A horizontal clothesline is tied between 2 poles, 20 meters apart.
When a mass of 5 kilograms is tied to the middle of the clothesline, it sags a distance of 4 meters.
What is the magnitude of the tension on the ends of the clothesline?
Requires algebra, trigonometry and physics, not calculus.
Total force down = total force up since the mass does not accelerate
Do half the problem at a time since it is symmetrical
So 2.5 kg down on left gives 2.5*9.8 = 24.5 Newtons down.
That 24.5 Newtons must be supported by the vertical component of the tension in the line on the left.
So T (4/sqrt (4^2+10^2) = 24.5
T = 24.5 (sqrt 116)/4 = 66 Newtons
If this is a mathematics rather than a physics question they may express force in kilograms (mathematicians do stuff like that) in which case divide by g which is about 9.8 m/s^2
T 4/sqrt (4^2+10^2) DOES NOT EQUAL 24.5
ignore my last comment i'm an idiot
To find the magnitude of the tension on the ends of the clothesline, we need to consider the forces acting on the mass in equilibrium.
In this scenario, the clothesline is in equilibrium when the gravitational force acting downward on the mass is balanced by the tension forces acting upward on both ends of the clothesline.
First, let's determine the total sag of the clothesline, considering both sides. Since the distance between the poles is 20 meters, and the sag in the middle is 4 meters, each side of the clothesline sags by half of this distance, which is 2 meters.
Next, let's visualize the forces acting on the mass when it is tied to the middle of the clothesline. We have two tension forces acting upward on each end of the clothesline, and the weight of the mass acting downward.
Since the clothesline is in equilibrium, the magnitudes of the tension forces at each end are equal. Therefore, we can divide the weight of the mass (5 kg) by the sag distance (2 meters) to find the magnitude of the tension forces at each end of the clothesline.
Magnitude of tension on each end = weight of the mass / sag distance
= 5 kg * 9.8 m/s^2 / 2 m
= 49 N
Therefore, the magnitude of the tension on the ends of the clothesline is 49 Newtons.