Problem Assignment No. 8 JUST C ± Conservation of Momentum 8 of 20 Learning Goal

Question

Problem Assignment No. 8

JUST C

± Conservation of Momentum

8 of 20

Learning Goal:

To be able to describe the motion of rigid bodies by applying the conservation of linear and angular momenta.

(syst. linearmomentum)1=(syst. linearmomentum)2

(syst. angularmomentum)1=(syst. angularmomentum)2

Part A

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Which of the following scenarios demonstrate the conservation of either linear or angular momentum?

Check all that apply.

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Part B

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A pendulum consists of a slender rod, AB, of weight Wr = 8.00 lb and a wooden sphere of weight Ws = 29.7 lb .(Figure 1) The length of the rod is d1 = 5.30 ft and the radius of the sphere is R = 0.400 ft . A projectile of weight Wp = 0.300 lb strikes the center of the sphere at a velocity of v1 = 946 ft/s and becomes embedded in the center of the sphere. What is , the angular velocity of the pendulum, immediately after the projectile strikes the sphere?

Express your answer numerically in radians per second to three significant figures.

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Part C

What is , the maximum angle measured from the vertical that the pendulum will swing, after the projectile impacts the pendulum?

Express your answer numerically in degrees to three significant figures.

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4242

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Learning Goal:

To be able to describe the motion of rigid bodies by applying the conservation of linear and angular momenta.

If the sum of all the linear impulses acting on a system of connected rigid bodies is zero, the linear momentum of the system is conserved. Mathematically, this relationship is expressed as

(syst. linearmomentum)1=(syst. linearmomentum)2

and is called the conservation of linear momentum. If the sum of all the angular impulses (created by the external forces that act on the system) is negligible or zero, then the angular momentum of a system of connected rigid bodies is conserved about the system's center of mass or about a fixed point. Mathematically, this relationship is expressed as

(syst. angularmomentum)1=(syst. angularmomentum)2

and is called the conservation of angular momentum.

Part A

Part complete

Which of the following scenarios demonstrate the conservation of either linear or angular momentum?

Check all that apply.

Check all that apply. A parent pushes a merry-go-round and, consequently, it spins faster. A penny is dropped from the top of a building and its velocity increases as it falls due to the acceleration from gravity. An ice skater tucks in her arms during a spin and her angular velocity increases. From opposite sides of a room, two identical balls of putty move toward each other, without friction, at the same velocity and, eventually, they collide; the result is one ball of putty with zero velocity.

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Part B

Part complete

A pendulum consists of a slender rod, AB, of weight Wr = 8.00 lb and a wooden sphere of weight Ws = 29.7 lb .(Figure 1) The length of the rod is d1 = 5.30 ft and the radius of the sphere is R = 0.400 ft . A projectile of weight Wp = 0.300 lb strikes the center of the sphere at a velocity of v1 = 946 ft/s and becomes embedded in the center of the sphere. What is , the angular velocity of the pendulum, immediately after the projectile strikes the sphere?

Express your answer numerically in radians per second to three significant figures.

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= 1.54   rad/s  

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Correct

Part C

What is , the maximum angle measured from the vertical that the pendulum will swing, after the projectile impacts the pendulum?

Express your answer numerically in degrees to three significant figures.

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=

4242

  degrees  

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Explanation / Answer

c)m1v(L+R) = (m1+m2)(L+R)2 omega + 1/3 m3 L^2 omega so
0.3*946*(5.30+0.400) = (29.7+0.3)(5.3+0.4)^2 omega + (1/3)*8*(5.3+0.4)^2 omega

Thus, omega = 1.54 rad/s

all rotational energy = (1/2) I omega^2 = (1/2) (974.7 + 86.64)* (1.54)^2 = 1226.52 lb.ft^2/s^2

This goes into potential energy = g (1 - costheta)( 8 x 5.3 + 30 x 5.7) = 2091.32(1 - costheta) =1226.52

so 1- costheta = 0.586 and costheta = 0.4135 then theta = 65 degrees

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