A mas of 100 Kg hangs from a cable secured to a steel pole and supported by another cable as shown below. Find the tension (T) in the support cable and the force (F) on the steel pole.
To find the tension in the support cable and the force on the steel pole, we need to analyze the forces acting on the system. Let's break it down step by step:
1. Draw a free-body diagram: Draw a diagram representing the mass and the forces acting on it. In this case, we have the weight of the mass acting downwards (mg) and the tension in the support cable (T) acting upwards. The weight of the mass can be calculated using the formula: weight = mass * acceleration due to gravity, where acceleration due to gravity is approximately 9.8 m/s^2.
2. Apply Newton's second law of motion: According to Newton's second law, the sum of all the forces acting on an object is equal to the mass of the object multiplied by its acceleration. In the vertical direction, the forces are balanced (since the mass is not accelerating vertically), so we have:
T - mg = 0
3. Solve for T: Rearrange the equation to solve for T:
T = mg
4. Calculate the force on the steel pole (F): The force on the steel pole is equal to the tension in the support cable (T). Therefore, F = T.
5. Substitute the given values: Given that the mass is 100 kg, we can substitute this value into the equations:
T = (100 kg) * (9.8 m/s^2) = 980 N
F = 980 N
Therefore, the tension in the support cable (T) is 980 N and the force on the steel pole (F) is also 980 N.