Download THIRD MIDTERM -- REVIEW PROBLEMS

Physics 2210
Spring 2009
George W illiams
THIRD MIDTERM -- REVIEW PROBLEMS
A data sheet is provided. This review set contains many problems related to Chapters 7 and 8. They are marked
with an *. I will discuss in class the exact coverage of the Third Midterm .
1.
(a)
(b)
(c)
(d)
(e)
Convert 756 J to foot-pounds.
A 675 kg object is raised vertically. If 19,000 J of work are expended, how high was it raised?
A spring is stretched 3.50 inches by a force of 14.6 pounds. Find the spring constant.
Convert 13,600 watts to horsepower.
A 10.5 kg mass moves at constant velocity across a horizontal surface when acted upon by a 18.0 N
horizontal force. Find the coefficient of sliding friction.
2.
(a)
(b)
(c)
Convert 324 J to English units.
Convert 472 kilowatts to horsepower.
The moon orbits the Earth in 27 1/3 days at a distance of 240,000 mi. Assume the mass of the moon is
small compared to the mass of the Earth. Calculate the inward acceleration of the moon in m/s 2.
A car skids to a stop from a speed of 60.0 mi/hr in a distance of 220 feet. Calculate the average value
of the coefficient of kinetic friction.
A block slides with constant velocity down the plane shown. The mass is
4.25 kg. Calculate the work done by friction while it slides 1.50 m.
(d)
(e)
3.*
4.
A non-Hooke's law spring follows the force law F = -kx - Bx 3 where k and B are positive constants, and x = 0
is the equilibrium position. An external force of 10.0 N compresses the spring 3.21 cm, and an external force
of 20.0 N compresses it 4.92 cm. (Be very careful about the sign you use for the 10 N and 20 N forces in
using the equation above.)
(a)
(b)
Find the constants k and B, with proper units.
Calculate the potential energy stored in the spring when it is compressed 9.00 cm. (Do this
symbolically if you can't do part (a).)
(a)
(b)
Convert 265 ft-lbs to joules.
A 1200 kg object is raised vertically a distance of 27.5 ft. How much work is done on the object?
(c)
A car of weight 3250 pounds is traveling at 65 mi/hr. The brakes are put on and it skids to a stop with
constant deceleration in a distance of 225 ft. Find the power being dissipated as heat after the car has
traveled 125 ft.
A block slides with constant velocity on a plane inclined at 29.0° from the horizontal. Calculate the
coefficient of kinetic friction.
A peculiar spring follows the force law F = !kx 5. (The sign convention is as used in Hooke's Law.) If
k = 37.5 N/m 5, find the energy stored in the spring when it is compressed 0.27 m.
(d)
(e)
5.
A very light rigid rod whose length is L has a ball of mass m attached to one
end as shown. The other end is pivoted without friction in such a way that the
ball moves in a vertical circle. The system is launched from the horizontal
position A with downward initial velocity v o. The ball just reaches point D
and then stops.
(a)
(b)
(c)
Derive an expression for v o in terms of L, m and g.
W hat is the tension in the rod when the ball is at B?
A little grit is placed on the pivot, after which the ball just reaches C
when launched from A with the same speed as before. How much work
is done by friction during this motion?
6.*
The system shown is released from rest with the spring in its
unstretched condition. m 1 is attached to the spring. The pulley is
massless. Use energy methods.
(a)
(b)
2 = 22.0°; k = 1200 N/m;
m 1 = 14.30 kg; m 2 = 17.25 kg
7.*
A massless Hooke's Law spring has unstretched length of 1.750 m. W hen a
37.5 kg mass is placed on it, and slowly lowered until the mass is at rest, the
spring is squeezed to a length of 1.712 m. A mass of 95.2 kg is dropped on
the spring from a height of 3.75 m. Use energy methods.
(a)
(b)
8.*
W hat is the length of the spring at maximum compression as a result of
the mass dropping on it? (Numerical answer.)
W hat is the energy stored in the spring when the velocity of the block is
2.50 m/s? (Numerical answer.)
(a)
Calculate
(b)
(c)
A force of 75.0 N acts through a distance of 45.0 m. Calculate the work done in ft@lbs.
Assume a spring with a force law given by F = -kx 3. If k = 250 N/m 3, calculate the work done to
compress the spring from x = 0 to x = 1.25 cm in joules.
Calculate the maximum safe speed for a car traveling around an unbanked curve of radius 400 ft if the
friction coefficients are :S = 0.75 and :K = 0.55. (The answer should be in ft/s.)
