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 = Potential Energy increase = M g H
d = 15 m
w = 5.3 kg
g = 10 m/s²
W = ?
F = mg
F = 5.3 kg x 10 m/s²
F = 53 N
W = F x d
W = 53 N x 15 m
W = 795 Joules
To determine the work done by the climber on the backpack, we can use the formula:
Work = Force × Distance × cos(θ)
Where:
- Force is the component of force exerted in the direction of motion
- Distance is the displacement of the object
- θ is the angle between the direction of motion and the force applied
In this case, the climber is moving vertically upwards, so the angle between the direction of motion and the force applied is 0 degrees. Therefore, cos(θ) equals 1.
The force exerted by the climber on the backpack is equal to the weight of the backpack, which can be calculated using the formula:
Force = mass × gravitational acceleration
Mass = 5.3 kg
Gravitational acceleration, denoted as g, is approximately 9.8 m/s^2.
Plugging in the values:
Force = 5.3 kg × 9.8 m/s^2 = 51.94 N
Now that we have the force and the distance (15 m), we can calculate the work done by the climber:
Work = 51.94 N × 15 m × cos(0)
= 51.94 N × 15 m × 1
= 778.5 Joules
Therefore, the climber does 778.5 Joules of work on the backpack while climbing the rock wall.