Question

The block has a mass of 50 kg. The coefficient of kinetic friction between the ice and the block is $LaTeX: \mu_k$ μk = 0.01 . How hard will you have to push on the block to keep it moving at a constant speed of 1.2 m/s? It is at an angle of 25 degrees pushing downwards. Show answer with units. Please and thank you.

Answer 1

m = mass of block = 50 kg

μ_k = coefficient of kinetic friction between ice and block = 0.01

Along the vertical direction , force equation is given as

F_n = F Sin25 + mg

kinetic frictional force is given as

f_k = μ_k F_n

f_k = μ_k (F Sin25 + mg) eq-1

Along the horizontal direction , force equation is given as

F Cos25 - f_k = 0

F Cos25 = μ_k (F Sin25 + mg) using eq-1

F Cos25 = (0.01)(F Sin25 + (50 x 9.8))

F = 5.4 N