Phys Int CC Ch 7 - Momentum - Answers PDF PDF

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Answers for the Physics Intro. course Lecture Notes. Full of answers. Find everything you need here. Answers from beginning of course to end of unit....

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CK-12 Physics Concepts - Intermediate Answer Key Chapter 7: Momentum 7.1 Momentum and Impulse Practice Questions 1. Why don't the glasses of water spill when the tablecloth is pulled out from under them? 2. How does the video get from momentum to impulse? Answers 1. The glasses of water do not spill because the force is applied to them over such a short period of time, the inertia of the glasses of water exceeds the impulse of the friction from the tablecloth. 2. The video undergoes the following manipulations of the equation: mvt mv t v a® mat t F ma ® Ft mv Ft Review Questions 1. A small car with a mass of 800. kg is moving with a velocity of 27.8 m/s. a. What is the momentum of the car? b. What velocity is needed for a 2400. kg car in order to have the same momentum? 2. A scooter has a mass of 250. kg. A constant force is exerted on it for 60.0 s. During the time the force is exerted, the scooter increases its speed from 6.00 m/s to 28.0 m/s. a. What is the change in momentum? b. What is the magnitude of the force exerted on the scooter? 3. The brakes on a 15,680 N car exert a stopping force of 640. N. The car’s velocity changes from 20.0 m/s to 0 m/s. a. What is the car’s mass? b. What was its initial momentum? 1

c. What was the change in momentum for the car? d. How long does it take the braking force to bring the car to rest? Answers 1.

a. Using 𝜌 = 𝑚𝑣 ∶ 800𝑘𝑔 ∗ 27.8 b. Using 𝑣 =

𝜌

𝑚

∶𝑣=

𝑚

22240 𝑘𝑔 𝑠 2400 𝑘𝑔

𝑚 𝑠

= 22240𝑘𝑔 𝑚/𝑠

= 9.27 m/s

2. a. The change in momentum is given by the equation 𝑚

m(v f

𝑚

v i : ∆𝜌 =

250𝑘𝑔 (28 𝑠 − 6 𝑠 ) . Thus the change in momentum is 5500 kg m/s. b. The magnitude of the force is found by dividing the answer from (a) by the 𝑚

time (6.00 sec). 3.

5500 𝑘𝑔 𝑠 6.00𝑠

= 916.66 . The magnitude of the force is 917 N.

a. Find the mass by dividing the car’s weight by the force of gravity. 𝑚 = 15680𝑁 9.8𝑚 𝑠2

𝑤

. The mass of the car is 1600 kg. 𝑚

𝑔

∶

𝑚

b. Find initial momentum using 𝜌 = 𝑚𝑣 ∶ (1600𝑘𝑔) (20.0 𝑠 ) = 32,000𝑘𝑔 𝑠 . c. Final momentum is 0, thus the change in momentum is -32000 kg m/s d. 𝑡 =

𝑚

−32 ,000 𝑘𝑔 𝑠 𝑚 −640 𝑘𝑔 2 𝑠

= 50 seconds.

7.2 Conservation of Momentum in One Dimension Practice Questions 1. What is Newton's Cradle? 2. How does Newton's Cradle work? 3. How does a Newton's Cradle show conservation of momentum? Answers 1. A Newton’s Cradle is usually a desktop toy, though the Mythbusters made significantly larger ones. It usually consists of five balls of equal mass and size, hanging from two wires in a single line. 2. When you release a ball (or more than one) from one side, it hits the ball(s) in the middle, and the ball(s) on the other side travel outward. It works much like a normal pendulum, but with barriers in the middle. If you draw back one ball, one

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ball will travel out on the other side. If you draw back two balls, two balls will travel out on the other side, etc. 3. A Newton’s Cradle shows conservation of momentum because the momentum passes through the balls in the middle, which stay relatively stationary, and onto the last ball, sending it out. This process is repeated over and over again. Each time a ball swings out, a calculation of the total momentum of the system will give the same total momentum as the initial momentum. Obviously, this is not perfect due to air resistance, but it is nearly so. Review Questions 1. A 0.111 kg hockey puck moving at 55 m/s is caught by a 80. kg goalie at rest. With what speed does the goalie slide on the (frictionless) ice? 2. A 0.050 kg bullet strikes a 5.0 kg stationary wooden block and embeds itself in the block. The block and the bullet fly off together at 9.0 m/s. What was the original velocity of the bullet? 3. A 0.50 kg ball traveling at 6.0 m/s due east collides head on with a 1.00 kg ball traveling in the opposite direction at -12.0 m/s. After the collision, the 0.50 kg ball moves away at -14 m/s. Find the velocity of the second ball after the collision. 4. Two carts are stationary with a compressed spring between them and held together by a thread. When the thread is cut, the two carts move apart. After the spring is released, one cart

has a velocity of 0.82 m/s east. What is the

magnitude of the velocity of the second cart released?

after the spring is

5. Compared to falling on a tile floor, a glass may not break if it falls onto a carpeted floor. This is because a. less impulse in stopping. b. longer time to stop. c. both of these d. neither of these. 6. A butterfly is hit by a garbage truck on the highway. The force of the impact is greater on the a. garbage truck. b. butterfly. c. it is the same for both.

