Day 7 Physics 131

HW Problem 8-3

• Calculate the work done by friction as a 3.7-kg box is slid along the floor from point A to point B in the figure along paths 1, 2, and 3.

• Assume k, the coefficient of kinetic friction, between the box and the floor is 0.26.

HW Problem 8-12

• The wing of the Hawkmoth deflects by a distance of x = 4.8 mm when a force of magnitude F = 3.0 mN is applied at the tip.

• Treat the wing as an ideal spring.• ? (a) find the force constant, k, of the wing ?• ? (b) find the energy, U, stored in the wing while

it is deflected. ?• ? (c) What force must e applied to the tip of the

wing to store twice the energy found in part (b) ?

HW Problem 8-26

• Basketball player passes 0.600-kg ball. • Ball leaves hands with speed of 8.30 m/g and

slows to 7.10 m/s at is highest point. • ? (a) Use conservation of energy to determine

how high above its release point is the ball when it is at its maximum height. ?

• ? (b) How would doubling the balls mass affect the result of (a) ?

HW Problem 8-29

• A 0.21–kg apple falls from a tree to the ground, 4.0 m below.

• Ignore air resistance.• Take ground level to be y = 0.• ? Determine kinetic energy K, the gravitational

potential energy of the system, U, and the total mechanical energy of the system, E, and the apple’s height above the round is (a) 4.0 m, (b) 3.0 m, (c) 2.0 m, (d) 1.0 m, and (e) 0.0 m. ?

HW Problem 8-32

• A 1.40-kg block slides with a speed of 0.950 m/s on a frictionless horizontal surface until it encounters a spring with a force constant of 734 N/m. The block comes to rest after compressing the spring 4.15 cm.

• ? Find the spring potential energy, U, the kinetic energy of the block, K, and the total mechanical energy of the system, E, for compressions of (a) 0 cm, (b) 1.00 cm, (c) 2.00 cm, (d) 3.00 cm, and (e) 4.00 cm. ?

HW Problem 8-47

• A 42.0-kg seal slides from rest down a ramp to the pool below.

• The top of the ramp is 1.75 m higher than the surface of the water.

• The ramp is inclines at an angle of 35.0o above the horizontal.

• The seal reaches the water with a speed of 4.40 m/s.• ? (a) What was the work done by kinetic friction ?• ? (b) What was the coefficient of kinetic friction

between the ramp and the seal. ?

HW Problem 8-50

• An 81.0-kg skater does +3420 J of nonconservative work by pushing against the ground with her skates. In addition, friction does -751 J of nonconservative work on the skater.

• Skater’s initial and final speeds are 2.50 m/s and 1.22 m/s respectively.

• ? (b) Calculate the change in height of the skater. ?

HW Problem 8-60

• A block of mass m = 0.95 kg is connected to a spring of force constant k = 775 N/m on a smooth, horizontal surface.

• ? (a) Sketch the potential energy of the spring vs x from x = -5.00 cm to x = +5.00 cm ?

• ? (b) Determine the turning points (the maximum and minimum values of x) of the block if its speed at x = 0 is 1.3 m/s. ?

HW Problem 8-68

• A sled slides without friction down a small, ice-covered hill. If the sled starts from rest at the top of the hill, its speed at the bottom is 7.50 m/s.

• ? (a) On a second run, the sled starts with a speed of 1.50 m/s at the top. What is its speed at the bottom?

• ? (b) Why is the answer to (a) not 9.00 m/s ?

HW Problem 8-76

• A child on a swing has a speed of 2.02 m/s when the swing is at its lowest point.

• ? (a) To what maximum vertical height does the child rise, assuming he sits still and “coasts”? Ignore air resistance. ?

• ? (b) How do your results change if the initial speed of the child is halved. ?

Chapter 9, Momentum

• Momentum defined as the product of mass and velocity.

• Momentum is a vector, has direction

Impulse

• Impulse, I, defined as the product of force times t.

• Impulse of force acting on an object equals the change in momentum of that object.

Crash

• In a crash test, a car of mass 1.50 x 103 kg collides with a wall and rebounds. The initial and final velocities of the car are vi = -15.0 m/s and vf = 2.60 m/s.

