Two forces, one with a magnitude of 3 N and the other with a magnitude of 5N, are applied to an object. For which orientations of the forces shown in the diagrams is the magnitude of the acceleration

Question

Two forces, one with a magnitude of 3 N and the other with a magnitude of 5N, are applied to an object. For which orientations of the forces shown in the diagrams is the magnitude of the acceleration of the object the least?

TestHub · Accepted Answer

The acceleration magnitude is a = F_net/m, so we compare the net force in each arrangement.

(A) Forces opposite: F = 5 - 3 = 2 N.

(B) Forces at 90°: F = $5^{2} + 3^{2}$ = $34$ $\approx$ 5.8 N.

(C) 3 N pulling partly along the 5 N force: F > 5 N.

(D) Same direction: F = 5 + 3 = 8 N.

(E) 3 N pulling partly against the 5 N force: F between 2 N and 5 N but greater than 2 N.

The least net force, and hence the least acceleration, is in arrangement (A).

Correct option: (A).

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