A car goes around an unbanked curve at 40.0 mi/hr. The curve has a radius of 500 ft. At what angle to
the vertical does a weight suspended on a string hang in the car?
(d)
(e)
9.*
How far will m 1 move until the system is instantaneously at
rest if the plane is frictionless?
If the coefficients of friction between the block and plane are
:k = 0.33 and :s = 0.44, how far will m 1 move before
instantaneously coming to rest for the first time?
, if
A block of mass m = 0.175 kg, is launched with an initial velocity v o
= 1.37 m/s down the incline. The coefficients of friction are :S =
0.65 and :K = 0.55. Use the work-energy theorem to calculate how
far down the incline the block slides before stopping. The plane is
as long as needed.
10.
(a)
Calculate
if
and
(b)
(c)
(d)
(e)
11.
A block of mass m (m = 1.80 kg) is pulled at constant speed down the
plane as shown. The coefficients of friction are: :s = 0.75 and :k = 0.55.
(a)
(b)*
(c)*
12.
A car goes around a curve that is not banked at 65.0 mi/hr. The curve has a radius of curvature of
720 ft. At what angle to the vertical does a weight suspended on a string hang in the car?
Convert 7,200 J to ft@ pounds.
If a spring has the force law F = !kx ! bx 3, calculate the work to stretch it from +x 1 to +x 2, where
neither x 1 nor x 2 are the unstretched length. (The unstretched position is x = 0.)
A mass of m = 4.70 kg is accelerated by a horizontal force of 27.0 N on a horizontal, frictionless
surface. How much work is done by the force in 2.00 seconds if the mass starts from rest?
(d)*
Calculate the numerical value of P.
Find the work done by P to move the block 2.50 m along the plane.
Determine the work done by gravity when the block moves 2.50 m
along the plane.
Calculate the work done by friction when the block moves 2.50 m along the plane.
(a)*
Calculate
(b)
(c)
Convert 62.7 Joules into footCpounds using the data given.
A non-Hookes Law spring has the force law F = !kx 3 (the sign convention is as in Hookes Law). If
k = 125 N/m 3, calculate the work done to stretch the spring from x = 0 to x = 0.360 m.
A car comes to a stop with constant acceleration. If the initial speed is 60.0 ft/s, and the stopping
distance 250 feet, calculate the angle from the vertical for a mass suspended on a string in the car
(while it is slowing down). Assume no oscillations, just the steady state.
An object weighing 275 pounds is raised vertically 4.20 m. Calculate the work (in Joules) necessary to
do this.
(d)
(e)
if
13.
The block of mass m (m = 2.75 kg) is pushed up the inclined plane at
constant speed by the force F, directed as shown. :s = 0.600, : k = 0.400
(a)
(b)*
(c)*
14.*
Calculate the magnitude of the force F.
Calculate the work done on the block by gravity when it moves
1.27 m up the plane.
Calculate the work done by friction on the block when it moves
1.27 m up the plane.
In this system the block, whose mass is given, is launched with an
initial velocity V o, as shown. The coefficients of friction are given.
The spring has a force constant k. The distance shown is from the
initial position (where the block has V = V o) to the end of the spring
when the spring is neither squeezed nor stretched. USE ENERGY
METHODS FOR BOTH PARTS.
V o = 4.70 m/s
:k = 0.40
:s = 0.60
(a)
(b)
15.
(a)
(b)
(c)
(d)
(e)
16.*
m = 1.25 kg
k = 350 N/m
Calculate the magnitude of the velocity of the mass just before
it first touches the spring.
Calculate the TOTAL distance the mass travels before its velocity first becomes zero.
A car weighing 3000 pounds is traveling at 25.0 mi/hr. Calculate its kinetic energy in Joules.
A 1500 kg car loses speed (40.0 m/s to 30.0 m/s) over a distance of 100 m when sliding with the
wheels locked. Calculate the coefficient of kinetic friction between the tires and road.
A block of mass 23.0 kg is moved at a steady speed of v = 15.0 m/s with an external force of 35.0 N.
Calculate the power delivered by this force.
If 1.25 hp are delivered by a force acting on a mass moving at 25.0 ft/s, what is the force.
Calculate the work (in Joules) needed to slowly raise a 756 pound object 13.0 feet vertically.
A block is launched up an inclined plane with an initial velocity of v o =
6.50 m/s. See figure. The coefficients of friction and other values are
given in the table. the spring is massless and is in its unstretched state.
Show clearly how you define PE = 0. USE ENERGY M ETHODS.
(a)
(b)
Calculate the magnitude of the amount the spring is squeezed
when the block comes to zero velocity.
