Open-Response Homework Problem 18.4 When she was an undergrad, Liz used to work
ID: 2308774 • Letter: O
Question
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.
Explanation / Answer
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 }
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