• The collision lasts for 0.150 s.• ? (a) Find the impulse delivered to the car ?• ? (b) Find the size and direction of the average

force exerted on the car. ?

Conservation of Momentum

• In an isolated system, momentum doesn’t change; total momentum is conserved.

Archer

• An archer stands at rest on frictionless ice and fires a 0.500-kg arrow horizontally at 50.0 m/s. The combined mass of the archer and the bow is 60.0 kg.

• ? With what velocity does the archer move across the ice after firing the arrow. ?

Collisions

• Elastic collisions – momentum conserved, energy conserved.

• Inelastic collisions – momentum conserved, energy NOT conserved.

• Perfectly inelastic collisions, momentum conserved, energy NOT conserved, objects stick together.

Coach and Player “Chest Bump”

• Lineman = 150 kg• Coach = 75 kg• Coach vi = 0

• Lineman vi = 2 m/s

• ? Find coach vf ?

• “Coach needed broader stance” ???

Woman vs Man

• A 70.0-kg man and a 55.0-kg women on ice skates stand facing each other.

• ? If the woman pushes the man backwards so that his final speed is 1.50 m/s, at that speed does the woman recoil ?

Identical Twins on Ice Skates

• Identical twins, each with mass 55.0 kg, are on ice skates and at rest on a frozen lake.

• Assume ice frictionless.• Twin A is carrying a backpack of mass 12.0 kg.

She throws it horizontally at 3.00 m/s to Twin B.

• ? What are the subsequent speeds of Twin A and Twin B ?

Bernard Cornwell, “Heretic”

• A story of Thomas, an English archer• “The force of an arrow’s strike was enough to

throw a man backwards.” • ? Is this statement reasonable? See previous

VG “Archer” ?

Bug and Bus

• A fast-moving bus and a slow-flying bug have a head-on collision. The unfortunate bug splatters over the windshield.

• ? During the collision, the greater force acts on (a) the bug, (b) the bus, or (c) same for both ?

• ? The greater impulse acts on (d) the bug, (e) the bus, or (f) same for both ?

• The greater change in momentum occurs for (g) the bug, (h) the bus, or (i) same for both.

Car Crash. Insurance problem• A car traveling due east strikes a car traveling due

north at and intersection, and the two move together as a unit.

• ? A property owner on the Southeast corner of the intersection claims that his fence was torn down in the collision. Should he be awarded damages by the insurance company ?

• ? Let first car have mass of 1300 kg and a speed of 30.0 km/hr and the second car a mass of 1100 kg and a speed of 20.0 km/hr. Find the velocity after the collision. ?

Box on a table

• A 8.00-g bullet is fired into a 250-g block that is initially at rest at the edge of a table of height 1.00 m. The bullet remains in the block, and after the impact the block lands 2.00 m from the bottom of the table.

• ? Determine the initial speed of the bullet ?

Ballistic Pendulum

• Bullet fired into a large block of wood suspended from some light wires. Bullet is stopped by the block. Block (with bullet) swing up a height h.

• Assume mass of bullet is 5.00 g.• Assume mass of block is 1.00 kg• Assume h is 5.00 cm.• ? What is the speed of the bullet ?

Tarzan and Jane

• Tarzan, whose mass is 80.0 kg, swings from a 3.00-m vine that is horizontal when he starts. At the bottom of his arc, he picks up 60.0-kg Jane in a perfectly inelastic collision.

• ? What is the height of the highest tree limb they can reach on their upward swing ?

Gayle on a sled

• Gayle leaps onto a sled at the top of an icy hill.• mG = 50.0 kg, vG = 4.00 m/s• msled = 5.00 kg, vinitialsled

= 0.0 m/s• h1 = 5.00 m, at which point Brother jumps on

sled with Gayle• mB = 30.0 kg, vB = 0.0 m/s• h2 = 10.0 m• ? What is the final speed of the sled + Gayle +

Brother ?

Center of Mass

• Also known as “Center of Gravity.”• Easy to determine if homogeneous with

simple shape.• Harder to determine if real, complicated

shape.• Center of mass of the baseball bat easy to

demonstrate.• Center of mass of the baseball bat will be

measured next week, when we study torque.