2. Two small-sized objects are placed on a uniform 9.00 kg plastic beam 3.00 m long, as shown in Figure 2 8.00 kg 7.50 kg 9.00 kg k 60.0 c 3.00 m Figure 2 (a) Find the location of the center of mass of this system by setting at x = 0 at the left end of the beam. (b) Find the location of the center of mass of this system by setting at x = 0 the

2. Two small-sized objects are placed on a uniform 9.00 kg plastic beam 3.00 m long, as shown in Figure 2 8.00 kg 7.50 kg 9.00 kg k 60.0 c 3.00 m Figure 2 (a) Find the location of the center of mass of this system by setting at x = 0 at the left end of the beam. (b) Find the location of the center of mass of this system by setting at x = 0 the

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter14: Static Equilibrium, Elasticity, And Fracture

Section: Chapter Questions

Problem 24PQ

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A uniform piece of sheet metal is shaped as shown in Figure P9.24. Compute the x and y coordinates of the center of mass of the piece. Figure P9.24
a man of mass m1 = 70.0 kg is skating at v1 = 8.00 m/s behind his wife of mass m2 = 50.0 kg, who is skating at v2 = 4.00 m/s. Instead of passing her, he inadvertently collides with her. He grabs her around the waist, and they maintain their balance. (a) Sketch the problem with before-and-after diagrams, representing the skaters as blocks. (b) Is the collision best described as elastic, inelastic, or perfectly inelastic? Why? (c) Write the general equation for conservation of momentum in terms of m1, v1, m2, v2, and final velocity vf. (d) Solve the momentum equation for vf. (e) Substitute values, obtaining the numerical value for vf, their speed after the collision.
Two metersticks are connected at their ends as shown in Figure P10.18. The center of mass of each individual meterstick is at its midpoint, and the mass of each meterstick is m. a. Where is the center of mass of the two-stick system as depicted in the figure, with the origin located at the intersection of the sticks? b. Can the two-stick system be balanced on the end of your finger so that it remains lying flat in front of you in the orientation shown? Why or why not? FIGURE P10.18 (a) The center of mass of the stick on the x axis would be at (0.5 m, 0), and the center of mass of the stick on the stick on the y axis be at (0, 0.5 m), assuming the sticks are uniform. We can then use Equation 10.3 to find the x and y coordinates of the center of mass. xCM=1Mj=1nmjxj=12m[m(0.50m)]=0.25myCM=1Mj=1nmjyj=12m[m(0.50m)]=0.25m The location of the center of mass is (0.25m,0.25m) (b) No. The location of the center of mass is not located on the object, so your finger would not be in contact with the object. In a different orientation, balancing by applying a force at the center of mass might be possible, but not in the orientation shown.
A 90.0-kg ice hockey player hits a 0.150-kg puck, giving the puck a velocity of 45.0 m/s. If both are initially at rest and if the ice is frictionless, how far does the player recoil in the time it takes the puck to reach the goal 15.0 m away?
(a) A car traveling due east strikes a car traveling due north at an intersection, and the two move together as a unit. A property owner on the southeast corner of the intersection claims that his fence was torn down in the collision. Should he be awarded damages by the insurance company? Defend your answer, (b) Let the eastward-moving car have a mass of 1.30 103-kg and a speed of 30.0 km/h and the northward-moving car a mass of 1.10 103-kg and a speed of 20.0 km/h. Find the velocity after the collision. Are the results consistent with your answer to part (a)?
Each Voyager spacecraft was accelerated toward escape speed from the Sun by the gravitational force exerted by Jupiter on the spacecraft. (a) Is the gravitational force a conservative or a nonconservative force? (b) Does the interaction of the spacecraft with Jupiter meet the definition of an elastic collision? (c) How could the space-craft be moving faster after the collision?
To get up on the roof, a person (mass 70.0 kg) places 6.00-m aluminum ladder (mass 10.0 kg) against the house on a concrete pad with the base of ladder 2.00 m from the house. The ladder rests against a plastic rain gutter, which we can assume to frictionless. The center of ladder is 2.00 m from the bottom. The person is standing 3.00 m from the bottom. Find the normal reaction and friction forces on the ladder at its base.
(a) What is the momentum of a garbage truck that is 1.20104 kg and is moving at 10.0 m/s ? (b) At what speed would an 8.00-kg trash can have the same momentum as the truck?
5. A system consists of three particles as shown in the figure. Mass 1 is 8.10 kg and located at (0, 1.00) - m. Mass 2 is 5.30 kg and located at (2.00, 1.00) m. Mass 3 is 1.00 kg and located at (2.00, 0) m. Calculate the center of mass of the system. y (m) m, m2 y m3 x (m) a. ( 0.875î+ 1.003 ) m b. ( 0.875î + 0.931ĵ ) m c. ( 1.00î + 2.00ĵ ) m d. ( 2.00î + 1.00ĵ ) m e. ( 0.931î + 0.875Î ) m е.
1. The four objects are positioned along the y-axis as follows: The object with 2.00 kg mass is at +3.00 m, the object with a mass of 3.00-kg is at 2.50 m, while the object with a mass of 2.50-kg is placed at the origin and the object with 4.00-kg mass is located at -0.500 m. Where's the mass center of these objects? 2. Determine the impulse of a 0.50 kg magazine at rest if thrown at 3 m/s. 3. A 450g ball is moving at a velocity of 4.8 m/s, east when it collides with 900g ball at rest. If the collision is perfectly elastic, find the velocity (magnitude and direction) of each ball after the collision.
The figure shows a homogeneous metal sheet with radius 2R obtained by removing a disk of diameter R.a) Using the x - y coordinate system shown in the figure, the plateFind the center of mass.b) The removed disc is added to the plate as shown in the figure. In this case, find the center of mass of the whole system.
2. A 67 kg man stands at the front end of a uniform boat of mass 179 kg and of length, L= 2.5 m. Assume there is no friction or drag between the boat and water. (a) What is the location of the center of mass of the system when the origin of our coordinate system (î) on the man's original location (ii) on the back end of the boat? (b) If the man walks from the front end to the back end of the boat, by how much is the boat displaced? (c) Now consider the man and his friend with identical mass of 67 kg are rowing the boat on a hot summer afternoon when they decide to go for a swim. The man jumps off the front of the boat at speed 3 m/s and his friend jumps off the back at speed 4 m/s. If the boat was moving forward at 1.5 m/s when they jumped, what is the speed of the boat after their jump?