OpenResponse Homework Problem 184 When she was an undergrad

Open-Response Homework Problem 18.4 When she was an undergrad, Liz used to work for a small company which produced and packaged sauces and other food items. She would routinely move 40kg crates of ingredients across the floor of the warehouse by pushing them at a velocity of 2 m s . These wooden crates had a coefficient of friction of µk = 0.1 with the polished concrete floor, and she would push with an applied force 30 from the horizontal.

(a)[8 pts] Find the applied force.

(b)[2 pts] Find the amount of work Liz had done after she had pushed one of these crates 10m across the warehouse floor.

Solution

a) angle of pushing force is 30 deg below the horizontal.

(it is not given whether force is 30 deg below or above the horizontal , so i will solve for both)

in vertical, Fnet = 0   (because crate is in equilibrium )

N - mg - Fsin30 = 0

N = mg + Fsin30

friction force, f = uk N = 0.1(mg + Fsin30)

in horizontal,

Fcos30 - f = 0

Fcos30 - 0.1(mg + Fsin30) = 0

F = 0.1mg / (cos30 - 0.1sin30) = (0.1 x 40 x 9.8 ) / (cos30 - 0.1sin30)

F = 48.04 N

{ if above then , F = (0.1 x 40 x 9.8 ) / (cos30 + 0.1sin30) = 42.79 N }

b) work done = F.d   (dot product )

     = |F| |d| cos@

= 48.04 x 10 x cos30 = 416.04 j

{ if above then, W = 42.79 x 10 x cos30 = 370.57 J }