Physics Homework Ch7

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Questions and comments are welcome!

1. A wheel has a radius of 3.6 m. How far (path length) does a point on the circumference travel if the wheel is rotated through the following angles, respectively
a) 31 °
_____ m

b) 31 rad
_____m

c) 31 rev
_____m






2. The tires on a new compact car have a diameter of 2.0 ft and are warranted for 64,000 miles.
 a) Determine the angle (in radians) through which one of these tires will rotate during the warranty period
_________ rad

b) How many revolutions of the tire are equivalent to your answer in (a)?
________ rev






3. A potter's wheel moves uniformly from rest to an angular speed of 0.19 rev/s in 29.0 s.
a) Find its angular acceleration in radians per second per second
 ________ rad/s²






4. A race car starts from rest on a circular track of radius 433 m. The car's speed increases at the constant rate of 0.320 m/s² . At the point where the magnitudes of the centripital and tangential accelerations are equal, find the following.
a) the speed of the race car
________m/s

b) the distance traveled
______ m

c) The elapsed time
______ s






5. A dentist drill starts from rest. After 3.30 s of constant angular acceleration it turns at a rate of 2.9 X 10⁴ rev/min.
a) Find the drill's angular acceleration
______ rad/s²

b) Determine the angle (in radians) through which the drill rotates during this period
_________ rad






6. A 53.4-cm diameter disk rotates with a constant angular acceleration of 2.60 rad/s². It starts from rest at t = 0, and a line drawn from the center of the disk to point p on the rim of the disk makes an angle of 57.3° with the positive x-axis at this time.
a) Find the angular speed of the wheel at t = 2.30 s
______ rad/s

b) Find the linear velocity and tangential acceleration of p at t = 2.30 s.
linear velocity _______ m/s
tangential acceleration  _____ m/s²

c) Find the position of P (in degrees, with respect to the positive x-axis) at t = 2.30 s
________ °




7. A rotating wheel requires 6.00 s to rotate 25.0 revolutions. Its angular velocity at the end of the 6.00-s interval is 96.0 rad/s. What is the constant angular acceleration (in rad/s^2/) of the wheel
______ rad/s^2/






8. A car initially traveling eastward turns north by traveling in a circular path at uniform speed as in the figure. The length of the arc ABC is 249 m, and the car completes the turn in 33.0 s

a) Determine the car's speed
_______ m/s

b) What is the magnitude and direction of the acceleration when the car is at point B?
magnitude _________ m/s²
direction   _________ ° counterclockwise from the +x-axis





9. It has been suggested that rotating cylinders about 11 mi long and 3.6 mi in diameter be placed in space and used as colonies. What angular speed must the cylinder have so that the centripetal acceleration at its ssurface equals the free-fall acceleration on Earth?
__________ rad/s






10. An adventurous archeologist (m = 80.5 kg) tries to cross a river by swinging from a vine. The vine is 11.0 m long, and his speed at the bottom of the swing is 8.5 m/s. The archeologist doesn't know that the vine has a breaking strength of 1,000 N. Does he make it safely across he river without falling in?
Yes
No






11. A 55.0-kg ice skater is moving at 4.03 m/s when she grabed the loose end of a rope, the opposite end of which is tied to a pole. She then moves in a circle of radius 0.805 m around the pole
a) Determine the force exerted by the horizontal rope on her arms.
_______N
b) Compare this force with her weight by finding the ratio of the force to her weight
_________







12. A certain light truck can go around a flat curve having a radius of 150 m with a maximum speed of 30.5 m/s. With what maximum speed can it go around a curve having a radius of 85.5 m?
_________m/s






13. A 50.0-kg child stands at the rim of a merry-go-round of radius 2.10 m, rotating with an angular speed of 2.6 rad/s
a) What is the child's centripetal acceleration?
________ m/s²
b) What is the minimum force between her feet and the floor of the carousel that is required to keep her in the circular path?
________N
c) What minimum coefficient of static friction is required?
__________
Is the answer you found reasonable? In other words, is she likely to stay on the merry-go-round?

