I need a step by step visual of how to do this question: A uniform horizontal beam 5.00m long and weighing 3.00x10^2 N is attached to a wall by a pin connection that allows the beam to rotate. Its far end is supported by a cable that makes an angle of 53 degree with the horizontal. A person weighing 6.00x10^2 N stands 1.50 m from the wall.
a) Determine the magnitude of the tension in the cable. b) Determine the vertical forces exerted by the wall on the beam.
My cable tension is 833.5 Newtons. Can't go further if that's not right.
To solve this question, we can follow these steps:
Step 1: Draw a diagram
Draw a diagram that represents the given situation. Mark the distances and angles provided in the question.
Step 2: Identify the forces acting on the beam
Identify all the forces acting on the beam. In this case, there are two forces - the weight of the beam acting downwards and the tension in the cable acting upwards at an angle.
Step 3: Resolve the forces
Resolve the forces into their vertical and horizontal components. This will make it easier to analyze the forces acting in different directions.
For the weight of the beam, resolve it into vertical and horizontal components. The vertical component can be found using the formula: Force = Mass x Gravity, where the given weight is in Newtons (N). The horizontal component is zero, as the weight acts vertically downwards.
For the tension in the cable, resolve it into vertical and horizontal components. The vertical component can be found using the formula: Force = Tension x cos(angle), where the given angle is 53 degrees. The horizontal component can be found using the formula: Force = Tension x sin(angle).
Step 4: Analyze the forces
Now, analyze the forces acting in the vertical direction.
The vertical forces acting on the beam are: the vertical component of the weight of the beam and the vertical component of the tension in the cable. These two forces should balance each other to keep the beam in equilibrium.
Step 5: Set up the equations
Set up the equation by considering the forces in equilibrium. The sum of the vertical forces should be equal to zero. Use this equation to solve for the tension in the cable.
Step 6: Calculate the tension in the cable
Using the equation from step 5, calculate the tension in the cable.
Step 7: Calculate the vertical forces exerted by the wall
To calculate the vertical forces exerted by the wall on the beam, consider the forces acting in the vertical direction. The vertical forces include the vertical component of the weight of the beam and the vertical component of the tension in the cable. These forces should be equal in magnitude and opposite in direction to keep the beam in equilibrium.
Step 8: Calculate the vertical forces
Calculate the vertical forces exerted by the wall on the beam based on the calculations from step 7.
By following these steps, you should be able to determine the magnitude of the tension in the cable (part a) and the vertical forces exerted by the wall on the beam (part b) in this question.