A Large Scoreboard Suspended in a Sports Arena - Finding its Mass

The Mass of the Scoreboard

Mass of the scoreboard is 1313.7 kg.

To find the scoreboard's mass, we need to calculate the total force acting on the scoreboard and then use the equation F = ma to find the mass.

First, let's calculate the vertical component of the force from the six cables that make an angle of 8.0° with the vertical. The vertical component of the force is given by:

Fv = F * cosθ

Where F is the tension in each cable (1300.0 N) and θ is the angle between the cable and the vertical (8.0°).

Fv = 1300.0 * cos(8.0°)

Fv = 1289.1 N

The total vertical force from these six cables is:

Fv,total = 6 * 1289.1

Fv,total = 7734.6 N

Now, let's calculate the vertical component of the force from the four cables that make an angle of 10.0° with the vertical. The vertical component of the force is given by:

Fv = F * cosθ

Where F is the tension in each cable (1300.0 N) and θ is the angle between the cable and the vertical (10.0°).

Fv = 1300.0 * cos(10.0°)

Fv = 1284.8 N

The total vertical force from these four cables is:

Fv,total = 4 * 1284.8

Fv,total = 5139.2 N

The total vertical force acting on the scoreboard is the sum of the vertical forces from the six cables and the four cables:

Fv,total = 7734.6 + 5139.2

Fv,total = 12873.8 N

Now, we can use the equation F = ma to find the mass of the scoreboard. The acceleration due to gravity is 9.8 m/s^2:

F = ma

12873.8 = m * 9.8

m = 12873.8 / 9.8

m = 1313.7 kg