The figure below shows an overhead view of a piece of wood, with a mass of 2.0 k

Question

The figure below shows an overhead view of a piece of wood, with a mass of 2.0 kg, that is resting on a slippery ice rink. The piece of wood has a length of L 1.10 m. Three horizontal forces are shown on the rod, and there is a fourth force of unknown magnitude, direction, and location that is not shown. The piece of wood remains at rest. 4.0N 0N L/4 8.0 (a) Determine the magnitude and direction of the mystery force. If the mystery force is directed to the right, use a plus sign to indicate the direction; if the force is directed left, use a minus sign (b) Determine the location of the mystery force. To do this, state the distance from the bottom of the piece of wood to where the force is applied.

Explanation / Answer

wood is on slippery ice rink , so no friction

m = 2 kg

L = 1.1 m

F1 = 4 N

F2 = 8 N

F3 = 10 N

F4 = ?

a. for the wood to remain at rest

from force balance

F1 + F2 - F3 + F4 = 0

4 + 8 - 10 + F4 = 0

F4 = -2 N ( to the left)

b. let distance form the bottom of the wood be x

then from torque balance about the bottom of the wood

F1*L + F2*3L/4 = F3*L - F4*x

4*1.1 + 8*3*1.1/4 = 10*1.1 + 2x

x = 0

hence the distance of the force F4 form the bottom of the log is 0 m

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