Yes
No






14. An air puck of mass m₁ = 0.30 kg is tied to a string and allowed to revolve in a circle of radius R = 1.3 m on a frictionless horizontal table. The other end of the string passes through a hole in the center of the table, and a mass of m₂ = 1.1 kg is tied to it (see the figure below). The suspended mass remains in equilibrium while the puck on the tabletop revolves.

a) What is the tension in the string?
_______ N
b) What is the horizontal force acting on the puck?
_______N
c) What is the speed of the puck?
_______m/s






15. The average distance separating Earth and the moon (center to center) is 384,000 km. Use the data in the table to find the net gravitational force exerted by the Earth and the Moon on a 3.00 x 104-kg spaceship located halfway between them.
________ N

Useful Planetary Data
Body	Mass (kg)	Mean Radius (m)	Period (s)	Distance from Sun (m)	T2/r3 (s2/m3)
Mercury	3.18 x 1023	2.43 x 106	7.60 x 106	5.79 x 1010	2.97 x 10−19
Venus	4.88 x 1024	6.06 x 106	1.94 x 107	1.08 x 1011	2.99 x 10−19
Earth	5.98 x 1024	6.37 x 106	3.156 x 107	1.496 x 1011	2.97 x 10−19
Mars	6.42 x 1023	3.37 x 106	5.94 x 107	2.28 x 1011	2.98 x 10−19
Jupiter	1.90 x 1027	6.99 x 107	3.74 x 108	7.78 x 1011	2.97 x 10−19
Saturn	5.68 x 1026	5.85 x 107	9.35 x 108	1.43 x 1012	2.99 x 10−19
Uranus	8.68 x 1025	2.33 x 107	2.64 x 109	2.87 x 1012	2.95 x 10−19
Neptune	1.03 x 1026	2.21 x 107	5.22 x 109	4.50 x 1012	2.99 x 10−19
Pluto	~1.4 x 1022	~1.5 x 106	7.82 x 109	5.91 x 1012	2.96 x 10−19
Moon	7.36 x 1022	1.74 x 106	-	-	-
Sun	1.991 x 1030	6.96 x 108	-	-	-

16. A satelite has a mass of 99 kg and is located at 2.05 x 10⁶ m above the surface of the Earth.
a) What is the potential energy associated with the satelite at this location?
________ J
b) What is the magnitude of the gravitational force on the satelite?
_______ N






17. A coordinate system (in meters) is constructed on the surface of a pool table, and three objects are placed on the table as follows: a 7.0-kg object at the origin of the coordinate system, a 16.0-kg object at (0, 2.0), and a 25.0-kg object at (4.0, 0). Find the resultant gravitational force exerted by the other two objects on the object at the origin.
Magnitude _________ N
direction    ________°






18. Objects with masses of 190 kg and a 490 kg are separated by 0.430 m.
a) Find the net gravitational force exerted by these objects on a 65.0-kg object placed midway between them.
magnitude _______ N
direction
 - Toward the 190-kg mass
 - Toward the 490-kg mass
 - The magnitude is zero






19. A satelite is in a circular orbit around the Earth at an altitude of 2.52 x 10⁶ m.

a) find the period of the orbit. (Hint: Modify Kepler's third law:

                               T² = 

4π2

GMS

r³
 so it is suitable for objects orbiting the Earth rather than the Sun. The radius of the Earth is 6.38 x 10⁶ m, and the mass of the Earth is 5.98 x 10²⁴ kg.)
__________ h
b) Find the speed of the satellite
_______km/s
c) Find the acceleration of the satelite.
_______ m/s² toward the center of the earth






20. A satellite of Mars, called Phobos, has an orbital radius of 9.4 x 10⁶ m and a period of 2.8 x 10⁴ s. Assuming the orbit is circular, determine the mass of Mars
___________ kg






