Calculate the Mass of a Suspended Scoreboard

What is the mass of the scoreboard suspended in the sports arena?

Calculate the mass of the scoreboard based on the given information about the tensions in the cables supporting it.

Final answer:

To find the scoreboard's mass, we can use trigonometry to calculate the tensions in each cable and then use the equilibrium condition for vertical forces. By resolving the tension into vertical and horizontal components, we can determine the vertical component that counteracts the weight of the scoreboard. Finally, we can calculate the total mass by adding the masses calculated from the two sets of cables.

Explanation:

To find the tension in each cable, we can use the equilibrium condition for the vertical forces. The force exerted by each cable can be resolved into vertical and horizontal components. The vertical components of the forces must add up to counteract the weight of the scoreboard. Since there are 6 cables making an angle of 8.0° with the vertical, and 4 cables making an angle of 10.0° with the vertical, we can calculate the tension in each cable using trigonometry.

For the cables making an angle of 8.0°, the vertical component of the tension will be T * cos(8.0°) = mg, where T is the tension and m is the mass of the scoreboard. Solving for m, we get m = (T * cos(8.0°)) / g. Substituting the given values, we have m = (1300.0 N * cos(8.0°)) / 9.8 m/s^2.

Similarly, for the cables making an angle of 10.0°, the vertical component of the tension will be T * cos(10.0°) = mg. Solving for m, we get m = (T * cos(10.0°)) / g. Substituting the given values, we have m = (1300.0 N * cos(10.0°)) / 9.8 m/s^2.

To calculate the total mass of the scoreboard, we can add the masses calculated from the two sets of cables.