Download Advanced Problems 3

Advanced Problems 3
These problems will contain:
1. Basic concepts of Work
2. Usage of the potential and
kinetic energy theorem
3. The concept of the
conservation of energy.
1. A 15kg block is dragged over a
rough, horizontal surface by a 70N
force acting 20° above the
horizontal. The block is displaced 5m,
and the coefficient of kinetic friction
is .3. Find the work done by the
(a)70N force
(b)The normal force
(c)The force of gravity
(d)What is the energy loss due to friction?
(e)Find the total change in the block’s
kinetic energy.
2. Vector A extends from the
origin to a point having polar
coordinates (7,70°), and vector
B extends form the origin to a
point having polar coordinates
(4,130°). Find A●B.
3. The force acting on a particle is
Fx=(8x-16)N, where x is in meters.
(a) Make a plot of this force verses x from x=0 to
x=3m.
(b) From your graph, find the net work done by
this force as the particle moves form x=0 to
x=3m.
4. A force F=(4xi + 3yj)N acts on an
object as it moves in the x direction
from the origin to x=5m. Find the
work W   F  dr done on the object
by the force.
5. When a 4kg mass is hung vertically
on a certain light spring that obeys
Hook’s law, the spring stretches
2.5cm. If the 4kg mass is removed,
(a)How far will the spring stretch if a
1.5kg mass is hung on it and
(b)How much work must an external
agent do to stretch the same spring
4cm from its unstretched position?
6. If it takes 4J of work to stretch a
Hook’s law spring 10cm from its
unstressed length, determine the
extra work required to stretch it an
additional 10cm.
7. A small mass m is pulled to the top of a
frictionless half cylinder.
(a) If the mass moves at a constant speed,
show that F=mgcosθ.
(b) By directly integrating W   F  ds find
the work done in moving the mass at
constant speed from the bottom to the
top of the half cylinder. Here ds
represents an incremental displacement
of the small mass.
F
m
r
θ
8. A 0.6kg particle has a speed of 2m/s at
point A and kinetic energy of 7.5J at point
B.
(a) What is its kinetic energy at A
(b) Its speed at B.
(c) The total work done on the particle as it
moves from A to B.
9. A 3kg mass has an initial velocity vi=(6i2j)m/s.
(a) What is its kinetic energy at this time?
(b) Find the total work done on the object if
its velocity changes to (8i+4j)m/s. (hint:
remember that v2=v●v
10. A mechanic pushes a 2500kg car, moving
it from rest and making it accelerate from
rest to a speed v. He does 5000J of work
in the process. During this time, the car
moves 25m. If friction between the car
and the road is negligible,
(a) What is the final speed v of the car?
(b) What constant horizontal force did he
exert on the car?
11. A 40kg box initially at rest is pushed 5m
along a rough, horizontal floor with a
constant applied horizontal force of
130N. If the coefficient of friction
between the box and the floor is .3, find
(a) The work done by the applied force.
(b) The energy loss due to friction.
(c) The work done by the normal force.
(d) The work done by gravity.
(e) The change in kinetic energy of the box.
(f) The final speed of the box.
12. A block of mass 12kg slides from
rest down a frictionless 35° incline
and is stopped by a strong spring
with k=3x104N/m. The block slides
3m from the point of release to the
point where it comes to rest
against the spring.
(a)When the block comes to rest, how
far has the spring been
compressed?
(b)What is the maximum compression
of the spring?
13. A 650kg elevator starts from rest.
It moves upward for 3 seconds with
constant acceleration until it
reaches its cruising speed of
1.75m/s.
(a)What is the average power of the
elevator motor during this period?
(b)How does this power compare with
its power when it moves at its
cruising speed.
14. At 650-kg elevator starts from
rest. It moves upward for 3s with
constant acceleration until it
reaches its cruising speed of 1.75
m/s.
(a)What is the average power of the
elevator motor during this period?
(b)How does this power compare with
its power when it moves at its
cruising speed?
15. A force acting on a particle moving in the xy
plane is given by F = (2yi + x2j)N, where x and y
are in meters. The particle moves from the origin
to a final position having coordinates x=5m and
y=m, as in the figure. Calculate the work done
by F along
y
(a)OAC
(5,5) m
B
C
(b)OBC
(c)OC
x
O
A
(d)Is F conservative or nonconservative? Explain.
16. A particle of mass 0.5kg is shot from P as
shown in the figure. The particle has an initial
velocity vi with a horizontal component of
30m/s. The particle rises to a maximum height
of 20m above P. Using the law of conservation
of energy, determine
(a) the vertical component of vi
(b) the work done by the gravitational force on the
particle during its motion from P to B
(c) the horizontal and the vertical components of
the velocity vector when the particle reaches B.
20m
60m
17. A bead slides without friction around a
loop-the-loop. If the bead is released
from a height h=3.5R, what is its speed
at point A? How great is the normal
force on it if its mass is 5g?
h
A
18. A 120g mass is attached to he
bottom end of an unstressed
spring. The spring is hanging
vertically and has a spring constant
of 40N/m. The mass has dropped.
(a)What is its maximum speed?
(b)How far does it drop before coming
to rest momentarily?
19. Two masses are connected by a light
string passing over a light frictionless
pulley, as shown in the figure. The 5kg
mass is released from rest. Using the
law of conservation of energy,
(a)determine the speed of the 3kg mass
just as the 5kg mass hits the ground
(b)find the maximum height to which the
3kg mass rises.
m1=5kg
m2=3kg
h=4m
20. A 2kg ball is attached to the
bottom end of a length of 10lb
(44.5N) fishing line. The top end of
the fishing line is held stationary.
The ball is released from rest while
the held stationary. The ball is
released from rest while the line is
taut and horizontal (=90°). At
what angle  (measured from the
vertical) will the fishing line break?
21. After its release at the top of the first rise, a roller coaster
car moves freely with negligible friction. The roller coaster
shown in the figure, has a circular loop of radius of 20m.
The car barely makes it around the loop: At the top of the
loop, the riders are upside down and feel weightless.
(a)find the speed of the roller coaster car at the top of the loop
(position 3)
(b)at position 1
(c)at position 2
(d)find the difference in height between positions 1 and 4 if the
speed at position 4 is 10 m/s.
3
2
1
4
22. A 10kg block is released from point A. The track
is frictionless except for the portion between B and
C, which has a length of 6m. The block travels
down the track, hits a spring force of constant
k=2250N/m, and compresses the spring 0.3m
from its equilibrium position before coming to rest
momentarily. Determine the coefficient of kinetic
friction between the block and the rough surface
between B and C.
A
B
C