Find the Magnitude of the force exerted by each cable to support the 625 N punching bag. One cable is connected to the ceiling with an angle of 37 degrees and the other cable is connected perpendicular to the side wall (Horizontal). HELPP
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To find the magnitude of the force exerted by each cable to support the punching bag, we can use trigonometry.
Let's consider the cable connected to the ceiling with an angle of 37 degrees.
Step 1: Identify the relevant forces:
- The force exerted by the cable (unknown).
- The weight of the punching bag, which is 625 N and acts vertically downwards.
Step 2: Resolve the forces:
- Resolve the weight of the punching bag into two components: one parallel to the cable and the other perpendicular to the cable.
Step 3: Find the components of the weight:
- The component of the weight parallel to the cable can be found using the formula: F_parallel = weight * sin(angle).
- The component of the weight perpendicular to the cable is simply the weight itself: F_perpendicular = weight * cos(angle).
Step 4: Find the force exerted by the cable:
- Since the cable is in equilibrium, the force exerted by the cable must be equal in magnitude, but opposite in direction, to the component of the weight parallel to the cable.
So, the magnitude of the force exerted by the cable connected to the ceiling can be found by using the formula:
Magnitude of force = F_parallel = weight * sin(angle)
= 625 N * sin(37°)
Now let's move on to the cable connected perpendicular to the side wall.
Step 1: Identify the relevant forces:
- The force exerted by the cable (unknown).
- The weight of the punching bag, which is 625 N and acts vertically downwards.
Step 2: Resolve the forces:
- The force exerted by the cable connected perpendicular to the side wall is equal in magnitude but opposite in direction to the weight of the punching bag. This is because the cable is oriented horizontally, which is perpendicular to the direction of the weight.
So, the magnitude of the force exerted by the cable connected perpendicular to the side wall is the same as the magnitude of the weight of the punching bag, which is 625 N.
Therefore, the magnitude of the force exerted by the cable connected to the ceiling is given by:
Magnitude of force = 625 N * sin(37°)
The magnitude of the force exerted by the cable connected perpendicular to the side wall is 625 N.
To find the magnitude of the force exerted by each cable, we can use trigonometric principles. Let's start by considering the cable connected to the ceiling.
For the cable connected to the ceiling at an angle of 37 degrees, we can break down the force into two components: the vertical component and the horizontal component.
1. Vertical Component: This component balances the weight of the punching bag, which is 625 N. The vertical component can be found using the equation: Fv = F * sin(theta), where Fv is the vertical component, F is the total force, and theta is the angle (37 degrees).
Fv = 625 N * sin(37 degrees)
Fv ≈ 375.85 N (rounded to two decimal places)
2. Horizontal Component: This component balances the force due to the tension in the cable. The horizontal component can be found using the equation: Fh = F * cos(theta), where Fh is the horizontal component.
Fh = 625 N * cos(37 degrees)
Fh ≈ 499.29 N (rounded to two decimal places)
Now let's move on to the cable connected perpendicular to the side wall (horizontal).
Since the cable is connected horizontally, only the vertical component of the force is present. This component also balances the weight of the punching bag, which is 625 N.
Therefore, the magnitude of the force exerted by the horizontal cable is also approximately 625 N.
So, to summarize:
- The magnitude of the force exerted by the cable connected to the ceiling is approximately 375.85 N vertically and 499.29 N horizontally.
- The magnitude of the force exerted by the cable connected perpendicular to the side wall (horizontal) is approximately 625 N vertically.
Note: The values mentioned above are approximations rounded to two decimal places.