Question

A contestant in a winter games event pushes a 46.0 kg block of ice across a frozen lake as shown in the figure below. The coefficient of static friction is 0.1 and the coefficient of kinetic friction is 0.03. (Assume θ = 25°.) (a) Calculate the minimum force F (in N) he must exert to get the block moving. 49.7 Correct: Your answer is correct. N (b) What is its acceleration (in m/s2) once it starts to move, if that force is maintained? Incorrect: Your answer is incorrect. Consider Newton's Second Law. m/s2

Answer 1

a)

F = minimum force applied

m = mass of the block = 46 kg

= coefficient of static friction = 0.1

Along the vertical direction, force equation is given as

N = F Sin25 + mg                                                  eq-1

Static frictional force is given as

f_s = N

using eq-1

f_s = ( F Sin25 + mg)                                             eq-2

Force equation along the horizontal direction is given as

F Cos25 = f_s

Using eq-2

F Cos25 = ( F Sin25 + mg)  

inserting the values

F Cos25 = (0.1) ( F Sin25 + (46 x 9.8))  

F = 52.2 N

b)

when the block starts moving, kinetic frictional force acts on the block instead of static frictional force.

Kinetic frictional force is given as

f_k = N

using eq-1

f_k = ( F Sin25 + mg)                                             eq-3

let the acceleration along the horizontal direction be "a"

Force equation along the horizontal direction is given as

F Cos25 - f_k = ma

Using eq-3

F Cos25 - ( F Sin25 + mg) = ma

inserting the values

(52.2) Cos25 - (0.03) ( (52.2) Sin25 + (46 x 9.8)) = 46 a

a = 0.72 m/s²