A man of mass m1 = 70.0 kg is skating at v1 = 8.00 m/s behind his wife of mass m

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. (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.) vf _______ (f) Substitute values, obtaining the numerical value for vf, their speed after the collision. vf, couple ______m/s vf, man _________m/s vf, wife ________m/s

Explanation / Answer

b) perfectly inelastic means that the 2 bodies stick together and have the same velocity after the collision. 2c) 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. Substitute the vf term and simplify the expression. d) That's just algebra. Rearrange for an expression with vf on the left. 3) You have the formula now. It's just arithmetic from here on out.

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