Vector Mechanics For Engineers
12th Edition
ISBN: 9781259977305
Author: BEER, Ferdinand P. (ferdinand Pierre), Johnston, E. Russell (elwood Russell), Cornwell, Phillip J., SELF, Brian P.
Publisher: Mcgraw-hill Education,
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Chapter 14.2, Problem 14.50P
Three small spheres A, B, C, each of mass m, are connected to a small ring D of negligible mall by means of three inextensible, inelastic cords of length l. The spheres can slide freely on a frictionless horizontal surface and are rotating initially at a speed
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Problem 4: Amerry-go-round is a playground ride that consists of a large disk mounted to
that it can freely rotate in a horizontal plane. The merry-go-round shown is initially at rest, has a
radius R = 1.1 meters, and a mass M= 286 kg. A small boy of mass m = 41 kg runs tangentially to
the merry-go-round at a speed of v = 2.5 m/s, and jumps on.
Randomized Variables
R = 1.1 meters
M= 286 kg
m = 41 kg
v= 2.5 m/s
Part (a) Calculate the moment of inertia of the merry-go-round, in kg · m?.
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Hint
Part (b) Immediately before the boy jumps on the merry go round, calculate his angular speed (in radians/second) about the central axis of the
merry-go-round.
Part (c) Immediately after the boy jumps on the merry go round, calculate the angular speed in radians/second of the merry-go-round and boy.
Part (d) The…
Slider C has a mass of 0.5 kg and
may move in a slot cut in arm AB,
which rotates at constant speed in a
horizontal plane. The slider is
attached to a spring of constant
k = 150 N/m, which is unstretched
when r = 0.
When arm AB rotates about the
vertical axis, the slider moves
without friction outward along the
smooth slot cut. Determine for the
position r = 80 mm:
a) The constant speed (V) of the
slider.
b) The normal force (N) exerted on
the slider by arm AB.
A
r=80mm
B
Two identical spheres A and B each of mass m , are attached to an inextensible inelastic cord of length L and are resting at a distance a from each other on a frictionless horizontal surface. Sphere B is given a velocity v0 in a direction perpendicular to line AB and moves it without friction until it reaches B ’ where the cord becomes taut. Draw the impulse-momentum diagram that can be used to determine the magnitude of the velocity of each sphere immediately after the cord has become taut.
Chapter 14 Solutions
Vector Mechanics For Engineers
Ch. 14.1 - A 30-g bullet is fired with a horizontal velocity...Ch. 14.1 - Two identical 1350-kg automobiles A and B are at...Ch. 14.1 - Prob. 14.3PCh. 14.1 - Prob. 14.4PCh. 14.1 - Two swimmers A and B, of weight 190 lb and 125 lb,...Ch. 14.1 - A 180-lb man and a 120-lb woman stand side by side...Ch. 14.1 - A 40-Mg boxcar A is moving in a railroad...Ch. 14.1 - Two identical cars A and B are at rest on a...Ch. 14.1 - A 20-kg base satellite deploys three...Ch. 14.1 - For the satellite system of Prob. 14.9. assuming...
