Download Advanced Problems 1

Advanced Problems 2
These problems will contain:
1. Basic concepts of force and
motion.
2. Usage of Newton’s laws of
motion.
3. The concept of net force in
multiple directions.
1. A fire helicopter carries a 620-kg bucket of
water at the end of a cable 20.0m long. As
the aircraft flies back from a fire at a
constant speed of 40.0m/s, the cable makes
an angle of 40° with respect to the vertical.
(a)
(b)
Determine the force of air resistance on the
bucket.
After filling the bucket with sea water, the pilot
returns to the fire at the same speed with the
bucket now making an angle of 7.00° with the
vertical. What is the mass of the water in the
bucket?
2. A block is given an initial velocity of
5.00m/s up a frictionless 20.0° incline.
How far up the incline does the block
slide before coming to rest?
3. Two masses are connected by a light string that
passes over a frictionless pulley, as shown in
the figure. If the incline is frictionless and if
m1=2.00kg, m2=6kg, and θ=55°, find:
(a)
(b)
(c)
the acceleration of the masses.
the tension of the string.
the speed of each mass 2.0s after being released from
rest.
m1
θ
4. A 72.0kg man stands on a spring scale in the
elevator. Starting from rest, the elevator
ascends, attaining its maximum speed of
1.20m/s in 0.800s. It travels with this constant
speed for the next 5.0s. The elevator then
undergoes a uniform acceleration in the
negative y direction for 1.50s and comes to rest.
What does the spring scale register:
a.
b.
c.
d.
before the elevator starts to move?
during the first 0.8s?
while the elevator is traveling at constant speed?
during the time it is slowing down?
5. A racing car accelerates uniformly from 0
to 80.0km/h in 8.0s. The external force
that accelerates the car is the frictional
force between the tires and the road. If
the tires do not slip, determine the
minimum coefficient of friction between
the tires and the road.
6. A 3.0kg block starts from rest at the top of a
30.0° incline and slides a distance of 2.0m
down the incline in 1.50s. Find:
a.
b.
c.
d.
The magnitude of the acceleration of the block.
The coefficient of friction between block and
plane.
The frictional force acting on the block.
The speed of the block after it has slid 2.0m.
7. To determine the coefficients of friction
between rubber and various surfaces, a
student uses a rubber eraser and an incline.
In one experiment, the eraser begins to slip
down the incline when the angle of inclination
is 36.0° and then moves down the incline
with constant speed when the angle is
reduced to 30.0°. From these data, determine
the coefficients of static and kinetic friction for
this experiment.
8. A block of mass 3.0kg is pushed up against a wall
by a force P that makes a 50.0° angle with the
horizontal as shown in the figure. The coefficient of
static friction between the block and the wall is
0.250. Determine the possible values for the
magnitude of P that allow the block to remain
stationary.
50.0°
P
9. A mass M is held in place by an applied force F
and a pulley system as shown in the figure. The
pulleys are massless and frictionless . Find:
•
the tension in each section of rope, T1, T2,
T3,T4,T5.
•
the magnitude of F.
(Hint: draw a free-body diagram for each pulley.)
T4
T1
F
T2
T5
M
T3
10. Two blocks of mass 3.50kg and 8.00kg are
connected by a string of negligible mass that
passes over a frictionless pulley. The inclines are
frictionless. Find:
a.
the magnitude of the acceleration of each block.
b.
the tension in the string.
8.00kg
3.50kg
35.0°
35.0°
11. Consider a conical pendulum with an
80kg bob on a 10m wire making an angle
of θ = 5° with the vertical.
a. Determine the tension in the wire.
b. Determine the tangential velocity of the
bob.
θ
12. A person stands on a scale in an elevator.
As the elevator starts, the scale has a
constant reading of 591N. As the elevator
stops, the scale reading is 391N. Assume
the magnitude of the acceleration is the
same during starting and stopping, and
determine …
a. The weight of the person.
b. The acceleration of the elevator.
13. A 50kg parachutist jumps from an airplane and
falls with a drag force proportional to the square
of the speed, R=Cv2. Take C= 0.2kg/m with the
parachute closed and C = 20kg/m with the
parachute open.
a. Determine the terminal speed of the jumper both
before and after the chute is open.
b. Write speed and position functions of time for
the jumper if the original altitude of the jump is
1000 m and he is in free fall for 10s before the
parachute opens.
14. Suppose the boxcar below is moving with
constant acceleration (a) up a hill that
makes an angle (Φ) with the horizontal. If
the hanging pendulum makes a constant
angle (θ) with the perpendicular to the
ceiling, what is a?
a
θ
Φ
15. A string under a tension of 50N is used to
whirl a rock in a horizontal circle of 2.5m at
a speed of 20.4m/s. The string is pulled in
and the speed of the rock increases. When
the string is 1m long and the speed of the
rock is 51m/s, the string breaks. What is
the breaking strength of the string?
16. A penny of mass 3.1g rests on a small 20g block
supported by a spinning disk. If the coefficients of
friction between the block and the disk are 0.75(static)
and 0.64(kinetic) while those for the penny and block
are 0.45(kinetic) and 0.52(static), what is the maximum
rate of rotation (in rpm) that the disk can have before
either the block or the penny starts to slip?
12.0cm
17. An amusement park ride consists of a large vertical
a.
b.
cylinder that spins about its axis fast enough that any
person inside is held up against the wall when the
floor drops away. The coefficient of static friction
between the person and the wall is μ, and the radius
of the cylinder is R.
Show that the maximum period of revolution
necessary to keep the person from falling is T=(4π2Rμ
/ g)2
Obtain a numerical value for T.
18. Suppose air resistance is negligible for a
golf ball. A golfer tees off from a location
precisely at Φ=35° north latitude. He hits
the ball due south, with range 285m. The
ball’s initial velocity is at 48° above the
horizontal.
a. For what length of time is the ball in flight?
18.(continued) The cup is due south of the
golfer’s location, and he would have a
hole in one if the Earth were not rotating.
The Earth’s rotation makes the tee move
in a circle of radius
REcosΦ=(6.37x106m)cos35° completing
one revolution each day.
b. Find the eastward speed of the tee,
relative to the stars.
18.(continued) The hole is also moving
eastward, but is 285m farther south and
thus a slightly lower latitude Φ. Because
the hole moves eastward in a slightly
larger circle, its speed must be greater
than that of the tee.
c. By how much does the hole’s speed
exceed that of the tee?
18.(continued) During the time the ball is in
flight, it moves both upward and
downward, as well as southward with
projectile motion, but it also moves
eastward with the speed you found in part
b. The hole moves to the east at a faster
speed, however pulling ahead of the ball
with the relative speed you found in part
c.
d. How far to the west of the hole does the
ball land?
REcosΦ
RE
Golf ball
trajectory
19. A single bead can slide with negligible friction on a
a.
b.
wire that is bent into a circle of radius 15cm. The
circle is always in a vertical plane and rotates
steadily about its vertical diameter with a period of
0.45s. The position of the bead is described by the
angle θ that the radial line from the center of the
loop to the bead makes with the vertical.
At what angle up from the lowest point can the bead
stay motionless relative to the turning circle?
What if the period of rotation is 0.85s?
θ
20. A model airplane of mass 0.75kg flies in a
horizontal circle at the end of a 60m control wire,
with a speed 35m/s. Compute the tension in the
wire if it makes a constant angle of 20° with the
horizontal.
Lift
20°
20°
T
mg