A man of mass m 1 = 70.0 kg is skating at v 1 = 8.00 m/s behind his wife of mass

Question

A man of mass m1 = 70.0 kg is skating at v1 = 8.00 m/s behind his wife of mass m2 = 50.0 kg, who is skating at v2 = 4.00 m/s. Instead of passing her, he inadvertently collides with her. He grabs her around the waist, and they maintain their balance.

(a) Sketch the problem with before-and-after diagrams, representing the skaters as blocks. (Do this on paper. Your instructor may ask you to turn in this work.)

(b) Is the collision best described as elastic, inelastic, or perfectly inelastic?

(c) Why?

(d) Write the general equation for conservation of momentum in terms of m1, v1, m2, v2, and final velocity vf. (Do this on paper. Your instructor may ask you to turn in this work.)

(e) Solve the momentum equation for vf. (Use the following as necessary: m1, v1, m2, v2. Do not substitute numerical values; use variables only.)

(f) Substitute values, obtaining the numerical value for vf, their speed after the collision.

Explanation / Answer

b) perfectly inelastic means that the 2 bodies stick together and have the same velocity after the collision.

c)

d) momentum before = momentum after
m1*v1 + m2*v2 = m1*v3 + m2*v4
If they have the same velocity after the collision v3 and v4 are the same

e)since v3=v4

so m1*v1+m2*v2=vf(m1+m2)

70*8+50*4=vf(70+50)

vf=6.3 m/s

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