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# Set of problems on mechanics

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Chapter 7:

11. Engine 1 does twice the work of engine 2. Is it correct to conclude that engine 1 produces twice as much power as engine 2 explain?

12. Engine 1 produces twice the power of engine 2. Is it correct to conclude that engine 1 does twice as much work as engine 2? Explain.

38. You raise a bucket of water from the bottom of a deep well. If your power output is 108 W, and the mass of the bucket and the water in it is 5.00kg, with what speed can you raise the bucket? Ignore the weight of the rope.

40. A kayaker paddles with a power output of 50.0 W to maintain a steady speed of 1.50 m/s.
(a) Calculate the resistive force exerted by the water on the kayak.
(b) If the kayaker doubles her power output, and the resistive force due to the water remains the same, by what fact
or does the kayakers speed change?

49. You push a 67kg box across a floor where the coeffient of kinetic friction is uk=0.55. The force you exert is horizontal.
(a) How much power is needed to push the box at a speed of 0.50m/s.
(b) How much work do you do if you push the box for 35s.

Chapter 8:

6. An object is thrown upward to a person on a roof. At what point is the object's kinetic energy at maximum? At what point is the potential energy of the system at maximum? At what locations do these energies have their minimum values?

12. You ride your bicycle down a hill, maintaining a constant speed the entire time.
(a) As you ride does the gravitational potential energy of the earth-bike -rider system increase, decrease, or stay
the same?
(b) Does the kinetic energy of you and your bike increase, decrease or stay the same?
(c) Has the mechanical energy of this system increased, decreased, or remained the same?

13. A leaf falls to the ground with a constant speed. Is Ui + Ki greater than, less than, or the same as Uf + Kf for this
system?

6. As an Acapulco cliff diver drops to the water from a height of 46m, his gravitational potential energy decreases by
25,000J. What is the diver's weight in newtons?

16. At an amusement park, a swimmer uses water slide to enter the main pool.
If the swimmer starts at rest, slides without friction, and descends through a vertical height of 2.61m, what is her
speed at the bottom of the slide?

Find the swimmer's speed at the bottom of the slide if she starts with an initial speed of 0.840 m/s

18. In a tennis match, a player wins a point by hitting the ball sharply to the ground on the opponent's side of the net.

(a) If the ball bounces upward from the ground with a speed of 16 m/s and is caught by a fan in the stands with a
speed of 12m/s, how high above the court is the fan? Ignore air resistance.
(b) Explain why it is not necessary to know the mass of the tennis ball?

50. A sled slides without friction down a small, ice covered hill. If the sled starts from rest at the top of the hill, its speed
at the bottom is 7.50 m/s.

(a) On a second run the sled, starts with a speed of 1.50 m/s at the top. When it reaches the bottom of the hill, is its
speed 9.00 m/s, more than 9.00 m/s, or less than 9.00 m/s? Explain??
(b) Find the speed of the sled at the bottom of the hill after the second run.

Chapter 11

1. Two forces produce the same torgue. Does it follow that they have the same magnitude? Explain.

6. At the local playground, a 16kg child sits on the end of a horizontal teeter-totter, 1.5m from the pivot point. On the other side of the pivot an adult pushes straight down on the teeter-totter with a force of 95 N . In which direction does the teeter-totter rotate if the adult applies the force at a distance of

(a) 3.0m
(b) 2.5m, or
(c) 2.0 m from the pivot?

22. A school yard teeter-totter with a total length of 5.2m and a mass of 36 kg is pivoted at its center. A 18 kg child sits on one end of the teeter-totter.

(a) Where should a parent push vertically downward with a force of 210N in order to hold the teeter-totter level?
(b) Where should the parent push with a force of 310 N?
(c) How would your answers to parts (a) and (b) change if the mass of the teeter-totter were doubled explain?

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## Mechanical Engineering Problem Sets

See attached file for full problem description.

1) The horizontal bar represented in figure is acted upon by the four vertical forces f1,f2,f3, and f4, whose location and characteristics are shown. Calculate the horizontal distance from point O at the base of F4 and horizontal line to the line of action of the resultant of the given forces.
F1=400lbs, F2=3500lbs, F3=4500lbs , F4=3000lbs

Between F1 and F2 is 6ft,between F2 and F3 is 6 ft, Between F3 and F4 is 8ft

F1 F2 F3 F4
2) A railroad car that weighs 20,000 lb is traveling eastward with a velocity whose magnitude is 5fps. A second car, on the same track, that weighs 40,000 lbs also traveling in an easterly direction with a velocity of 7.8fps. When the cars collided, they became coupled together and then both cars moved with the same velocity. If friction between the cars and the rails is neglected, what were the magnitude and the direction of the velocity of the car after the collision?

Fluid Mechanics

3) A cylinder tank is 20ft in diameter and contains fresh water to a dept of 60 feet.
a) What is the unit pressure, in pounds per square inch, at a depth of 30 ft below the water surface?
b) What is the unit pressure, in pounds per square foot, at a depth of 40ft.
c) What is the total pressure, in pounds, on the bottom of the tank ?

4) Water is flowing uniformly through a pipe with a diameter of 14 inches if the mean velocity of the water is 4.12, what is the rate of discharge in gallons per minute.

5) A canal dug in the ground has a trapezoidal cross section. The width at the bottom is 16.00 feet, and the rate of slope of each inclined side is 1.5 ft horizontal to 1 ft vertical. When the depth of water is 6 ft, what is the hydraulic radius.

Mechanics of Materials

6) A group of rivets ¾ inch in diameter are to connect steel plates 5/16in. thick, and they are to be in single shear. If the allowable unit stresses are 15,000 psi in shear and 48,500 psi in bearing,how many rivets are needed to transmit a total load of 52,000 lb?

7) A simple beam supports a concentrated load at midspan. Describe and show by means of a rough sketch, how the shear varies from the left end to the right end of the beam. (Neglect the weight of the beam.)

8) A simple beam supports two equal concentrated loads placed symmetrically on the beam. Describe and show by means of a rough sketch, how the bending moment varies from the left end to the right end of the beam. (Neglect the weight of the beam.)

9) In the figure, the magnitude of either force P is 160 lb and the arm p is 25 in . Also the arm p' is 30 in.

P P should be at top

p

p
P

P

a) What is the torque in the cylinder?

b) What is the magnitude of either force P' ?

Technical Math II

10) A) Find the following values .

1) sin 79 degrees 23 min. 30 seconds
2) Cos 22 degrees 43 min.

11) Express each of the following functions as the same function of a positive acute angle.
Example: cos 165d egrees = -cos 15 degrees

(a) sin 175 degrees
(b) cos 215 degrees

12) The three sides of a triangle ABC are a=16, b=32, and c= 40 meters.

Use the law of cosines to find angle B to the nearest second.

Fluid Mechanics

13) Name four factors that contribute to frictional loss during a uniform liquid flow inside a constant diameter pipe?

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