Final answer:
To estimate the power required for an 80-kg patient on a 12° incline at 3.6 km/h, convert the velocity to m/s, use the formula P = (mg sin(θ))v, and compute the value by inserting mass, gravitational acceleration, the sine of the slope angle, and velocity.
Step-by-step explanation:
To estimate the power required from an 80-kg patient when the treadmill is sloping at an angle of 12° and the velocity is 3.6 km/h, we can use the concept of work and power. Power is the rate of doing work, and when walking on an incline, work is done against the gravitational force. To do this calculation, we need to convert the velocity to meters per second by dividing 3.6 km/h by 3.6, which gives 1 m/s.
We can estimate the power required to work against gravity by using the formula power (P) = force (F) × velocity (v). Since the force needed is the component of the weight along the incline, we use F = mg sin(θ), where m is mass, g is the acceleration due to gravity (9.8 m/s²), and θ is the angle of the slope. Thus, P = (mg sin(θ))v.
For an 80-kg patient, P = (80 kg × 9.8 m/s² × sin(12°)) × 1 m/s, which calculates to an estimated power required. The exact value would be the result of the multiplication of the terms.