Determine the position of the block when it comes to rest on the
way down. Measure this as the distance from its initial position.
Up is positive, down is negative from there.
:k = 0.65
d = 1.25 m
k = 2100 N/m
:s = 0.75
m = 0.70 kg
17.*
A small block is launched into a frictionless tube as shown. The
curved part is a circle of radius R. The plane of the drawing is the
vertical plane, with up shown. The spring constant is k.
(a)
(b)
(c)
18.
(a)
Calculate
(b)
(c)
Convert 427 Joules into ftAlbs using the data given.
An object whose weight is 350 pounds is lifted a distance of 75.0 ft. Calculate the work, in Joules,
necessary to do this.
The coefficient of static friction between the block and plane
shown is 0.75. Calculate the frictional force on the block.
(d)
(e)
19.*
if
Assume a peculiar spring with the force law F = !kx 5. If k = 175 N/m 5, calculate the work that must be
done on the spring to stretch it from x = 0 to x = 2.0 cm.
Block m starts at rest as shown in the drawing. The spring is initially
unstretched and not squeezed. This spring is a normal Hooke's Law
spring.
(a)
(b)
(c)
(d)
20.
Calculate the minimum compression of the spring, d, that
will cause the block to arrive at the top with zero velocity
If the spring is compressed a distance d before launching the
block, what is the normal force on the block at point B,
exactly at the same vertical position as the center of the
loop? d is large enough that the velocity at A is greater than
zero. [Not the same as (a).]
For the case in (a), find the normal force on the block at C,
the exact bottom. (Here the velocity at A is infinitesimally greater than zero.)
(a)
(b)
(c)
(d)
(e)
Calculate the work done by F on the block to move the block
0.500 m up the plane.
Find the work done by friction on the block when the block is
moved 0.500 m up the plane.
Determine the work done by gravity on the block when the block
is moved 0.500 m up the plane.
W hat is the work done by the spring on the block when it moves 0.500 m up the plane?
How much work is done by a person moving a 5.00 kg box up a frictionless hill with s = 10.0 m and h
= 3.00 m?
Convert 105 horsepower into watts.
How much work is done by gravity when a 10.0 kg object is lifted 5.00 m?
A Hooke's Law spring with k = 37.5 N/m is compressed 20.0 cm. Find the work that must be done on
the spring to achieve this.
A car rounds a curve at 65.0 mph. The curve has a radius of 700 ft. A weight is suspended on a string
inside the car. W hat is the angle of the string with respect to the vertical?
21.*
A spring has a force law of F = -k 1x - k 2x 3. The sign convention is as discussed in class.
(a)
(b)
Calculate the work done to compress the spring by 1.50 cm from the equilibrium position.
Determine the work done to stretch the spring by 0.75 cm from the equilibrium position.
k 2 = 75 N/m 3
k 1 = 200 N/m
22.
(a)
(b)
(c)
(d)
(e)
23.*
24.
Calculate the kinetic energy, in Joules, of a 2.45 × 10 6 kg asteroid at 15,000 m/s as it enters the Earth’s
atmosphere.
A block slides with constant velocity down an inclined plane at an angle of 33° from the horizontal.
Calculate the coefficient of kinetic friction.
Convert 17,120 watts to ftApounds/s.
In this drawing the coefficient of static friction is 0.60. The block (mass = 4.75
kg) is not moving. Find the frictional force acting on it.
A Hooke’s Law spring with a spring constant of k = 75,000 N/m, is compressed 22.0 cm. W hat is the
work done by an external force to achieve this?
The block shown has a mass of 1.58 kg. The block is pulled up the incline
an external force F, as shown. The coefficients of friction are :s = 0.70 and
:k = 0.55. The force F is 7.50 N. The block stays in contact with the plane
at all times. If the block is moved 2.25 m up the incline, calculate (including
signs):
(a)
(b)
(c)
(d)
the
the
the
the
(a)
The driver of a moving car slams on the brakes and leaves 250 ft of skid marks before stopping. If the
friction coefficients are :s = 0.75 and :k =0.60, what was the original speed of the car at the beginning
of the skid marks?
In the drawing shown the block has a mass of 17.5 kg. The friction
coefficients are :s = 0.75 and :k = 0.60. If the block is not moving,
calculate the friction force on it.
(b)
(c)
(d)
(e)
work
work
work
work
done
done
done
done
by
on
by
by
gravity on the block;
the block by the normal force;
F on the block;
friction on the block.
