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
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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 ha = 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
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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
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 μs = 0.300, determine the following.
a). The minimum value of
________ N
b). the normal force exerted by the incline on the block
________N
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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)
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 aθ = 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. μstatic _______μkinetic ______
18. In the figure below, m1 = 9.5 kg and m2 = 3.5 kg. The coefficient of static friction between m1 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? μk = ________
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
applied in the direction shown in the figure below. If the coefficient of static friction between block and incline is 