21. A 549-kg satellite is in a circular orbit about the Earth at a height above the Earth equal to the Earth's mean radius.
a) Find the satellite's orbital speed
_________m/s
b) Find the period of its revolution.
________ h
c) Find the gravitational force acting on it.
_________ N

Physics Homework Ch6

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1. Calculate the magnitude of the linear momentum for the following cases.
a) a proton with mass 1.67 X 10^-27 kg, moving with a speed of 5.45 X 10⁶ m/s
__________kg * m/s
b) a 12.5 g bullet moving with a speed of 350 m/s
_________kg * m/s
c) a 71.5 kg sprinter running with a speed of 11.5 m/s
________kg *m/s
d) the Earth (mass = 5.98 X 10²⁴ kg) moving with an orbital speed equal to 2.98 X 10⁴ m/s
_________kg * m/s




2. A pitcher claims he can throw a 0.159-kg baseball with as much momentum as a 2.10-g bullet moving with a speed of 1.50 X 10³ m/s
a). What mus the baseball's speed be if the pitcher's claim is valid?
______m/s
b). Which has greater kinetic energy, the ball the or the bullet?

Mode:
The bullet has greater kinetic energy
The ball has greater kinetic energy
Both have the same kinetic energy





3. An object has a kinetic energy of 232 J and a momentum of magnitude 21.6 kg * m/s.
a). Find the speed of the object
______m/s
b) Find the mass of the ojbect
_______ kg




4. A 0.252 kg volleyball approaches a player horizontally with a speed of 12.9 m/s. The player strikes the ball with her fist and causes the ball to move in the opposite direction with a speed of 22.0 m/s
a). What impulse is delivered to the ball by the player?
___________kg * m/s
b). If the player's fist is in contact with the ball for 0.0600 s, find the magnitude of the average force exerted on the player's fist.
___________ N





5. A ball of mass 0.120 kg is dropped from rest from a height of 1.25 m. It rebounds from the floor to reach a height of 0.600 m. What impulse was given to the ball by the floor?
magnitude _____ kg * m/s

Direction: (upward or downward)





6. A tennis player receives a shot with a ball (0.0600 kg) traveling horizontally at 54.0 m/s and returns the shot with the ball traveling horizontally at 32.0 m/s in the opposite direction.
a). What is the impulse delivered to the ball by the racket?
__________N*s  (direction: +x or -x)
b) What work does the racket do on the ball?





7. High speed stroboscopic photographs show that the head of a 210 - g golf club is traveling at 41 m/s just before it strikes a 46-g golf ball at rest on a tee. After the collision, the club head travels (in the same direction) at 30 m/s. Find the speed of the golf ball just after impact
________m/s





8. A rifle with a weight of 40 N fires a 6.0-g bullet with a speed of 230 m/s
a) Find the recoil speed of the rifle
______m/s
b) If a 750-N man holds the rifle firmly with his shoulder, find the recoil of the man and rifle.
________m/s






9. A 78-kg fisherman in a 119-kg boat throws a package of mass m = 15 kg horizontally toward the right with a speed of v_i = 4.3 m/s as in the figure below. Neglecting water resistance, and assuming the boat is at rest before the package is thrown, find the velocity of the boat after the package is thrown.
magnitude _______m/s
Direction (toward the right or toward the left)

 

10. A 70.0-kg person throws a 0.0470-kg snowball forward with a ground speed of 29.0 m/s. A second person with a mass of 59.0 kg, catches the snowball. Both people are on skates. The first person is initially moving forward with a speed of 2.00 m/s, and the second person is initially at rest. What are the velocities of the two peopel after the snowball is exchanged?
Disregard the friction between the skates and the ice.
Thrower _______ m/s
Catcher _______ m/s





11. A railraod car of mass 3.5 X 10⁴ kg moving at 4.00 m/s collides and couples with two coupled railroad cars, each of the same mass as the single car and moving in the same direction at 1.2 m/s
a). What is the speed of the three coupled cars after the collision?
________m/s
b) How much kinetic energy is lost in the collision?
_______ J






