Forces in Equilibrium: Calculating Weight of a Frame

What is the weight of the frame held by two cables with a tension of 30 N each at a 45° angle with the horizontal?

A) 10.2 N
B) 21.2 N
C) 32.4 N
D) 42.4 N

Answer:

The correct answer is D) 42.4 N.

The weight of the frame can be determined by the upward force exerted by the two cables to maintain equilibrium. Each cable exerts a vertical force of 21.2 N, which sums up to a total of 42.4 N. Therefore, the weight of the frame is 42.4 N.

This problem can be solved by applying the principle of forces in equilibrium. When an object is stationary and not falling, the resultant force is zero, indicating that the upward forces counterbalance the downward forces. The tension force in the cable consists of components both parallel and perpendicular to the direction of gravity. However, we only need to focus on the vertical component, which represents the weight of the frame.

The vertical component of the tension in one cable is given by Tsinθ = 30 N * sin(45°) = 21.2 N. Since there are two cables supporting the frame, the total upward force amounts to 2 * 21.2 N = 42.4 N, which matches the downward force, i.e., the weight of the frame at 42.4 N. Hence, the correct answer is D) 42.4 N.