Download Extra Credit Problems

Extra Credit Problems
Physics 1
Mr. Kiledjian
1) A rock is dropped from rest into a well. The sound of the splash is heard 3.25 seconds
after the rock is released from rest. The speed of sound in air is 336 m/s. How far below
the top of the well is the surface of the water?
Answer: H = 47.39 meters
2) Setting a new world record in a 100 meter race, Maggie and Judy cross the finish line
in a dead heat, both taking 10.2 seconds. Accelerating uniformly, Maggie took 2 seconds
and Judy took 3 seconds to attain maximum speed, which they maintained for the rest of
the race. a) What was the acceleration of each sprinter? b) What were their respective
maximum speeds? c) Which sprinter was ahead at the 6 second mark, and by how
much?
Answer: a) 5.43 m/s2 and 3.83 m/s2 b) 10.9 m/s and 11.5 m/s
c) Maggie by 2.62 meters
3) The acceleration of a marble in a certain fluid is proportional to the speed of the
marble squared, and is given by a = -3.00v2 for v > 0. If the marble enters this fluid with
a speed of 1.50 m/s, how long will it take before the marble’s speed is reduced to half of
its initial value?
Answer: .222 seconds
4) A pirate has buried his treasure on an island with five trees, located at the following
points: A (30 m, -20 m), B (60 m, 80 m), C (-10 m, -10 m), D (40 m, -30 m), and E
(-70 m, 60 m). His ship’s log instructs you to start at tree A and move toward tree B, but
to cover only half the distance between A and B. Then move toward tree C, covering one
third the distance between your current location and C. Next, move toward D, covering
one fourth the distance between where you are and D. Finally, move towards E, covering
one fifth the distance between you and E, stop, and dig. What are the coordinates of the
point where his treasure is buried?
Answer: (10 m, 16 m)
5) A skier leaves the ramp of a ski jump with a velocity of 10.0 m/s, 15 degrees above
the horizontal (this is actually a Winter Olympics sport). The slope of the mountain is
inclined at 50 degrees and air resistance is negligible. Find a) the distance from the
ramp to where the jumper lands b) the velocity components just before the landing.
Answer: a) 43.2 meters
b) vx = 9.66 m/s
vy = -25.5 m/s
6) An enemy ship is on the east side of a mountain island. The enemy ship has
maneuvered to within 2,500 meters of the 1,800 meter-high mountain peak and can shoot
projectiles with an initial speed of 250 m/s. If the western shoreline is horizontally 300
meters from the peak, what are the distances from the western shore at which a ship can
be safe from the bombardment of the enemy ship?
Answer: Less than 270 meters or Greater than 3,480 from the western shore
7) A 1.30 kg toaster is not plugged in. The coefficient of static friction between the
toaster and a horizontal countertop is .350. To make the toaster start moving, you
carelessly pull on its electric cord. a) For the cord tension to be as small as possible, you
should pull at what angle above the horizontal? b) With this angle, how large must the
tension be?
Answer: a) 19.30
b) 4.21 Newtons
8) A time-dependent force, F = 8i – 4tj N, is exerted on a 2.00 kg object initially at rest.
a) At what time will the object be moving with a speed of 15 m/s? b) How far is the
object from its initial position when its speed is 15 m/s? c) Through what total
displacement has the object traveled at this moment?
Answer a) 3.00 sec b) 20.1 m d) (18i – 9j) m
9) A single bead can slide with negligible friction on a wire that is bent into a circular loop
of radius 15.0 cm. The circle is always in a vertical plane and rotates steadily about its
vertical diameter with a period of .450 seconds. The position of the bead is described by the
angle that the radial line, from the center of the loop to the bead, makes with the vertical.
a) At what angle up from the bottom of the circle can the bead stay motionless relative to
the turning circle? b) Repeat the problem if the period is .85 sec.
Answer: a)  = 70.4o and 0o
b)  = 0o (only at the bottom of the loop)
10) A light spring has an unstressed length of 15.5 cm. It is described by Hook’s law
with spring constant 4.30 N/m. One end of the horizontal spring is held on a fixed
vertical axle, and the other end is attached to a puck of mass m that can move without
friction over a horizontal surface. The puck is set into motion in a circle with a period of
1.30 sec. (Chapter 7, #53)
11) A ball is tied to one end of a string. The other end of the string is held fixed. The
ball is set moving around a vertical circle without friction, and with speed vi = (Rg)1/2. At
what angle from the bottom should the string be cut so that the ball will then travel
through the center of the circle on its way to the ground?
Answer: 100.6 degrees
12) A uniform chain of length 8.0 meters initially lies stretched out on a horizontal table.
