An 78.9 kg person carries a 23 N package up a flight of stairs. The vertical height of the stairs is 23.8 m. How much work is done?
To calculate the work done, we can use the formula:
Work (W) = Force (F) x Distance (d) x cos(theta)
Where:
- Force (F) is the force applied to carry the package, which is 23 N.
- Distance (d) is the vertical height of the stairs, which is 23.8 m.
- theta (θ) is the angle between the force and the direction of movement, which is 0 degrees when carrying straight up stairs.
Since the force is applied vertically upwards, theta can be assumed to be 0 degrees, and cos(0) equals 1:
W = 23 N x 23.8 m x cos(0)
W = 23 N x 23.8 m x 1
W = 548.6 Joules
Therefore, the work done to carry the package up the flight of stairs is 548.6 Joules.
To calculate the work done, you can use the formula:
Work = Force x Distance x Cos(theta)
Where:
- Work is the amount of work done, measured in joules (J)
- Force is the force applied to move the package, measured in newtons (N)
- Distance is the vertical height of the stairs, measured in meters (m)
- Cos(theta) is the cosine of the angle between the force and the displacement vectors
In this case, the force applied is 23 N, and the vertical height of the stairs is 23.8 m. However, we need to calculate the angle theta to determine the cosine value.
Since the person is carrying the package up the stairs, the angle between the force and displacement vectors is 0 degrees (or 180 degrees if measured downwards). Therefore, the cosine of theta is equal to 1.
Let's substitute the given values into the formula:
Work = 23 N x 23.8 m x 1
Work = 546.4 J
Therefore, approximately 546.4 joules of work is done to carry the package up the flight of stairs.