12. In a Broadway performance, an 71.6-kg actor swings from a 3.80-m-long cable that is horizontal when he starts. At the bottom of his arc, he picks up his 55.0 kg costar in an inelastic collision. What maximum height do they reach after their upward swing?
_________m






13. Two shuffleboard disks of equal mass, one orange and the other green, are involved in a perfectly elastic glancing collision. The green disk is initially at rest and is stuck by the orange disk moving initially to the right at _oi = 3.35 m/s as in figure (a) shown below. After the collision, the orange disk moves in a direction that makes an angle of θ = 39.0 ° with the horizontal axis while the green disk makes an angle of = 51.0°with this axis as in figure (b). Determine the speed of each disk after the collision.
_of = _______ m/s
_gf = _______ m/s

 

14. A 0.032-kg bullet is fired vertically at 215 m/s into a 0.15-kg baseball that is initially at rest. How high does the combined bullet and baseball rise after teh collision, assuming the bullet embeds itself in the ball?
__________m





15. A 26.0 g object moving to the right at 18.0 cm/s overtakes and collides elastically with a 10.0-g object moving in the same direction at 15.0 cm/s. Find the velocity of each object after the collision.
26.0 g object ________ cm/s
10.0 g object ________ cm/s






16. A billiard ball rolling across a table at 1.55 m/s makes a head on elastic collision with an identical ball. Find the speed of each ball after the collision when each of the following occurs.

a) The second ball is initially at rest.
frist ball _________m/s
second ball ________m/s

b) The second ball is moving toward the first at speed of 1.05 m/s
first ball ___________m/s
second ball ___________m/s

c) The second ball is moving away from the first at a speed of 1.10 m/s
first ball _________ m/s
second ball _________ m/s

Physics: Find Delta Y using Kenetic and Potential Energy

Because of the number of views on the Chapter five homework, especially problem number 12, I decided to rework 12 in a new video. I have found a faster (and more correct way of solving the problem)

12. A daredevil on a motorcycle leaves the end of a ramp with a speed of 28.0 m/s as in the figure below. If his speed is 26.4 m/s when he reaches the peak of the path, what is the maximum height that he reaches? Ignore friction and air resistance.
________m

Here is the initial video that I posted. It provides a way of finding the correct solution, but it is not the best or fastest way





Here is the video that shows how to solve using Kenetic Energy and Potential Energy and the law of conservation of energy. Much easier and faster

Physics Homework Ch5

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1. A weight lifter lifts a 310-N set of weights from ground level to a position over his head, a vertical distance of 1.75 m. How much work does the weight lifter do, assuming he moves the weights at a constant speed?
__________J





2. The record number of boat lifts, including the boat and its ten crew members was achieved by Sami Heinonen and Juha Rasanen of Sweden in 2000. They lifted a total mass of 653.2 kg approximately 4in off the ground a total of 24 times. Estimate the total mechanical work done by the two men in lifting the boat 24 times, assuming they applied the same force to the boat during each lift. (Neglect any work they may have done allowing the boat to drop back to the ground).
_________J





3. A horizontal force of 150 N is used to push a 41.0-kg packing crate a distance of 6.45 m on a rough horizontal surface. If the crate moves at a constant speed, find each of the following.
a). The work done by the 150-N force
_______J
b). the coefficient of kinetic friction between the crate and the surface
_______





4. A sledge loaded with bricks has a total mass of 18.4 kg and is pulled at constant speed by rope inclined at 20.1 degrees above the horizontal. The sledge moves a distance of 20.2 m on a horizontal surface. The coefficient of kinetic friction between the sledge and surface is 0.500
a). What is the tension in the rope
________N
b). How much work is done by the rope on the sledge?
__________KJ
c). What is the mechanical energy lost due to friction
__________KJ