The coefficient of static friction between the chain and the table is .60. a) How much of
the chain should hang over the edge of the table before it begins to slide off the table?
b) Determine the speed of the chain as all of it leaves the table, given that the coefficient
of kinetic friction between the chain and the table is .40.
Answer: a) 3.0 meters b) 7.42 m/s
13) A 4 kg ball moving to the right and a 1 kg ball moving to the left experience a
perfectly elastic collision. Their initial speed is 2 m/s. After the collision, the 1 kg ball
moves downward at right angles to its initial direction. Find the final speeds of the two
masses and the final scattered angle for the 4 kg ball.
Answer: V4 kg = 1.673 m/s, V1 kg = 2.967 m/s, 4 kg = 26.310 above the horizontal
14) A chain of length 1.2 meters and total mass 2.5 kg is released from rest with its lower
end just touching the top of a table. Find the force exerted by the table on the chain after
the chain has fallen through a distance x.
Answer: F = 61.25x Newtons
15) Sand from a stationary hopper falls onto a moving conveyor belt at the rate of 5 kg/s.
The conveyor belt is supported by frictionless rollers and moves at a constant speed of
.75 m/s under the action of a constant horizontal external force supplied by the motor.
Find a) the sand’s rate of change of momentum in the horizontal direction b) the force
of friction exerted by the belt on the sand c) the external force d) the work done by the
external force in 1 second, and e) the kinetic energy acquired by the falling sand each
second due to the change in its horizontal motion.
Answer: a) 3.75 Newtons b) 3.75 N c) 3.75 N d) 2.81 Joules e) 1.41 J
16) As a result of friction, the angular speed of a wheel changes with time according to
e-t where and  are constants. The angular speed changes from 3.50 rad/s at
t = 0 to 2.00 rad/s at t = 9.30 sec. Use this information to determine  and Then
determine a) the magnitude of the angular acceleration at t = 3.00 sec, b) the number of
revolutions the wheel makes in the first 2.50 sec, and c) the number of revolutions it
makes before coming to rest.
Answer : a) -.176 rad/s2
b) 1.29 revs
c) 9.26 revs
17) A large, cylindrical roll of tissue paper of initial radius R lies on a long, horizontal
surface with the outside end of the paper nailed to the surface. The roll is given a slight
shove (vinitial = 0) and commences to unroll. Determine the speed of the center of mass of
the roll when its radius has diminished to r = 1.0 mm, assuming R = 6.0 meters.
Answer: 5.31 x 104 m/s
18) A plank with a mass M = 6.0 kg rides on top of two identical solid cylindrical rollers
that have R = 5.0 cm and m = 2.0 kg. The plank is pulled by a constant horizontal force
F of magnitude 6.0 Newtons applied to the end of the plank and perpendicular to the axes
of the cylinders. The cylinders roll without slipping on a flat surface. There is also no
slipping between the cylinders and the plank. a) Find the acceleration of the plank and
of the rollers. b) Find the friction force between the plank and each roller c) Find the
friction force between the ground and each roller
Answer: a) aplanck = .80 m/s2, arollers = .40 m/s2 b) .60 Newtons backward
c) .20 Newtons forward
19) A Solid Cylindrical Disk of Radius 10 cm is given an angular speed of 60 rad/sec
and then lowered to a horizontal surface whose coefficient of friction is .30. Find how
much time the Disk will take to reach Pure Rolling Motion without slipping. Also, find
the distance that the disk will have traveled during this time.
Answer: T = .680 seconds
D = .680 meters
20) A uniform pole is propped between the floor and the ceiling of a room. The height of
the room is 7.80 ft, and the coefficient of static friction between the pole and the ceiling
is 0.576. The coefficient of static friction between the pole and the floor is greater than
that. What is the length of the longest pole that can be propped between the floor and the
ceiling?
Answer: 9.00 ft
21) A solid sphere (radius = .8 meters) rolls without slipping in a cylindrical trough
(radius = 4 meters). If the sphere executes simple harmonic motion with small
displacements from the equilibrium perpendicular to the length of the trough, find the
period of this motion.
Answer: 4.25 seconds
22) A block of mass 5 kg is connected to a spring of mass .75 kg and oscillates in simple
harmonic motion on a horizontal, frictionless track. The force constant of the spring is
200 N/m and the equilibrium length is .35 meters. Assume that all portions of the spring
oscillate in phase and that the velocity of a segment dx is proportional to the distance x
from the fixed end; that is, vx = (x/.35)v. Also, note that the mass of a segment of the
spring is dm = (m/.35)dx. Find a) the kinetic energy of the system when the block has a
speed v = 3.8 m/s. b) the period of oscillation
Answer: a) 37.905 Joules b) 1.018 seconds