Answer :
Final answer:
To determine the force exerted by the right support on a 20.0 kg horizontal plank resting on two supports, the static equilibrium principle is used, and the resulting force is found to be approximately 131 N, corresponding to option (d).
Explanation:
The problem involves a 20.0 kg horizontal plank which is 4.00 m long and rests on two supports with one at each end. To find the magnitude of the force exerted by the right support (1.00 m from the right end), we use the concept of static equilibrium where the sum of moments around any point is zero.
Let FL and FR be the forces by the left and right supports respectively. The plank's weight, W = mg = 20.0 kg × 9.81 m/s2 = 196 N, acts downward at the center of the plank (2.00 m from either end).
Taking the moment about the left support:
- FR × 3.00 m (distance from left support to right support) = W × 2.00 m (distance from left support to center of gravity)
- FR = (196 N × 2.00 m) / 3.00 m
- FR = 130.67 N
Thus, the magnitude of the force exerted by the support near the right end is approximately 131 N (when rounded to three significant figures), which corresponds to option (d).
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