5. A block of mass m= 2.3 kg is pushed a distance of d=4.40 m along a frictionless horizontal table by a constant force of magnitude F= 16.0 N directed at an angle θ = 28° below the horizontal as shown in the figure below.
a). Determine the work done on the block by the applied force.
_______J
b). Determine he work done on the block by the normal force exerted by the table.
_______J
c). Determine the work done on the block by the force of gravity.
_______J
d). Determine the work done by the net force on the block
_______J

















6. A mechanism pushes a 3.60 X 10 ³ -kg car from rest to a speed of v, doing 4,600 J of work in the process. During this time, the car moves 22.0 m. Neglecting friction between the car and road, find each of the following.
a) the speed v
_________m/s
b). The horizontal force exerted on the car
_________N






7. A 7.00-kg bowling ball moves at 2.05 m/s. How fast must a 2.80-g Ping-Pong ball move so that the two balls have the same kinetic energy?
________m/s






8. A 75-kg base runner begins his slide into second base when he is moving at a speed of 4.4 m/s. The coefficient of friction between his clothes and Earth is 0.70. He slides so that his speed is zero just as he reaches the base.
a) How much mechanical energy is lost due to friction acting on the runner?
__________J
b) How far does he slide?
__________m





9.A 0.30-kg stone is held 1.2 m above the top edge of a water well and then dropped into it. The well has a depth of 4.7 m.
a) Taking Y = 0 at the top edge of the well, what is the gravitational potential energy of the stone-Earth system before the stone is released?
_________J
b) Taking Y = 0 at the tope edge of the well, what is the gravitational potential energy of the stone-Earth system when it reaches the bottom of the well?
_________J
c) What is the change in gravitational potential energy of the system from release to reaching the bottom of the well?
_________J



10. When a 2.50-kg object is hung vertically on certain light spring described by Hooke's law, the spring stretches 3.21 cm.
a). What is the force constant of the spring?
________N/m
b) If the 2.50-kg object is removed, how far will the spring stretch if a 1.25-kg block is hung on it?
________cm
c) How much work must an external agent do to stretch the same spring 8.80 cm from its un-stretched position?




11. A 2,200-kg pile driver is used to drive a steel I-beam into the ground. The pile driver falls 4.40 m before coming into contact with the top of the beam, and it drives the beam 13.8 cm farther into the ground as it comes to rest. Using energy considerations, calculate the average force the beam exerts on the pile driver while the pile driver is brought to rest.
magnitude ________N
direction (Upward or Downward)?





12. A daredevil on a motorcycle leaves the end of a ramp with a speed of 28.0 m/s as in the figure below. If his speed is 26.4 m/s when he reaches the peak of the path, what is the maximum height that he reaches? Ignore friction and air resistance.
________m

This (above) video is an update to show a "better" way of solving the problem using work-energy analysis / conservation of energy.
The original video (below) is the original post solving the problem using kinematics.






13. A 44-kg pole vaulter running at 12 m/s vaults over the bar. Her speed when she is above the bar is 1.0 m/s. Neglect air resistance, as well as any energy absorbed by the pole, and determine her altitude as she crosses the bar.
_______m





14. A child and sled with a combined mass of 55.0 kg slide down a frictionless slope. If the sled starts from rest and has a speed of 2.10 m/s at the bottom, what is the height of the hill?
__________m




15. A 0.280-kg block along a horizontal track has a speed of 1.40 m/s immediately before colliding with a light spring of force constant 37.2 N/m located at the end of the track.
a) What is the spring's maximum compression if the track is frictionless?
________m
b) If the track is not frictionless, would the spring's maximum compression be greater than, less than, or equal to the value obtained in part (a)?




