A 3m long weightless beam is supported at each end by cables (a scaffold). A painter weighing 900N stands 1m from the left cable. Calculate the tension (force) in each cable.
I really don't understand this question.
450
No problem! Let me break it down for you.
First, let's understand the setup. We have a 3-meter long weightless beam that is supported at each end by cables, forming a scaffold. At one end of the beam, there is a painter standing 1 meter away from the left cable. The weight of the painter is given as 900N.
To calculate the tension (force) in each cable, we need to consider the equilibrium of forces acting on the beam.
At the left end of the beam, we have the tension force in the left cable, acting towards the left, and the weight of the painter, acting downwards.
At the right end of the beam, we have the tension force in the right cable, acting towards the right.
Since the beam is weightless, it exerts no downward force. So, the net force acting upwards at the left end must be equal to the net force acting downwards at the right end for the beam to be in equilibrium.
To find the tension in each cable, we need to set up an equation. Let's use the left cable as the reference point.
Summing up the forces in the vertical direction, we have:
Tension in the left cable - Weight of the painter = Tension in the right cable
Let's plug in the given values:
Tension in the left cable - 900N = Tension in the right cable
To calculate the tension in each cable, we need another equation. This equation involves the torque (moment) about the left cable.
The torque about a point is the force applied multiplied by the perpendicular distance from the point to the line of action of the force. In this case, the torque is balanced since the beam is in equilibrium.
We can write the torque equation as:
Moment of tension in the left cable - Moment of weight of the painter = 0
The moment of a force is the force multiplied by the distance perpendicular to the line of action.
Using the equation:
(Tension in the left cable) x (3m) - (900N) x (1m) = 0
Simplifying the equation, we get:
Tension in the left cable = 900N
Now, we can substitute this value back into our previous equation to find the tension in the right cable:
900N - 900N = Tension in the right cable
Tension in the right cable = 0N
Therefore, the tension in the left cable is 900N, and the tension in the right cable is 0N.