Question

Bethany, who weighs 540 N, lies in a hammock suspended by ropes tied to two trees. The left rope makes an angle of 45∘ with the ground; the right one makes an angle of 30∘ a) Find the tension in the left rope. b) Find the tension in the right rope.

Answer 1

The tension in the left rope (T1) is 382.4 N, and the tension in the right rope (T2) is 624.7 N.

Explanation:

To solve this problem, we can analyze the forces acting on Bethany and use trigonometric relationships.

Let's assume that the tension in the left rope is T1 and the tension in the right rope is T2.

a) To find the tension in the left rope (T1):

We can consider the vertical component of T1, which counteracts Bethany's weight.

The vertical component of T1 can be found using trigonometry.

In this case, the angle between the left rope and the ground is 45 degrees.

Using the cosine function:

cos(45°) = adjacent/hypotenuse

cos(45°) = Bethany's weight (540 N) / T1

Rearranging the equation, we can solve for T1:

T1 = Bethany's weight (540 N) / cos(45°)

T1 = 540 N / sqrt(2)

Calculating the value, T1 is approximately 382.4 N.

b) To find the tension in the right rope (T2):

Similarly, we can consider the vertical component of T2, which counteracts Bethany's weight. The angle between the right rope and the ground is 30 degrees.

Using the cosine function:

cos(30°) = adjacent/hypotenuse

cos(30°) = Bethany's weight (540 N) / T2

Rearranging the equation, we can solve for T2:

T2 = Bethany's weight (540 N) / cos(30°)

T2 = 540 N / (sqrt(3)/2)

Calculating the value, T2 is approximately 624.7 N.

Therefore,

The tension in the left rope (T1) is 382.4 N, and the tension in the right rope (T2) is 624.7 N.