physics i need help

Question

A block rests on a rough horizontal table. A rope is attached to the block and is pulled with a force of 82 N to the left. As a result, the block accelerates at 3.4 m/s^2. The coefficient of kinetic friction (μ) between the block and the table is 0.15. What is the mass of the object? 

Answer 1

Draw a free body diagram:

Let "T" be the tension in the rope therefore T = 82 N

Let "F_G" be the force of gravity (the object's weight) F_G = mg = 9,81m

Let "F_N" be the normal force

Let "F_F" be the force of friction and since μ = 0.15 then F_F = 0.15F_N

Since a = 3.4 to the left, then a = -3.4 (to be consistent with right as positive, left as negative.

Sum the forces in the y-direction:

∑F_y = F_N - F_G = 0 (there is no motion in the y-direction)

Therefore F_N = F_G and since F_G = 9.81m then F_N = 9.81m

Sum the forces in the x-direction:

∑F_x = F_F - T = ma

Since T = 82, F_F = 0.15F_N but F_N = 9.81m, Also a = -3.4. So, plugging those into the equation gives:

0.15(9.81m) - 82 = m(-3.4)

1.4715m - 82 = -3.4m

1.4715m + 3.4m = 82

4.8715m = 82

m = 82/4.8715 = 16.83 kg or, rounding to 2 sig figs, m = 17 kg