A box is pulled straight down by gravity with a force of 10 N. (This is its "weight.")
The box hangs from a massless rope of length 3 m and is pulled to the side with a second rope. It is
pulled until the rope it hangs from makes an angle of 30° with vertical. At that point, the rope pulling it is
20 below horizontal.
What forces do each rope exert? (In other words, what is their "tension"?)

Let's break this down. The weight of the box is 10 N, pulling it down. The rope it hangs from makes a 30° angle, so the tension in that rope is 10 N x cos(30°) = 8.66 N, upward. The second rope pulls the box 20° below horizontal, so its tension is 8.66 N x sin(20°) = 3.58 N, to the left...

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vdimas1 vdimas1 · Answer 2 · 2024-01-21T00:06:29+01:00

Answer:

Explanation: The tension in each rope can be determined by analyzing the forces acting on the box.

First, let's consider the forces acting vertically. The weight of the box is pulling it downward with a force of 10 N. This force is balanced by the tension in the rope it hangs from.

Next, let's examine the forces acting horizontally. The rope pulling the box to the side creates a horizontal tension force. This force can be resolved into two components: one parallel to the ground and one perpendicular to the ground.

Now, let's break down the given information. The rope the box hangs from makes an angle of 30° with the vertical. At this point, the perpendicular component of the tension force is equal to the weight of the box. Therefore, the tension in the rope the box hangs from is also 10 N.

The rope pulling the box to the side is 20° below horizontal. Since the box is not moving horizontally, the horizontal component of the tension force must balance the horizontal component of the weight force.

Since the box hangs vertically, the horizontal component of the weight force is zero. Therefore, the horizontal component of the tension force in the rope pulling the box to the side is also zero.

In summary, the tension in the rope the box hangs from is 10 N, while the tension in the rope pulling the box to the side is zero.