A 100,000 pound railroad car is pushed with a steady horizontal force of 50 pounds. It starts at rest. If
there is no friction, what is the speed, in ft/s, of this car after 30.0 seconds?
A car goes around an unbanked curve, which has a radius of 300 m, at a steady speed of 40.0 m/s. A
mass is suspended from a string inside the car. W hat is the angle between the string and the vertical
direction?
A block slides down an incline at a constant speed. The incline has an angle of 37.0°
from the horizontal. W hat is the coefficient of kinetic friction?
25.
A car on a frictionless roller-coaster is released from rest
at a height h as shown. At the top of the hump the radius
of the curvature of the track is R. The height of the top of
the hump is shown in the diagram.
(a)
(b)
26.
A small object of mass M is launched with a velocity v o at the top
of the frictionless track shown. Calculate the normal force on the
object at point A. The curved portion of the track has a radius of
curvature R. A is the exact bottom of the curve.
27.
28.
If the apparent weight of a person in the car 1/3 of
his normal weight at the top of the hump (point B),
calculate h in terms of R, g and numbers. The
person and car are assumed small compared to R.
For the same starting conditions, calculate the
apparent weight of a 100 kg person at point C, if the
radius of the curvature at C is 2R.
A spring of spring constant k is used to launch a block of
mass m up the curved track shown. The track is in a
vertical plane. The maximum height observed for the
block is given by h. If k = 2.75 × 10 4 N/m, m = 3.25
kg, h = 7.50 cm and the initial compression of the
spring is 2.25 cm, find the energy lost to friction.
In the roller coaster loop-the-loop shown, the
frictionless car starts with zero velocity at a height h.
The normal force at the top of the loop (point A) is
found to be three times the weight of the cart. Take
the radius of the loop as R.
(a)
(b)
Calculate h in terms of R and g.
Calculate the normal force on the car at point B
where 2 = 30° from the horizontal. Express
this as a number or fraction times the weight of
the car.
29.
A small block is launched on the frictionless loop-theloop shown. The spring launcher has a spring
constant k.
(a)
(b)
(c)
30.
A small block of mass m slides along the frictionless
loop-the-loop shown.
(a)
(b)
If it starts from rest at P, what is the normal
force acting on it at Q?
At what height above the bottom of the loop
should the block be released so that the force it
exerts against the track at the top of the loop is
equal to its weight?
31.
A mass of m = 4.75 kg is attached to a massless rod of length L = 1.32 m. The rod is
pivoted at P so that it can rotate in the vertical plane. When the mass is directly above
P it is given an initial horizontal velocity of 2.75 m/s.
(a)
(b)
32.
Find the velocity at the top of the loop as a
function of the displacement x of the spring
launcher from its equilibrium length.
Find the minimum value of x such that the
block goes over the top in contact with the
track.
Find the normal force on the block at A as a
function of x.
Calculate the tension in the rod (in newtons) when the mass is exactly below the
pivot point P.
Calculate the kinetic energy of the mass when the rod is at an angle of 45° from
the vertical as shown.
A frictionless plane is at an angle 2 with the horizontal. A pivot
in the middle is attached to a string of length R. Attached to the
string is a mass m, so that the mass can move in a circular path
about the pivot. When the mass is at its lowest point it is given an
initial tangential velocity v o. When the mass is at its topmost
point the tension in the string is measured to be 2 times the weight
of the mass. Calculate the initial velocity v o, in terms of m, g, R
and 2 .
33.
On the incline shown, a block of mass 2 kg is launched upward with
an initial velocity at point A of v o. The block strikes a massless
spring at B and compresses it. The relaxed length of the spring, Ro,
is 0.5 m. The distance AB is 2.5 m. The coefficient of sliding
friction is 0.3 and the spring constant k is 2500 N/m. If the spring
is compressed to a length 0.3 m by the impact of the block (before
the block stops), find the value of v o. (Use energy methods.)
34.
A block of mass 3.00 kg is launched down the inclined
plane with a velocity of 2.25 m/s. when it reaches the
bottom it has a velocity of 4.15 m/s.
(a)
(b)
Using energy methods, calculate the coefficient
of kinetic friction between the block and the
plane.
If it is launched up the plane from the bottom
with a velocity of 2.25 m/s, find how far up the
plane it goes.
35.
36.
A block is moved up an inclined plane by a
constant horizontal force, P. The block starts
with an initial velocity, V o = 1.50 m/s, and stops
exactly at the top.
(a)
(b)
Draw a clear free body diagram for the
block.
Find the value of P. (Use energy
methods.)
: s = 0.70
m = 3.25 kg
: k = 0.55
2 = 30.0°
37.