16. A block of mass m= 4.10 kg is released from rest from point A and slides on the frictionless track shown in the figure below. (Assume h_a = 6.9 m.)

a) Determine the block's speed at points B and C
Point B ________ m/s
Point C _________m/s

b) Determine the net work done by the gravitational force on the block as it moved from point A to point C
__________J





17. Tarzan swings on a 30.0-m-long vine initially inclined at an angle of 31.0 ° with the vertical.
a) what is his speed at the bottom of the swing if he starts from rest?
__________m/s
b) What is his speed at the bottom of the swing if he pushes off with a speed of 2.00 m/s?
__________m/s




18. The electrci motor of a model train accelerates the train from rest to 0.760 m/s. in 15.0 ms. The total mass of the train is 530 g. Find the average power delivered to the train during its acceleration.
_________W

Physics Homework Ch4

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1. A football punter accelerates a football from rest to a speed of 13 m/s during the time in which his toe is in contact with the ball (about 0.24 s). If the football has a mass of 0.50 kg, what average force does the punter exert on the ball?
 __________ N

Try out the calculator (Must be using Chrome) or download the Calculator for this problem

2. A 11.0-kg object undergoes an acceleration of 2.9 m/s².
a). What is the magnitude of the resultant force acting on it?
_________ N
b). If the same force is applied to a 22.0-kg object, what acceleration is produced?
________ m/s².




3. One or more external forces are exerted on each object enclosed in a dashed box shown in the figure below. Identify the reaction to each of these forces. (Assume that (a), (b), and (c) occure on Earth while (d), (e), and (f) occur far from any outside gravitational influences. Select all that apply).

A)	The spring exerts a force		B)	The wagon exerts a force
□	downward on the Earth		□	downward on the Earth due to contact
□	to the right on the hand		□	upward on the Earth due to contact
□	upward on the Earth		□	downward on the Earth due to gravitational attraction
□	to the right on the wall		□	downward to the left on the handle
□	to the left on the hand		□	upward on the Earth due to gravitational attraction
□	to the left on the wall		□	upward to the left on the handle
C)	the ball exerts a force		D)	m exerts a force
□	downward to the left on the player		□	to the left on M
□	upward to the right on the player		□	to the right on M
□	downward on the Earth		□	upward on M
□	downward to the right on the player		□	downward on M
□	upward on the Earth
E)	-q exerts a force		F)	The iron exerts a force
□	to the right on Q		□	downward on the magnet
□	upward on Q		□	upward on the magnet
□	to the left on Q		□	to the left on the magnet
□	downward on Q		□	to the right on the magnet

4. A bag of sugar weighs 6.00 lb on Earth. What would it weigh in newtons on the moon, where the free-fall acceleration is one-sixth that on Earth?
________N

Repeat for Jupiter, where g is 2.64 times that on Earth.
________N

Find the mass of the bag of sugar in kilograms at each of the three locations
Earth ____ kg
Moon ____kg
Jupiter____kg




5. A freight train has a mass of 1.3 X 10⁷ kg. If the locomotive can exert a constant pull of 7.4 X 10⁵ N, how long does it take to increase the speed of the train from rest to 78 km/h?
_________min



6. A 73-kg man standing on a scale in an elevator notes that as the elevator rises, the scale reads 842 N. What is the acceleration of the elevator?
_____m/s² upward.




7. A 5.6-g bullet leaves the muzle of a rifle with a speed of 320 m/s. What force (assumed constant) is exerted on the bullet while it is traveling down the 0.75-m-long barrel of the rifle?
______N



8. A boat moves through the water with two forces acting on it. One is a 1,500-N forward push by the water on the propeller, and the other is an 1,200-N resistive force due to the water around the bow.
a). What is the acceleration of the 800-kg boat?

b). If it starts from rest, how far will the boat move in 5.0 s?
______m

c). What will its velocity be at the end of that time?
________m/s





9. A 891-kg car starts from rest on a horizontal roadway and accelerates eastward for 5.00 s when it reaches a speed of 30.0 m/s. What is the average force exerted on the car during this time?
_______N eastward





10. A 2.00 kg block is held in equilibrium on an incline of angle θ = 65° by a horizontal force  applied in the direction shown in the figure below. If the coefficient of static friction between block and incline is μ_s = 0.300, determine the following.

a). The minimum value of 
________ N
b). the normal force exerted by the incline on the block
________N

Purchase the Excel Calculator For Problem #10 ($1.35), to solve quickly and easily

NOTE: I recommend you watch the video if you're having problems, but the calculator that I built will be able to get you at the right solution if you're in a hurry.
When you pay on paypal, click "back to mike b" and it will automatically download the file.

