A rock climber climbs a 15 m vertical rock wall while wearing a 5.3 kg backpack. How much work does the climber do on the backpack?
Work = M g H
To find the amount of work the climber does on the backpack, we can use the equation:
Work = Force × Distance × cos(θ)
Where:
- Force is the force applied on the backpack (in this case, the force due to gravity)
- Distance is the vertical distance the backpack is moved (15 m)
- θ is the angle between the force and the displacement (in this case, since the climber is moving vertically, θ is 0 degrees)
First, let's calculate the force applied on the backpack. The force due to gravity is given by:
Force = mass × acceleration due to gravity
Mass = 5.3 kg
Acceleration due to gravity = 9.8 m/s² (approximately)
Substituting the values into the equation, we have:
Force = 5.3 kg × 9.8 m/s²
Now let's calculate the work:
Work = Force × Distance × cos(0°)
Substituting the values, we have:
Work = (5.3 kg × 9.8 m/s²) × 15 m × cos(0°)
Since cos(0°) equals 1, we can simplify the equation:
Work = (5.3 kg × 9.8 m/s²) × 15 m × 1
Now we can calculate the work:
Work = 5.3 × 9.8 × 15 Joules
Using a calculator, we find that the work done on the backpack by the climber is approximately 764.1 Joules.