Question

Chapter 07, Problem 44 GO Your answer is partially correct. Try again A 57.1-kg person, running horizontally with a velocity of +3.77 m/s, jumps onto a 13.1-kg sled that is initially at rest. (a) Ignoring the effects of friction What is the coefficient of kinetic friction between the sled and the sno away. (b) The sled and person coast 30.0 m on level snow before coming to rest. (a) 3.25 m/s Number Units (b) Number 0.0179 No units Units

Answer 1

(a) Solve this problem using conservation of momentum.

Mass of person, m1 = 57.1 kg

initial velocity of the person, u1 = 3.77 m/s

Mass of the sledge, m2 = 13.1 kg

initial velocity of the sledge, u2 = 0

Suppose final velocity of the sledge and the person = V

Apply conservation of momentum -

Pi = Pf

=> m1*u1 + m2*u2 = (m1+m2)*V

=> 57.1*3.77 + 13.1*0 = (57.1+13.1)*V

=> V = (57.1*3.77) / (57.1+13.1) = 3.07 m/s (Answer)

(b) Distance traveled by sledge and the person before stopping, d = 30.0 m

Suppose the retardation = a

Final velocity after stopping, V' = 0

use the expression -

V'^2 = V^2 + 2*a*d

=> 0 = 3.07^2 + 2*a*30.0

=> a = -3.07^2 / (2*30.0) = - 0.157

Suppose, kinetic friction coefficient = $\mu k$

write the relationship between $\mu k$ and 'g' -

a = $\mu k$*g

=> $\mu k$ = a/g = 0.157/9.8 = 0.016 (Answer)