two lifting ropes are connected at bthier lower ends to a common shackle from which a load of 53kN hangs. if the rops make angles of 35degree and 45 degree respectively to the vertical. find the tension in each rope.
To find the tension in each rope, we can resolve the load force (53 kN) into horizontal and vertical components using trigonometry. Here's how you can calculate the tension in each rope:
1. Start by determining the vertical components of the load force. The vertical component can be found using the sine of the angle.
Vertical component = Load force * sin(angle)
For the rope making an angle of 35 degrees:
Vertical component of rope 1 = 53 kN * sin(35 degrees)
For the rope making an angle of 45 degrees:
Vertical component of rope 2 = 53 kN * sin(45 degrees)
2. Next, determine the horizontal components of the load force. The horizontal component can be found using the cosine of the angle.
Horizontal component = Load force * cos(angle)
For the rope making an angle of 35 degrees:
Horizontal component of rope 1 = 53 kN * cos(35 degrees)
For the rope making an angle of 45 degrees:
Horizontal component of rope 2 = 53 kN * cos(45 degrees)
3. Now, we have the individual horizontal and vertical components of the load force for each rope. The tension in each rope is equal to the magnitude of the vector sum of the horizontal and vertical components. We can use the Pythagorean theorem to find the magnitude.
For rope 1:
Tension in rope 1 = sqrt((Vertical component of rope 1)^2 + (Horizontal component of rope 1)^2)
For rope 2:
Tension in rope 2 = sqrt((Vertical component of rope 2)^2 + (Horizontal component of rope 2)^2)
Simply plug in the values calculated in the previous steps to determine the tension in each rope.