A Crane Moving a Scoreboard: Work Calculation

A crane moves a 250 kg scoreboard from the ground to the height of 100 m. What is the work done on the scoreboard?

A crane is used to lift a 250 kg scoreboard to a height of 100 meters. In order to calculate the work done on the scoreboard, we can use the formula for work:

Work = Force x Distance x cos(θ)

Where:

• Force: This is the force required to lift the scoreboard against gravity. In this case, it is equal to the weight of the scoreboard, which can be calculated using the formula Weight = Mass x Gravity.
• Distance: This is the vertical distance the scoreboard is lifted, in this case 100 meters.
• θ: The angle between the force and the direction of motion, which is 0 degrees in this case as the force is acting vertically upwards.

First, let's calculate the weight of the scoreboard:

Weight = 250 kg x 9.8 m/s^2 = 2450 N

Now, we can calculate the work done on the scoreboard:

Work = 2450 N x 100 m x cos(0) = 245,000 Joules

Therefore, the work done on the scoreboard as it is lifted to a height of 100 meters is 245,000 Joules.