Ch. 14.1 - A system consists of three identical 19.32-lb...Ch. 14.1 - A system consists of three identical 19.32-lb...Ch. 14.1 - A system consists of three particles A, B, and C....Ch. 14.1 - For the system of particles of Prob. 14.13,...Ch. 14.1 - A 13-kg projectile is passing through the origin O...Ch. 14.1 - A 300-kg space vehicle traveling with a velocity...Ch. 14.1 - A 2-kg model rocket is launched vertically and...Ch. 14.1 - An 18-kg cannonball and a 12-kg cannonball are...Ch. 14.1 - Prob. 14.19PCh. 14.1 - Prob. 14.20PCh. 14.1 - An expert archer demonstrates his ability by...Ch. 14.1 - Two spheres, each of mass m, can slide freely on a...Ch. 14.1 - Prob. 14.23PCh. 14.1 - A 6-kg shell moving with a velocity...Ch. 14.1 - A 6-kg shell moving with a velocity...Ch. 14.1 - In a scattering experiment, an alpha particle A is...Ch. 14.1 - Derive the relation Ho=rmv+HG between the angular...Ch. 14.1 - Show that Eq. (14.23) may be derived directly from...Ch. 14.1 - Consider the frame of reference Ax'y'z' in...Ch. 14.1 - Show that the relation MA=HA where HA is defined...Ch. 14.2 - Determine the energy lost due to friction and the...Ch. 14.2 - Prob. 14.32PCh. 14.2 - In Prob. 14.6. determine the work done by the...Ch. 14.2 - Determine the energy lost as a result of the...Ch. 14.2 - Two automobiles A and B, of mass mA and mB,...Ch. 14.2 - It is assumed that each of the two automobiles...Ch. 14.2 - Solve Sample Prob. 14.5, assuming that cart A is...Ch. 14.2 - Ball B is suspended from a cord of length l...Ch. 14.2 - A 15-lb block B starts from rest and slides on the...Ch. 14.2 - A 40-lb block B is suspended from a 6-ft cord...Ch. 14.2 - In a game of pool, ball A is moving with a...Ch. 14.2 - In a game of pool, ball A is moving with a...Ch. 14.2 - Three spheres, each with a mass of m, can slide...Ch. 14.2 - In a game of pool, ball A is moving with the...Ch. 14.2 - The 2-kg sub-satellite B has an initial velocity...Ch. 14.2 - A 900-lb space vehicle traveling with a velocity...Ch. 14.2 - Four small disks A, B, C, and D can slide freely...Ch. 14.2 - In the scattering experiment of Prob. 14.26, it is...Ch. 14.2 - Prob. 14.49PCh. 14.2 - Three small spheres A, B, C, each of mass m, are...Ch. 14.2 - In a game of billiards, ball A is given an initial...Ch. 14.2 - For the game of billiards of Prob. 14.51, it is...Ch. 14.2 - Two small disks A and B of mass 3 kg and 1.5 kg,...Ch. 14.2 - Two small disks A and B of mass 2 kg and 1 kg,...Ch. 14.2 - Prob. 14.55PCh. 14.2 - Prob. 14.56PCh. 14.3 - A stream of water with a density of =1000kg/m3 is...Ch. 14.3 - A jet ski is placed in a channel and is tethered...Ch. 14.3 - Tree limbs and branches are being fed at A at the...Ch. 14.3 - The nozzle shown discharges water at the rate of...Ch. 14.3 - A rotary power plow is used to remove snow from a...Ch. 14.3 - A hose discharges water at a rate of 8 m3/min with...Ch. 14.3 - Sand falls from three hoppers onto a conveyor belt...Ch. 14.3 - The stream of water shown flows at a rate of 550...Ch. 14.3 - The nozzle shown discharges water at the rate of...Ch. 14.3 - A stream of water flowing at a rate of 1.2 m/min...Ch. 14.3 - A stream of water flowing at a rate of 1.2 m3/min...Ch. 14.3 - Prob. 14.68PCh. 14.3 - The total drag due to air friction on a jet...Ch. 14.3 - Prob. 14.70PCh. 14.3 - In order to shorten the distance required for...Ch. 14.3 - The helicopter shown can produce a maximum...Ch. 14.3 - Prior to takeoff, the pilot of a 3000-kg...Ch. 14.3 - The jet engine shown scoops in air at A at a rate...Ch. 14.3 - A jet airliner is cruising at a speed of 900 km/h...Ch. 14.3 - A 16-Mg jet airplane maintains a constant speed of...Ch. 14.3 - The propeller of a small airplane has a...Ch. 14.3 - The wind turbine generator shown has an...Ch. 14.3 - A wind turbine generator system having a diameter...Ch. 14.3 - While cruising in level flight at a speed of 570...Ch. 14.3 - In a Pelton-wheel turbine, a stream of water is...Ch. 14.3 - A circular reentrant orifice (also called Borda’s...Ch. 14.3 - A railroad car with length L and mass mg when...Ch. 14.3 - The depth of water flowing in a rectangular...Ch. 14.3 - Determine the rate of flow in the channel of Prob....Ch. 14.3 - A chain of length I and mass m lies in a pile on...Ch. 14.3 - Solve Prob. 14.86, assuming that the chain