If all three collisions below are totally inelastic, which one(s) will bring the car on the left to a complete halt?

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1 ConcepTest 8.1 Crash Cars I If all three collisions below are totally inelastic, which one(s) will bring the car on the left to a complete halt? 1) I 2) II 3) I and II 4) II and III 5) all three

2 ConcepTest 8.1 Crash Cars I If all three collisions below are totally inelastic, which one(s) will bring the car on the left to a complete halt? 1) I 2) II 3) I and II 4) II and III 5) all three In case I, the solid wall clearly stops the car. In cases II and III, since p tott tot t = 0 before the collision, then p tot must also be zero after the collision, which means that t the car comes to a halt in all three cases.

3 ConcepTest 8.2 Crash Cars II If all three collisions below are totally inelastic, which one(s) will cause the most damage (in terms of lost energy)? 1) I 2) II 3) III 4) II and III 5) all three

4 ConcepTest 8.2 Crash Cars II If all three collisions below are totally inelastic, which one(s) will cause the most damage (in terms of lost energy)? 1) I 2) II 3) III 4) II and III 5) all three The car on the left loses the same KE in all 3 cases, but in case III, the car on the right loses the most KE because KE = 1/2 m v 2 and the car in case III has the largest velocity.

5 ConcepTest 8.3 Motion of CM Two equal-mass particles (A and B) are located at some distance from each other. Particle A is held stationary while B is moved away at speed v. What happens to the center of mass of the two-particle system? 1) it does not move 2) it moves away from A with speed v 3) it moves toward A with speed v 4) it moves away from A with speed 1/2 v 5) it moves toward A with speed 1/2 v

6 ConcepTest 8.3 Motion of CM Two equal-mass particles (A and B) are located at some distance from each other. Particle A is held stationary while B is moved away at speed v. What happens to the center of mass of the two-particle system? 1) it does not move 2) it moves away from A with speed v 3) it moves toward A with speed v 4) it moves away from A with speed 1/2 v 5) it moves toward A with speed 1/2 v Let s say that A is at the origin (x = 0) and B is at some position x. Then the center of mass is at x/2 because A and B have the same mass. If v = Δx/Δt tells us how fast the position of B is changing, then the position of the center of mass must be changing like Δ(x/2)/Δt, which is simply 1/2 v.

7 ConcepTest 8.4 Momentum and KE At time t = 0, a particle initially at rest is subject to a resultant force in the +x direction which causes its momentum to increase proportional to t 3. If the value of the force at t = 0 is zero, the kinetic energy of the particle subsequently increases at a rate proportional to: 1) t 2) t 2 3) t 3 4) t 5 5) t 6

8 ConcepTest 8.4 Momentum and KE At time t = 0, a particle initially at rest is subject to a resultant force in the +x direction which causes its momentum to increase proportional to t 3. If the value of the force at t = 0 is zero, the kinetic energy of the particle subsequently increases at a rate proportional to: 1) t 2) t 2 3) t 3 4) t 5 5) t 6 The momentum of the particle is p = mv. Since p increases proportional to t 3, this implies v increases proportional to t 3. Kinetic energy is ½ mv 2 so kinetic energy increases proportional to (t 3 ) 2 = t 6.

9 ConcepTest 8.5 Shut the Door! You are lying in bed and you want to shut your bedroom door. You have a superball and a blob of clay (both with the same mass) sitting next to you. Which one would be more effective to throw at your door to close it? 1) the superball 2) the blob of clay 3) it doesn t matter -- they will be equally effective 4) you are just too lazy to throw anything

10 ConcepTest 8.5 Shut the Door! You are lying in bed and you want to shut your bedroom door. You have a superball and a blob of clay (both with the same mass) sitting next to you. Which one would be more effective to throw at your door to close it? 1) the superball 2) the blob of clay 3) it doesn t matter -- they will be equally effective 4) you are just too lazy to throw anything The superball bounces off the door with almost no loss of speed, so its Δp (and that of the door) is 2mv. The clay sticks to the door and continues to move along with it, so its Δp is less than that of the superball, and therefore it imparts less Δp to the door.

11 ConcepTest 9.1 Bonnie sits on the outer rim of a merry-go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one complete revolution every two seconds. Klyde s angular velocity is: Bonnie and Klyde I 1) same as Bonnie s 2) twice Bonnie s 3) half of Bonnie s 4) 1/4 of Bonnie s 5) four times Bonnie s ω Klyde Bonnie

12 ConcepTest 9.1 Bonnie sits on the outer rim of a merry-go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one complete revolution every two seconds. Klyde s angular velocity is: Bonnie and Klyde I 1) same as Bonnie s 2) twice Bonnie s 3) half of Bonnie s 4) 1/4 of Bonnie s 5) four times Bonnie s The angular velocity ω of any point on a solid object rotating about a fixed axis is the same. Both Bonnie & Klyde go around one revolution (2π radians) every two seconds. Klyde ω Bonnie

13 ConcepTest 9.2 Bonnie and Klyde II Bonnie sits on the outer rim of a merry- 1) Klyde go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one revolution every two seconds. Who has the larger linear (tangential) velocity? 2) Bonnie d k l ti 3) both the same 4) linear velocity is zero for both of them ω Klyde Bonnie

14 ConcepTest 9.2 Bonnie and Klyde II Bonnie sits on the outer rim of a merrygo-round, and Klyde sits midway between the center and the rim. The merry-go-round round makes one revolution every two seconds. Who has the larger linear (tangential) velocity? 1) Klyde 2) Bonnie 3) both the same 4) linear velocity is zero for both of them Their linear speeds v will be different since v = Rω and Bonnie is located further out (larger radius R) than Klyde. V = 1 Klyde V 2 Bonnie Klyde ω Bonnie Follow-up: Who has the larger centripetal acceleration?

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