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Exam 8: Systems of Particles and Extended Objects

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Question 31

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A system consists of two particles: particle 1,having the mass m₁ = 4.0 kg is located at (-4.0 m,1.0 m) and particle 2,having the mass m₂ = 5.0 kg is located at (2.0 m,1.0 m) .The x-coordinate of the center of mass of the system is

A) -1.0 m.
B) 0.92 m.
C) -0.67 m.
D) -2.0 m.
E) -1.3 m.

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Question 32

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A 16 cm by 16 cm checkerboard has a mass of 207 g.There are three 31.0-g checkers located on the checkerboard as shown in the figure.Relative to O,the origin,located at the bottom,left-hand corner of the checkerboard,where is the center of mass of the checkerboard and checkers system?

A) (7.9 cm,6.5 cm)
B) (8.1 cm,6.7 cm)
C) (8.1 cm,7.1 cm)
D) (8.3 cm,6.5 cm)
E) (8.3 cm,6.8 cm)

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Question 33

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Three faces of a cube of side L are removed,therefore,it has three faces in xy,xz,and yz planes.The center of mass of the system relative to the origin,where the three remaining faces meet,is

Find the x-coordinate of the center of mass of a 10-cm square plate whose density (in kg/m³) is .The lower left-hand side of the plate is at the origin and the upper right-hand corner is at (10 cm,10 cm) .The plate is 0.30 cm thick.

A 1.3-kg booster attached to a 6-kg rocket is initially traveling at a speed of 175 m/s.If the booster is ejected in backward direction with speed of 60 m/s relative to the rocket/booster rest frame,how fast will the rocket then travel?

Which of the following statements is the one that is true?

The center of mass of a uniform,symmetric object may be located

A thin rectangular plate of uniform density $\sigma$ ₁ = 1.67 kg/m² has a length a = 0.740 m and a width of b = 0.330 m.The lower left hand corner is placed at the origin,(x,y) = (0,0) .A circular hole is cut in the plate of radius r = 0.064 m with center at (x,y) = (0.084 m,0.084 m) and replaced with a circular disk with the same radius composed of another material of the same thickness with uniform density $\sigma$ 2 = 5.94 kg/m².What is the distance of the resulting plate's center of mass from the origin? (in m)

A cartoon character can levitate himself from the thrust obtained by firing his two revolvers down into the ground.If the bullets have a mass of 16 g and a downward velocity of 330 m/s,find his maximum weight if he can fire 12 bullets from each revolver in 10 seconds.

A long thin rod has its one end at x = 0 and the other end at x =1 m.Its composition is such that the linear mass density changes with length according to $\lambda$ (x) = ax² + bx+c,where x is the distance from one end of the rod.Given: a = 0.75 kg/m³,b = 0.5 kg/m²,and c = .25 kg/m,the center of mass of the rod relative to x = 0 is

A 25-kg boy jumps off of a raft.If the boy jumps off at a speed of 3.90 m/s relative to the lake and the raft moves in the opposite direction with a speed of 1.0 m/s relative to the lake,find the mass of the raft.Ignore the effects of water resistance.

A particle of mass 3 kg moving at 8 m/s makes an elastic collision with a particle of mass 5 kg moving at -4 m/s.The velocity of the center mass of the particles is

The coordinates for the center of mass for the extended object shown in figure are (L/4,-L/5) .What are the coordinates of the 2-kg mass?

A student with a mass of 40 kg can throw a 15-kg ball with a relative speed of 5.0 m/s.The student is standing at rest on a cart with a mass of 12 kg that can move over the ground without friction.If the student throws the ball horizontally,what is the speed of the ball relative to the ground?

A cylindrical bottle of oil and salt water with 1/2 volume oil ( $\rho$ =0.910 g/cm³) and 1/2 volume salt water ( $\rho$ = 1.03 g/cm³) is at rest on a table.Initially the oil and salt water are separated,with the oil floating on top of the water.The bottle is shaken so the oil and water uniformly mix and the bottle is returned to the table.How has the height of the center of mass changed after mixing?

Find the weight of a 10-cm square plate whose density (in kg/m³) is .The lower left-hand side of the plate is at the origin and the upper right-hand corner is at (10 cm,10 cm) .The plate is 0.30 cm thick.

Mass of the Saturn V rocket is 2.5 * 10⁶ kg.It burns fuel at the rate of 2 *10⁴ kg/s and has an exhaust speed of 2.8 km/s relative to the rocket.The thrust of the rocket is

A 4500-kg truck traveling due east at a speed of 101 km/h approaches a 650-kg car traveling due west at 130 km/h.The net momentum of the system consisting of the car and truck is

Suppose we have a rocket in outer space.The rocket consists of a payload of 5280.0 kg and 121000 kg of fuel.Assume that the rocket starts from rest,accelerates to its final velocity.After reaching this final velocity it begins its 3.82 * 10⁵ km trip to the moon.The speed at which the rocket expels propellant is 4.22 km/s.If the rocket is to make the trip from the Earth to the Moon,a distance of 3.82 * 10⁵ km,how long will the trip take to complete ?

Starting at rest,two students standing on massless carts pass a 7.0-kg ball back and forth.The student on the left has a mass of 40 kg and can throw the ball with a relative speed of 9.0 m/s.The student on the right has a mass of 30 kg.If the ball is thrown horizontally from the student on the left to the student on the right,how fast,relative to the student on the left will the student on the right move after catching the pass?