# 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