is...Ch. 14.3 - The ends of a chain lie in piles at A and C. When...Ch. 14.3 - A toy car is propelled by water that squirts from...Ch. 14.3 - A toy car is propelled by water that squirts from...Ch. 14.3 - The main propulsion system of a new space...Ch. 14.3 - The main propulsion system of a new space...Ch. 14.3 - A rocket sled bums fuel at the constant rate of...Ch. 14.3 - A space vehicle describing a circular orbit about...Ch. 14.3 - A 540-kg spacecraft is mounted on top of a rocket...Ch. 14.3 - The rocket used to launch the 540-kg spacecraft of...Ch. 14.3 - The weight of a spacecraft, including fuel, is...Ch. 14.3 - The rocket engines of a spacecraft are fired to...Ch. 14.3 - Determine the distance traveled by the spacecraft...Ch. 14.3 - A rocket weighs 2600 lb. including 2200 lb of...Ch. 14.3 - Determine the altitude reached by the spacecraft...Ch. 14.3 - For the spacecraft and the two-stage launching...Ch. 14.3 - In a jet airplane, the kinetic energy imparted to...Ch. 14.3 - In a rocket, the kinetic energy imparted to the...Ch. 14 - Three identical cars are being unloaded from an...Ch. 14 - A 50-kg mother and her 26-kg son are sledding down...Ch. 14 - An 80-Mg railroad engine A coasting at 6.5 km/h...Ch. 14 - In a game of pool, ball A is moving with a...Ch. 14 - Mass C, which has a mass of 4 kg, is suspended...Ch. 14 - A 15-lb block B is at rest and a spring of...Ch. 14 - A 6000-kg dump truck has a 1500-kg stone block...Ch. 14 - For the ceiling-mounted fan shown, determine the...Ch. 14 - An airplane with a weight W and a total wing span...Ch. 14 - The final component of a conveyor system receives...Ch. 14 - A garden sprinkler has four rotating arms, each of...Ch. 14 - A chain of length I and mass m falls through a...
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- The two blocks shown are originally at rest. Neglect the masses of the pulleys and the effect of friction in the pulleys and between the blocks and the incline. Consider WA = 206 lb and WB = 306 lb.arrow_forwardPROBLEM NO. 3 A 5-kg collar slides from A to B along a frictionless vertical rod as shown. The spring attached to the collar has an undeformed (initial) length of 4 m and a spring constant of 30 N/m. What is the collar's velocity at point B? 8.0 m A B 1.5 marrow_forwardTwo 2.6-lb collars A and B can slide without friction on a frame, consisting of the horizontal rod OE and the vertical rod CD, which is free to rotate about CD . The two collars are connected by a cord running over a pulley that is attached to the frame at O and a stop prevents collar B from moving. The frame is rotating at the rate 0 =12 rad/s and r= 0.6 ft when the stop is removed allowing collar A to move out along rod OE . Neglecting friction and the mass of the frame, determine, for the position r= 1.2 ft, (a) the transverse component of the velocity of collar A, (b) the tension in the cord and the acceleration of collar A relative to the rod OE.arrow_forward
- Two beads of mass m are initially at rest at the top of a frictionless hoop of mass M and radius R, which stands vertically on the ground. The beads, being strung on the hoop, are constrained to move along the hoop’s circular path. The beads are given tiny kicks, and they slide down the hoop, one to the right and one to the left. What is the largest value of m/M for which the hoop never rises up off the ground? (Given a sufficiently large ratio of m/M the normal force of the beads on the hoop can indeed cause it to jump off of the ground!) Some thoughts/hints about this problem:(a) It is important to think about the direction of the Normal force as the beads move around the hoop. The hoop is exerting a normal force on the beads which are constraining them to stay on the wire as they move around the hoop. The beads are also exerting a normal force on the hoop which is what will make the hoop jump.(b) What happens to the direction of the normal force exerted by the hoop on the beads as…arrow_forwardA particle of mass 2.6 kg is attached to two cables CB and CA as shown. it revolves in a horizontal circle of radius 1.3 m at a constant speed of 8.45 m/s.arrow_forward(e) Once the mass m is released from rest, what is its speed when it has risen by a height h?arrow_forward
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