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7. A rifle recoils from firing a bullet. The speed of the rifle’s recoil is small compared to the speed of the bullet because a. the force on the rifle is small. b. the rifle has a great deal more mass than the bullet. c. the momentum of the rifle is unchanged. d. the impulse on the rifle is less than the impulse on the bullet. e. none of these. Answers 1. Using

𝑚𝑖 𝑣𝑖 𝑚𝑓

= 𝑣𝑓 ∶

(0.111𝑘𝑔∗55

𝑚

80.111𝑘𝑔

𝑠

)

=𝑥

𝑚 𝑠

→ The goalie slides with a speed of 0.076

m/s. 2. Using 𝑣𝑖 = 3. Using

𝑣𝑓 𝑚𝑓 𝑚𝑖

∶

𝑚

(9 𝑠 )(5.05𝑘𝑔) 0.5𝑘𝑔

(𝑚1 𝑣1 +𝑚2 𝑣2 −𝑚1′ 𝑣1′ )

west).

𝑚2′

= The bullet originally had a velocity of 909 m/s.

= 𝑣2′ ∶ The second ball has a velocity of -2 m/s (1 m/s

4. To solve this problem, we assume that the spring exerts an equal force on both carts. Using m/s. 5. b 6. c 7. b

(𝑚1 𝑣1 ) 𝑚2

= 𝑣2 ∶

(3.00𝑘𝑔∗0.82 1.70𝑘𝑔

𝑚 ) 𝑠

= (𝑥

𝑚

𝑠

) The second cart’s velocity is 1.45

7.3 Conservation of Momentum in Two Dimensions Practice Questions 1. Why do the fliers scrunch up in the air while spinning and twisting? 2. What happens to the rate at which they spin when they change shape in the air? Answers 1. The fliers scrunch up in the air to increase their rotational velocity, which allows them to complete more spins and flips before they land or are caught. 2. When they make themselves smaller, they spin faster. When they make themselves larger, they spin slower.

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Review Questions 1. Billiard ball , mass 0.17 kg, moving due east with a velocity of 4.0 m/s, strikes stationary billiard ball , also mass of 0.17 kg. After the collision, ball moves off at an angle of 30° north of east with a velocity of 3.5 m/s, and ball moves off at an angle of 60° south of east. What is the speed of ball ? 2. A bomb, originally sitting at rest, explodes and during the explosion breaks into four pieces of exactly 0.25 kg each. One piece flies due south at 10 m/s while another piece flies due north at 10 m/s. a. What do we know about the directions of the other two pieces and how do we know it? b. What do we know about the speeds of the other two pieces and how do we know it? 3. In a head-on collision between protons in a particle accelerator, three resultant particles were observed. All three of the resultant particles were moving to the right from the point of collision. The physicists conducting the experiment concluded there was at least one unseen particle moving to the left after the collision. Why did they conclude this? Answers 𝑚

1. Using 𝑚1 𝑣1 𝑐𝑜𝑠𝜃1 + 𝑚2 𝑣2 𝑐𝑜𝑠𝜃2 = 𝑚1 𝑣1′ 𝑐𝑜𝑠𝜃1′ + 𝑚2 𝑣2′ 𝑐𝑜𝑠𝜃2′ ∶ (0.17𝑘𝑔) (4 𝑠 ) (1) + 𝑚 𝑚 0 = (.17𝑘𝑔)(3.5 𝑠 )(cos 30°) + (.17𝑘𝑔)(𝑥 )(cos 60°) → Ball B’s final velocity is 2 𝑠

m/s at 60 South of East.

2. a. We know that the other two pieces travel in opposite directions. We know this because their total momentum must be zero; the initial momentum is zero and the two pieces we know the motion of are equal and opposite (the sum of their final momentum is also zero). b. Since each of the pieces has the same mass and is acted upon by the same force, we know the other two pieces also travel at 10 m/s. 3. The momentum must be conserved. Going into the collision, there is a momentum traveling to the left and to the right. After the collision, if all the particles traveled to the right, the momentum would not be conserved. Therefore, the scientists conclude there must be at least one particle moving to the left.

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