A horizontal clothesline is tied between 2 poles, 14 meters apart.

When a mass of 4 kilograms is tied to the middle of the clothesline, it sags a distance of 5 meters.

What is the magnitude of the tension on the ends of the clothesline? Use gravitational acceleration of for this problem as that is what webwork is grading based on.

Draw a free body diagram and set the net vertical force equal to zero. The answer will be a multiple of M g. You will need to compute the angle that the sides of the clothesline devate from horizontal.

To find the magnitude of the tension on the ends of the clothesline, we need to calculate the total force acting on the clothesline. In this case, there are two forces acting on the clothesline: the force due to the weight of the mass and the tension in the clothesline.

The force due to the weight of the mass can be calculated using the formula F = mg, where F is the force, m is the mass, and g is the acceleration due to gravity. In this case, the mass is 4 kilograms, and the acceleration due to gravity is given as . By substituting these values into the formula, we can find the force due to the weight of the mass.

F = (4 kg) * ( )
F = 4 *

The force due to the tension in the clothesline is the same throughout the entire line since the clothesline is massless and in equilibrium. Let's call this force T.

Now, we have two equal and opposite vertical forces - the force due to the weight of the mass acting downward and the tension in the clothesline acting upwards. These forces should balance each other to keep the clothesline in equilibrium.

To find the magnitude of the tension on the ends of the clothesline, we need to calculate the force acting on each end of the clothesline. Since the clothesline is horizontal, the vertical component of the force due to the tension on one end will balance the vertical component of the force due to the weight of the mass.

The horizontal distance from each end of the clothesline to the point where the mass is tied is half of the total length of the clothesline, which is 14/2 = 7 meters. Let's call this distance D.

Now, we can use the properties of similar triangles to determine the magnitude of the tension on the ends of the clothesline. The ratio of the vertical component of the force acting on one end to the total force acting on the clothesline is equal to the ratio of the vertical distance to the length of the clothesline.

(VT / FT) = (5 meters / 14 meters)

The vertical component of the force at each end of the clothesline is equal to the total force acting on the clothesline multiplied by this ratio.

Now, we can substitute the known values to find the magnitude of the tension on the ends of the clothesline.

(VT / FT) = (5 meters / 14 meters)
VT = FT * (5 meters / 14 meters)
VT = * (5 meters / 14 meters)

Since the clothesline is in equilibrium, the force on each end of the clothesline is the same. Therefore, the magnitude of the tension on each end is given by

T = * (5 meters / 14 meters)

So, the magnitude of the tension on the ends of the clothesline is * (5 meters / 14 meters).