floor! These vibrations are a wasted form of energy!

Notice this tennis ball’s rebound: less than velocity the ball hit the floor with! Velocity on rebound If the collision with the floor is not perfectly elastic, the ball will not bounce as high as the point of its release! Notice this is not the same as a ball falling back from the height it was thrown to!

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 Where did the “missing” energy go?

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

golf ball0.858 billiard ball0.804 hand ball0.752 tennis ball0.712 hollow plastic ball0.688 glass marble0.658 wooden ball0.603 steel ball bearing0.597 Results in fact are different for rebounding off a steel or glass plate. Examples of some coefficients of restitution from a concrete surface

The coefficient of restitution of the surface hit (its elasticity) can make a difference as well. The elastic netting of a tennis racquet is more “lively” than the clay surface of a court.

There are interactions that do meet the ideal of totally elastic collisions! Negatively charged electron scattered by a fast-moving negatively charged muon Here a positively charged alpha particle colliding with a proton (hydrogen nucleus) Nuclear and high energy particle reactions Electron beam scattering off other electrons.

The head-on collision between a car traveling 65 mph that strays across the median and strikes an identical model (and total mass) car traveling 65 mph in the opposite direction is equivalent to a collision between a parked car of this same model, and a second hitting it head-on at A) 32.5 mph B) 65 mph C) 97.5 mph D) 130 mph v v

A rear-end collision between a car traveling 65 mph and a slower identical model (and total mass) car traveling 35 mph in front of it does damage roughly equivalent to a collision between a parked car of this model, and a second hitting from behind at A) 30 mph B) 35 mph C) 65 mph D) 100 mph

So when rebounding off surfaces that are not stationary it’s the relative speed between them that matters. coefficient of restitution = speed of separation speed of approach 0.55 baseball on wooden bat 0.44 softball on wooden bat

A 100 mph fastball is struck by a bat with swing speed of 40 mph. How fast is the batted ball? But that’s how fast the ball is racing from the bat, so that 77 mph is “on top of” the bat’s 40 mph swing. The ball is moving at 77mph+40mph = 117 mph

You’re twirling a valuable pendant at the end of a delicate gold chain when a fragile link snaps off. Viewed from above, it snaps at the position illustrated. Which of the paths shown best represents the likely trajectory of the pendant? A B C D E The only force that acting in this horizontal plane (gravity pulls down, of course, but that’s vertically) was the tension from the chain. With that gone NO FORCE acts on the pendant, so it should, of course, move off in a straight line (continuing FORWARD).

A force acting FORWARD on a moving object will increase its speed. A force acting BACKWARD on a moving object will decrease its speed. What will a force acting NEITHER FORWARD NOR BACKWARD but perpendicular to the direction of motion do to a moving object? Steer it in a new direction (without changing its speed).

Crash test dummy seated in stationary vehicle Car accelerates: suddenly lurching forward

Seat accelerates forward, compressing back cushion against driver Contents of car settles into the moving frame of the car

At ignition ( t o ), explosive fuel combustion carries the rocket from its stationary position near the space outpost by producing a ~steady thrust F over the t seconds of the brief burn. t o t o +t Select the best graphical representation of the ship’s speed: t o t o +t

How do you tell when you are completely stopped? Sitting in class, at “rest” in your seat you are in fact moving, along with your seat, the lecture room to which its attached, the building, and the ground its anchored in…

The swaying of follicles within the fluid of the chochlea give us our sensation of motion. But like the hanging fuzzy dice, these only respond to accelerations, not constant velocity. The sensations of just how our internal organs (heart, stomach) normally hang within the connective tissue that holds it, also change under accelerations. You DO feel acceleration in the pit of your stomach!

v 0 = 8 m/sec a=g After the 1 st 10 th of a second ball has moved out and down but it has also built vertical speed: v 0 = 8 m/sec v y = 0.98 m/sec It has turned!

What is YOUR experience as you sit in a turning car?

Its your own inertia (trying to simply move along a straight line) that feels like it pushes you out. It’s the walls pushing inward that hold you in a circle. Like the car’s fuzzy dice hanging outward on these Swings is evidence that you’re accelerating inward!

F = 2 Centripetal force: F

Turning right on level ground relies entirely on friction A banked curve let’s the car’s own weight help negotiate the turn

B h SOME ANSWERS Question 1