How much work is done in raising a 10.0 kg backpack from the floor to a shelf 1.50 m above the floor?
To calculate the work done in raising the backpack, we need to use the formula:
Work (W) = Force (F) × Distance (d) × cos(theta)
Where:
- Force (F) is the force applied to lift the backpack,
- Distance (d) is the vertical distance the backpack is raised, and
- Theta (θ) is the angle between the applied force and the direction of motion (which is 0 degrees in this case since the force and motion are both vertical).
In this scenario, we are given:
- Mass (m) of the backpack = 10.0 kg,
- Distance (d) = 1.50 m, and
- Acceleration due to gravity (g) ≈ 9.8 m/s².
First, we need to find the force (F) applied to lift the backpack. The force can be calculated using Newton's second law:
Force (F) = Mass (m) × Acceleration due to gravity (g)
Plugging in the values, we get:
F = 10.0 kg × 9.8 m/s² = 98.0 N.
Now, we can calculate the work done using the formula:
Work (W) = Force (F) × Distance (d) × cos(theta)
Since cos(0) = 1, the formula simplifies to:
Work (W) = Force (F) × Distance (d)
Plugging in the values, we get:
W = 98.0 N × 1.50 m = 147 J (Joules).
Therefore, the work done in raising the 10.0 kg backpack from the floor to a shelf 1.50 m above the floor is 147 Joules.