a. A small mass m 1 = 0.001 kg initially moving with speed v 1 = 2001 m/s collid

Question

a. A small mass m1 = 0.001 kg initially moving with speed v1 = 2001 m/s collides with and sticks to a larger mass m2 = 1.000 kg initially at rest. What is the final speed of the two-mass combination?

b. What was the initial kinetic energy of the small mass before the collision?

c. What is the kinetic energy of the two-mass combination after the collision?

d. An object of mass m and initial speed v0 sliding on a horizontal frictionless surface encounters a frictionless ramp. To what vertical height will the object rise before coming to rest?

Explanation / Answer

a)
use conservation of momentum:
m1*v1i + m2*v2i = (m1+m2)*vf
0.001*2001 + 1*0 = (0.001 + 1)*vf
vf=1.999 m/s
Answer: 1.999 m/s

b)
initial kinetic energy = 0.5*m1*vi^2
= 0.5*0.001*(2001)^2
=2002 J

c)
final kinetic energy = 0.5*(m1+m2)*vi^2
= 0.5*(0.001+1)*(1.999)^2
=2.000 J

d)
use conservation of energy:
0.5*m*v^2 = m*g*h
0.5*v^2 = g*h
0.5*vo^2 = g*h
h=0.5*vo^2/g

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