Question

Two ropes are attached to a 50-kg object. The first rope applies a force of 35 N and the second, 55 N. If the two ropes are perpendicular to each other, what is the resultant acceleration of the object?A. 1.3 m/s2B. 35 m/s2C. 1.8 m/s2D. 65 m/s2E. 0.77 m/s2

Answer 1

F1 = 35 N F2 = 55 N

There will be no sidewise force on the resultant force

F1 sin θ1 = F2 sin (90 - θ1) since the ropes are at right angles

35 sin θ1 = 55 cos θ1 cos θ1 = sin (90 - θ1)

tan θ1 = 55 / 35 = 1.57 θ1 = 57.5 deg 90 - θ1 = 32.5 deg

F1 cos 57.5 + F2 cos 32.5 = 35 cos 57.5 + 55 cos 32.5 = 65.2 N

R (resultant) = 65.2 N

a = 65.2 N / 50 kg = 1.30 m/s^2

A) is correct