Transcript Day 7 Physics 131

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 mk, 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 Dt.
• 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”
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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
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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
Dh1 = 5.00 m, at which point Brother jumps on
sled with Gayle
• mB = 30.0 kg, vB = 0.0 m/s
• Dh2 = 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.