Do not round intermediate calculations; however, for display purposes report int

Question

Do not round intermediate calculations; however, for display purposes report intermediate steps rounded to five significant figures. Give your final answer(s to five significant figures. A worker inside a truck at point A applies a force to rope ABC to slowly lower a box C down a ramp.DE. The box has 500.00 N weight and slides without friction on the ramp, and the pulley at B is frictionless. The box is 3/4 the distance from point D to point E, determine the force the worker must apply to the rope and the reaction between the box and ramp. Neglect the size of the box and pulley. 0.90000 m 4.2000 m 20 B 2.4000 m 1.4000 m ABC

Explanation / Answer

suppose tension is T.

angle of DE with horizontal,

@ = tan^-1(1.4 / 4.2) = 18.43 deg

DE = sqrt(1.4^2 + 4.2^2 ) = 4.43 m
for box position ,

x = (3* 4.43 / 4) cos18.43 = 3.15 m

y = 3 * 4.43 /4 sin18.43 = 1.05 m

angle of rope with horizontal = tan^-1 ( (0.9 + 3.15) / (2.4 + 1.05))

= 49.57 deg

angle of rope wrt to ramp = 49.57 - 18.43 = 31.34 deg

so along the ramp, Fnet = 0

Tcos31.34 - mgsin18.43 = 0

T = 500 sin18.43 / cos31.34 = 184.69 N ..........Ans (force by worker)

R = mgcos18.43 - Tsin31.34

R = (500 cos18.43) - (184.69 sin31.34) = 378.30 N ,....Ans

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