a boy whose mass is 69kg climbs a tree 10m high in 12s .calculate the work done and power developed
W = F*d = M*g * d = 69*9.8 * 10 = 6762 Joules.
P = W/t = 8762 J./12s. = 564 J./s = 564 Watts.
To calculate the work done by the boy and the power developed, we need to use the formulas related to work, power, mass, height, and time. Here's how you can calculate them:
1. Work Done:
Work is the product of force and displacement, given by the formula:
Work = Force x Distance x cos(θ)
Since the only force acting on the boy is his weight, the formula becomes:
Work = Weight x Height x cos(θ)
Weight is the force due to gravity, given by:
Weight = mass x gravity
Using the given values:
mass = 69 kg
gravity = 9.8 m/s²
Height = 10 m
θ (angle between the direction of force and displacement) = 0° (since the boy is climbing straight up)
Substituting the values into the formulas:
Weight = 69 kg x 9.8 m/s² = 676.2 N
Work = 676.2 N x 10 m x cos(0°) = 6762 J
Therefore, the work done by the boy while climbing the tree is 6762 Joules.
2. Power Developed:
Power is the rate at which work is done, given by the formula:
Power = Work / Time
Using the given value:
Time = 12 s
Substituting the values into the formula:
Power = 6762 J / 12 s = 563.5 W
Therefore, the power developed by the boy while climbing the tree is 563.5 Watts.