38.
A small block of mass 0.375 kg is launched up the plane
shown with an initial speed of 12.0 m/s. The distance from
the initial point to the spring is 2.12 m. Initially the spring is
in its relaxed state. The spring is very long and massless If
the spring constant is 2.32 N/m, find how much the spring is
compressed when the block comes to rest. The coefficient of
static friction is 0.750 and the coefficient of kinetic friction is
0.650.
A block, of mass 1.75 kg, slides down the plane shown. The
coefficients of friction are : s = 0.470, : k = 0.415. The block
starts at rest and slides 1.25 m before striking a spring of
spring constant k = 130 N/m. Calculate the amount by which
the spring is compressed when the block is brought to a stop.
A constant force, F = 40.0 N, is applied to the massless string.
A block starts at rest.
(a)
(b)
(c)
Calculate the kinetic energy of the block after it has
traveled 1.75 m up the plane.
Determine the work done by friction while the block is
traveling 1.75 m up the plane.
Find the work done by gravity on the block while
traveling 1.75 m up the plane.
39.
A sphere m of mass 0.750 kg is attached to a massless rod whose length is 1.45 m. The rod
is pivoted at P so that it moves in a vertical plane. W hen the mass is directly above P it is
given an initial velocity of v o = 2.55 m/s.
(a)
(b)
40.
A block of mass m is moved down the plane with a constant force P
(constant in magnitude and direction). Initially the block is at rest, and
at the bottom it has a velocity of v = 1.75 m/s. A clear free body
diagram and separate force diagram for the block are essential for full
credit. Calculate using these numerical values: : s = 0.75, : k = 0.55
and m = 1.35 kg
(a)
(b)
41.
Find the work done by friction on the block.
Calculate the work done by P on the block.
A block moves on the frictionless loop-the-loop shown. The initial position is at a height h and has an
initial velocity v o. The block is to be considered very small.
(a)
(b)
(c)
42.
Calculate the velocity of m when it is directly below P.
Determine the tension in the rod when it is at 30° from the vertical as shown by the
dotted lines.
If h = 2R, calculate the minimum value of v o so that the
block remains in contact with the loop all the way around.
If v o = (2gR) 1/2 and h = 2R, calculate the normal force on
the block at point B, exactly opposite the center of the loop.
If v o = (2gR) 1/2 and h = 2R, calculate the normal force on
the block at C, exactly at the bottom. (At C, the track is
curved in the circular shape of the loop with radius R.)
A small sphere of mass m = 2.30 kg is attached to a massless, rigid rod. The
length of the rod is 0.870 cm, and it is pivoted at point P. The spring has a
spring constant of 205 N/m. It is initially squeezed 0.25 m from its
equilibrium length, and is in contact with the sphere. The left end of the
spring is rigidly fixed.
(a)
(b)
(c)
Calculate the speed of the sphere at A (directly above P).
Determine the force on the sphere due to the rod, including direction
(in or out), at A.
W hat is the minimum compression of the spring such that the sphere
reaches point A, directly above P.
43.
The block shown starts at rest and slides 1.25 m before striking the spring. The
coefficients of friction are :s = 0.70 and :k = 0.60. The mass of the block is .375
kg. The spring constant is 210 N/m.
(a)
(b)
44.
Calculate the amount of compression from equilibrium of the spring at the
point when the block first comes to v = 0.
W hat is the maximum distance back up the plane the block will slide.
Measure this from A, the equilibrium point of the spring.
The block shown has a mass of 1.75 kg and is launched down the inclined
plane at an initial velocity V o of 2.35 m/s. The spring is 0.75 m long when
unstretched and unsqueezed, and its spring constant is 1400 N/m.
(a)
(b)
In the absence of friction, calculate the length of the spring when the
block is brought to rest.
In the presence of friction, calculate the length of the spring when the
block is brought to rest.
V o = 2.35 m/s; m = 1.75 kg; k = 1400 N/m;
:s = 0.70; :k = 0.55
Data: Use these constants (where it states for example, 1 ft, the 1 is exact for significant figure purposes).
1 ft = 12 in (exact)
1 m = 3.28 ft
1 mile = 5280 ft (exact)
1 hour = 3600 sec = 60 min (exact)
1 day = 24 hr (exact)
g ea rth = 9.80 m/s 2
= 32.2 ft/s 2
g m oon = 1.67 m/s 2
= 5.48 ft/s 2
1 year = 365.25 days
1 kg = 0.0685 slug
1 N = 0.225 pound
1 horsepower = 550 ftApounds/s (exact)