A 100Kg stone is dragged 15m over a frozen lake. If the coefficient of friction between the stone and the ice is 0.1 and the whole process takes 8 seconds, how much work is done and how much power is required?
Now wait a minute. Dr WLS showed you exactly how to do this with and arbitrary mass stone. Substitute 100 Kg for M and run your calculator.
To determine the work done and the power required to drag the stone over the frozen lake, we need to use the formulas for work and power.
1. Work (W) is calculated using the formula:
W = F * d * cos(θ)
Where:
- F is the force applied (in this case, the force of friction).
- d is the displacement (15m).
- θ is the angle between the force vector and the displacement vector (in this case, θ = 0° since the force is parallel to the displacement vector).
2. Power (P) is calculated using the formula:
P = W / t
Where:
- W is the work done.
- t is the time taken (8 seconds).
Now let's calculate the work done:
First, we need to find the force of friction (F). The formula for the force of friction is given by:
F = μ * N
Where:
- μ is the coefficient of friction (0.1).
- N is the normal force, which is equal to the weight of the stone (mass * gravity).
The weight of the stone can be calculated as:
Weight = mass * gravity
Given:
Mass = 100 kg
Gravity = 9.8 m/s² (approximate value)
Weight = 100 kg * 9.8 m/s² = 980 N
Now, calculate the force of friction:
F = 0.1 * 980 N = 98 N
Now, calculate the work done:
W = F * d * cos(θ) = 98 N * 15 m * cos(0°) = 1470 Joules (J)
Next, let's calculate the power required:
P = W / t = 1470 J / 8 s = 183.75 Watts (W)
Therefore, the work done to drag the stone over the frozen lake is 1470 Joules, and the power required is 183.75 Watts.