Problem

(II) Arlene is to walk across a "high wire" strung horizontally between two buildings 10.0 m apart. The sag in the rope when she is at the midpoint is 10.0°, as shown in Fig. 4-47. If her mass is 50.0 kg, what is the tension in the rope at this point?

Solution 23P: When a force is applied at any point on the string, internal force developed inside the wire which is known as tension, and this we have to calculate in this particular situation. Step 1 of 4 Concept: A body is said to be in equilibrium, if summation of all the forces is equal to zero. Figure below shows the free body diagram of the string under tension as per problem. When a force is applied at any point on the string, internal force developed inside the wire which is known as tension which always acts along the rope. At middle point of the string the string is under the action of three forces,as shown in the figure above, 1)Weight of the Arlene mg, acting vertically downward 2) Tension T in the string towards the left point 1 3) Tension T in2the string towards the right point Step 2 of 4 Resolving the tensions T an1 T into2its components along the horizontal and vertical direction as shown in figure above. Taking all the forces along the positive x and y axes to be positive and vice versa, as shown in figure above. Also any component perpendicular to the rope would cause the rope to bend. Assuming the rope is massless, those two tensions T an1 T will2be of the same magnitude, since the point is not accelerating the sum of the forces must be zero. Step 3 of 4 As the body to be in equilibrium, therefore net force acting on the body should be equal to zero. From the above diagram we can say that, along x-direction, F = T cos10 + T cos10 = 0 o x 1 2 o o T 1os10 = T cos20 T 1 T 2 …..(1)