A 24 kg beam is attached to a wall with a hinge and its far end is supported by a cable. The angle between the beam and the cable is 90 degrees and the beam is inclined at an angle of 13.6 degrees with respect to the horizontal. What is the magnitude of the force that the beam exerts on the hinge?
I think that I'm supposed to find Fx and Fy and then use the pythagoreom theorm but, I having trouble finding Fy.??? please help
To find the magnitude of the force that the beam exerts on the hinge, you can use the following steps:
Step 1: Draw a diagram of the beam and label the given information.
From the given information, we know that the angle between the beam and the cable is 90 degrees and the beam is inclined at an angle of 13.6 degrees with respect to the horizontal.
Step 2: Resolve the weight of the beam into its vertical and horizontal components.
The weight of the beam acts vertically downwards. We need to find its vertical and horizontal components.
The vertical component (Fy) can be calculated using the equation: Fy = m * g * cos(θ),
where m is the mass of the beam, g is the acceleration due to gravity, and θ is the angle of inclination.
Given that the mass of the beam is 24 kg, the acceleration due to gravity is approximately 9.8 m/s^2, and the angle of inclination is 13.6 degrees, we can calculate Fy as follows:
Fy = 24 kg * 9.8 m/s^2 * cos(13.6 degrees)
Step 3: Calculate the magnitude of the force exerted by the beam on the hinge.
The magnitude of the force exerted by the beam on the hinge can be calculated using the Pythagorean theorem.
The Pythagorean theorem states that the square of the hypotenuse (the resultant force) is equal to the sum of the squares of the other two sides (Fy and Fx):
Resultant force^2 = Fy^2 + Fx^2
Given that the angle between the beam and the cable is 90 degrees, the horizontal component (Fx) is equal to zero.
Therefore, the magnitude of the force exerted by the beam on the hinge can be calculated as follows:
Resultant force = √(Fy^2 + Fx^2) = √(Fy^2 + 0^2) = √(Fy^2)
Substituting the value of Fy from Step 2 into the equation, the magnitude of the force exerted by the beam on the hinge can be calculated.
To find the force exerted by the beam on the hinge, we can break it down into its horizontal (Fx) and vertical (Fy) components. Let's go step by step:
1. Start by drawing a diagram of the problem to visualize it better. Draw the beam attached to the wall at an angle of 13.6 degrees with respect to the horizontal, and draw the cable at a 90-degree angle to the beam.
2. Now, decompose the force of gravity acting on the beam into its horizontal and vertical components. The vertical component of the force of gravity (Fg) can be found by multiplying the mass of the beam (24 kg) by the acceleration due to gravity (9.8 m/s^2): Fg = (24 kg) x (9.8 m/s^2).
3. Calculate the horizontal component of the force of gravity. Since the beam is inclined at an angle, the horizontal component (Fx) of the force of gravity can be found using trigonometry. Fx = Fg * cos(13.6 degrees).
4. Now, to find the vertical component of the force that the beam exerts on the hinge (Fy), we need to consider the forces acting in the vertical direction. The tension in the cable will balance out the vertical component of the force of gravity, so Fy = Fg.
5. Finally, we can find the magnitude of the force that the beam exerts on the hinge using the Pythagorean theorem. The magnitude of the force (F) can be calculated as the square root of the sum of the squares of Fx and Fy: F = sqrt(Fx^2 + Fy^2).
Substitute the calculated values of Fx and Fy into the equation and solve for F to get the magnitude of the force that the beam exerts on the hinge.