11. Consider the figure below.















a). Find the tension in each cable supporting the 700-N cat burglar. (Assume the angle θ of the inclined cable is 32.0° )
Inclined cable        ________N
Horizontal Cable   ________N
Vertical Cable       ________N

b). Suppose the horizontal cable were reattached higher up on the wall. Would the tension in the inclined cable
__increase,
__decrease,
__or stay the same?




12. The leg and cast in the figure below weigh 347 N(w₁). Determine the weight w₂ and angle α needed so that no force is exerted on the hip joint by the leg plus cast.
w₂ = _______ N
α =  _________ °






13. A crate of mass m = 25 kg rides on the bed of a truck attached by a cord to the back of the cab as in the figure. The cord can withstand a maximum tension of 63 N before breaking. Neglecting friction between the crate and truck bed, find the maximum acceleration the truck can have before the cord breaks.
_______m/s²












14. Two packing crates of masses m₁ = 10.0 kg and m₂ = 4.00 kg are connected by a light string that passes over a frictionless pulley as in the figure. The 4.00-kg crate lies on a smooth incline of angle 34.0°















a). Find the acceleration of the 4.00-kg crate.
________m/s²  (up the incline)

b). Find the tension in the string
_________ N

Free - Download Calculator for Ch4 number 14

15. Assume the three blocks (m₁ = 1.0 kg, m₂ = 2.0 kg, and m₃ = 4.0 kg) portrayed in the figure below move on a frictionless surface and a force F = 44 N acts as shown on the 4.0-kg block.







a) determine the acceleration given this system
 ________m/s² (to the right)

b). Determine the tension ion the cord connecting the 4.0-kg and the 1.0-kg blocks
________N

c). Determine the force exerted by the 1.0-kg block on the 2.0-kg block.
_________N





16. A block of mass m = 5.3 kg is pulled up a θ = 26° incline as in the figure with a force of magnitude F = 33 N.

a). Find the acceleration of the block if the incline is frictionless

b). Find the acceleration of the block if the coefficient of kinetic friction between the block and the incline is 0.12
________m/s²





17. A dockworker loading crates on a ship finds that a 17-kg crate, initially at rest on a horizontal surface, requires a 73-N horizontal force to set in motion. However, after the crate is in motion, a horizontal force of 52 N is required to keep it moving with a constant speed. Find the coefficient of static and kinetic friction between the crate and floor.
μ_{static _______}μ_{kinetic ______}






18. In the figure below, m₁ = 9.5 kg and m₂ = 3.5 kg. The coefficient of static friction between m_{1 and the horizontal surface is 0.5, and the coefficient of kinetic friction is 0.30.}

















a) If the system is released from rest, what will its acceleration be?
_________m/s²b) If the system is set in motion with m₂ moving downward, what will be the acceleration of the system?
________m/s²










19. A 1,400-N crate is being pushed across a level floor at a constant speed by a force  of 330 N at an angle of 20.0° below the horizontal, as shown in the figure (a) below.

a). What is the coefficient of kinetic friction between the crate and the floor?
μ_k = ________

b). If the 330-N force is instead pulling the block at an angle of 20.0° above the horizontal, as shown in the figure (b), what will be the acceleration of the crate?
Assume that the coefficient of friction is the same as that found in part (a).
_________m/s²






20. The coefficient of static friction between the m = 3.30-kg crate and the 35.0° incline of the figure below is 0.295. What minimum force  must be applied to the crate perpendicular to the incline to prevent the crate from sliding down the incline?
_________N