Day 6

HW Problem 6-12

• A 48-kg crate is placed on an inclined ramp. When the angle the ramp makes with the horizontal is increased to 26o, the crate begins to slide downward.

• ? (a) What is the coefficient of static friction between the crate and the ramp ?

• ? (b) At what angle does the crate begin to slide if its mass is doubled ?

HW Problem 6-14

• Coffee on the car roof• s = 0.24 between car roof and bottom of cup• ? (a) What is the maximum acceleration the

car can have without causing the cup to slide? • ? (b) What is the smallest amount of time in

which the person can accelerate the car from rest to 15 m/s and still keep the coffee cup on the roof ?

• Ignore air resistance.

HW Problem 6-26

• The equilibrium length of a certain spring with a force constant of k = 250 N/m is 0.18 m.

• ? (a) What is the magnitude of the force that is required to hold this spring at twice its equilibrium length ?

• ? (b) Is the magnitude of the force required to keep the spring compressed to half its equilibrium length greater than, less than, or equal to the force found in (a) ? Explain

HW Problem 6-39

• A 0.15-kg ball is placed in a shallow wedge with an opening angle of 120o, as shown in the figure. For each contact point between the wedge and the ball, determine the force exerted on the ball.

• Assume the system is frictionless.

HW Problem 6-58

• A car goes around a curve on a road that is banked at an angle of 33.5o. Even though the road is slick, the car will stay on the road without any friction between its tires and the road when its speed is 22.7 m/s.

• ? What is the radius of the curve ?

HW Problem 6-100

• A child sits on a rotating merry-go-round, 2.3 m from its center.

• ? (a) If the speed of the child is 2.2 m/s, what is the minimum coefficient of static friction between the child and the merry-go-round that will prevent the child from slipping ?

HW Problem 7-17

• Water skiers off to the side, outside the wake• Boat traveling at 15 m/s and the tension on

the rope is 75 N. Boat does 3500 J of work on the skier as the skier (and the boat) go 50.0 m.

• ? What is the angle between the tow rope and the center line of the boat ?

HW Problem 7-24

• A 0.14-kg pinecone falls 16 m to the ground, where it lands with a speed of 13 m/s.

• ? (a) With what speed would be pinecone have landed if there had been no air resistance ?

• ? (b) Did air resistance to positive work, negative work, or zero work on the pinecone ?

• Explain

HW Problem 7-27

• Softball player slides into third base• The mass of the player is 62.0 kg.• The player begins to slide 3.40 m from the

base with a speed of 4.35 m/s. She comes to rest right on the base.

• ? (a) How much work was done on the player by friction ?

• ? (b) what was the coefficient of kinetic friction between the player and the ground ?

HW Problem 7-37

• A block of mass m and a speed v collides with a spring, compressing it a distance x.

• ? What is the compression of the spring if the mass of the block is halved and its speed is doubled ?

HW Problem 7-50

• Human-powered Gossamer Albatross flew across the English Channel in 2 hr, 49 min.

• Human power of 0.30 hp• ? (a) How much energy did the pilot expend

during the flight ?• ? (b) Assuming 100% human muscle efficiency,

if a single Snickers candy bar yields 280 Kcal per bar, how many bars would the pilot have to consume on this flight ?

Conservative and Nonconservative Forces

• The force of gravity is an example of a conservative force.

• Frictional forces are Nonconservative forces.

Conservation of Energy

• K = ½ mv2

• Uspring = ½ kx2

• Ugravitational = mgh

• We will demonstrate the conservation of energy in many forms.

Block on a Spring

• A 0.250-kg block is placed on a light vertical spring (k = 5.00 x 103 N/m) and pushed downwards, compressing the spring 0.100 m.

• After the block is released, it leaves the spring and continues to travel upwards.

• ? What height above the point of release will the block reach if air resistance is negligible ?

Bungee Jumping

• Student jumps from hot air balloon. • Unstretched length of the cord is 25.0 m, the

student weighs 700 N, and the balloon basket is 36.0 m above the surface of a lake.

• ? What is the required force constant, k, of the cord if the student is to stop safely 4.00 m above the lake. ?

A Child’s Swing

• A 25.0-kg child on a 2.00-m-long swing is released from rest when the ropes of the swing make and angle of 30.0o with the vertical.

• ? (a) Neglecting friction, find the child’s speed at the lowest position. ?

• ? (b) If the actual speed of the child at the lowest position is 2.00 m/s, what is the mechanical energy lost due to friction. ?

Dangerous Swing

• ? (a) What speed does the swing need at the bottom to get the swing to the top? Assume the swing is suspended by rods, not chains or ropes ?

• ? (b) If the swing is suspended by chains, what speed at the bottom is required to get it to the top (with chains extended straight up). ?

Frictionless Track

• A bead of mass m = 5.00 kg is released from point “A” and slides on down a frictionless track.

• ? (a) Determine the bead’s speed at points “B” and “C” ?

• ? (b) What is the net work done by the force of gravity in moving the bead from “A” to “C” ?

“Aviation History” March 2012

• In October 1944, four British Meteor jets were tasked with finding some way to defend bomber crews from the German Me-262 jets fighters that were appearing over the skies of Germany.

The flight of a projectile

• A projectile is launched with a speed of 40 m/s at an angle of 60o above the horizontal.

• ? USE CONSERVATION OF ENERGY to find the maximum height reached by the projectile during its flight. ?

Power needed to go up a mountain

• Power = mgh/s• Truck and trailer of mass m• Slope =

Toy gun

• Toy gun with spring, k unknown• Spring compressed a distance of 0.120 m• 20.0-g projectile launched vertically reaches a

height of 20.0 m above the starting point of the projectile (before the spring is compressed).

• ? (a) determine the spring constant ?• ? (b) the speed of the projectile as it moves

through the equilibrium position of the spring ?

“Dry Tortugas”

• Mako is a fast fish. It has been observed to reach speeds of almost twenty-five mi/hr (11.17 m/s) and jump about twenty feet (6.096 m) in the air.

• ? Are these numbers consistent ?

Emperor Penguin

• Wants to leap up onto ice flow• Assume launch at = 45o

• Assume v = 10 m/s• ? How high might the ice flow top surface be

above water level ?

BMX Bike Tripfrom “Bones” TV show, 2011

• Bike and dead rider found on top of 40-foot tall building.

• The body is found well back from the edge of the flat roof. The “Bones” crew cleverly decides that there must have been a ramp and that the rider must have been towed by a car or truck to get up to speed.

• Assume that the maximum height of the trajectory is 60 feet.

• ? What’s the required launch speed ?

Base Runner

• Initial speed of runner = 4.0 m/s• k = 0.70

• Final speed of runner = 0.0• ? (a) How much energy lost due to friction ?• ? (b) How far does she slide ?