An airplane passenger carries a 250 N suitcase up the stairs, a displacement of 4.70 m vertically, and 5.30 m horizontally.
How much work does the passenger do?
For the Vertical work:
W = F.d => W = 250*4.70*cos(theta) where tan(theta) = 4.7/5.3 . Do the math :)
Fro the Horizontal work:
W = F.d => W = 250*5.30*sin(theta) where tan(theta) = 4.7/5.3 . Do the math :)
*find theta using tan inverse and then find the cos and sin of the theta to use in the above equations
To calculate the work done by the passenger, we need to use the formula:
Work = force x displacement x cosine(theta)
where:
- Work is the amount of work done (in joules, J)
- force is the applied force (in newtons, N)
- displacement is the distance traveled in the direction of force (in meters, m)
- theta is the angle between the force and displacement vectors (in degrees)
In this case, the suitcase is being carried vertically and horizontally, so we can break down the displacement into its vertical and horizontal components. Since we need to calculate the total work done, we'll calculate the work done in each direction separately and then sum them up.
1. Vertical work:
The displacement in the vertical direction is 4.70 m. Since the suitcase is being carried vertically, the force and displacement vectors are in the same direction (theta = 0 degrees). Thus, the formula simplifies to:
Work_vertical = force x displacement_vertical
Given that the force is 250 N and the vertical displacement is 4.70 m, we can calculate the vertical work:
Work_vertical = 250 N * 4.70 m
2. Horizontal work:
The displacement in the horizontal direction is 5.30 m. However, the force and displacement vectors are perpendicular to each other, with an angle of 90 degrees (theta = 90 degrees). In this case, the cosine(theta) term becomes 0, so the formula simplifies to:
Work_horizontal = force x displacement_horizontal x cosine(90)
Given that the force is 250 N and the horizontal displacement is 5.30 m, we can calculate the horizontal work:
Work_horizontal = 250 N * 5.30 m * cos(90)
Finally, we can find the total work done by summing up the vertical and horizontal work:
Total work = Work_vertical + Work_horizontal
You can now substitute the values into the equations and perform the calculations to find the total work done by the passenger.