Question

1. A 10.0 g object moving to the right at 25.0 cm/s makes an elastic head-on collision with a 15.0 g object moving in the opposite direction at 36.0 cm/s. Find the velocity of each object after the collision.

10.0 g object:

15.0g object:

2. A dentist's drill starts from rest. After 3.00 s of constant angular acceleration it turns at a rate of 2.00 multiplied by 104 rev/min.

(a) Find the drill's angular acceleration.

(b) Determine the angle (in radians) through which the drill rotates during this period.

Answer 1

well since everything is in cm and seconds and grams we can stay in the centimeter, gram, second or"cgs" units.

Initial momentum = 10*25 - 15*36
= -290 (to the right is positive)
final momentum =same = -290 = 10 U + 15 V
elastic so initial KE = final KE
(1/2) 10 (625) + (1/2) 15 (1296)
3125+9720
=12,845 dynes
final KE =12,845 = 5 U^2 + 7.5 V^2
so two equations, two unknowns:

-290 = 10 U + 15 V
12,845 = 5 U^2 + 7.5 V^2

U = - (1.5 V + 29)
U^2 = 2.25 V^2 + 87 V + 841

12,845 = 5(2.25 V^2 + 87 V + 841) + 7.5 V^2

You can solve the quadratic I think

Answer 2

in 3 seconds from 0 to 2*10^4 revs/min
first change rev/min to radians/sec
2*10^4rev/min (1 min/60 s)(2 pi rad/rev)
=2094 radians/s

alpha = change in speed/change in time = 2094/3 = 698 radians/s^2

angle = (1/2) alpha t^2
=349*9 = 3141 radians