A box weighing 450 N is hanging from two chains attached to an overhead beam at angles of 70 degrees and 78 degrees to the horizontal. Determine the tensions in the chains.

To determine the tensions in the chains, we can use the concept of resolving forces. Here are the steps to solve this problem:

Step 1: Identify the forces acting on the box. In this case, the box has its own weight, which acts vertically downward (opposite to the direction of the tension in the chains).

Step 2: Resolve the weight of the box into its horizontal and vertical components. The vertical component is equal to the weight of the box, which is 450 N. The horizontal component is given by the formula:

Horizontal component = Weight * cosine (angle)

For the chain with an angle of 70 degrees:

Horizontal component = 450 N * cosine (70 degrees)

Step 3: Calculate the tension in the chain using the horizontal components. Since there are two chains, we need to split the weight of the box equally between them. Therefore, each chain will have a force equal to half the horizontal component:

Tension in chain 1 = 0.5 * Horizontal component
Tension in chain 2 = 0.5 * Horizontal component

For the chain with an angle of 78 degrees, repeat steps 2 and 3 using the appropriate angle.

Using these steps, you can calculate the tensions in the chains.

T1 cos 70 - T2 cos 78 = 0 (no horizontal force)

T1 sin 70 + T2 sin 78 = 450 (weight = total force up)
solve 2 equations, two unknowns.