In a common test for cardiac function (the "stress test"), the patient walks on an inclined treadmill (Figure 6-46). Estimate the power required from a 70 kg patient when the treadmill is sloping at an angle of 15° and the velocity is 3.10 km/h.
this is very wrong, the question says on an inclined plane hence the force is supposed to be given by mgsin15 degrees
F=mgsin15°
=70×9.8sin 15°
=177.55N
V=3.1km/h (1000m÷1km)×(1h÷3600s)
=0.86m/s
P=FV
=177.55×0.86
=152.69W
We are going to calculate force first
F=mgsinÕ
F=(70g)(9.8)sin15°
F=177.55N
now calculate the velocity in m/s
3.1km/h×(1000m/1km)×(1h/3600s
This is dimensions analysis, cancelling km and h we get
0.86m/s
Then we can calculate for power using the formula P=FV where F is the force in N and V is the velocity in m/s.
P=FV=(177.55*0.86)=152.69watts
Thank you
P= Fv
F=mgsin° v=3.1*100/3600= 0.86m/s
P=70*9.8*sin°(0.86) W
Why did the treadmill go to therapy?
Because it was feeling inclined!
But seriously, to estimate the power required from a 70 kg patient, we can use the equation:
Power = Work / Time
First, let's calculate the work done. Work is equal to the force exerted by the patient multiplied by the displacement. In this case, the displacement is the distance traveled by the patient, which is given by:
Distance = Velocity * Time
So, let's calculate the distance traveled over a certain period of time. Since the velocity is given in km/h, we need to convert it to m/s:
Velocity = 3.10 km/h * (1000 m / 1 km) * (1 h / 3600 s)
Now, let's calculate the distance traveled:
Distance = Velocity * Time
Distance = (3.10 km/h * (1000 m / 1 km) * (1 h / 3600 s)) * Time
Let's assume that the patient exercises for 10 minutes, which would be 0.16 hours:
Distance = (3.10 km/h * (1000 m / 1 km) * (1 h / 3600 s)) * 0.16 hours
Now that we have the distance, we can calculate the force exerted by the patient. The force can be calculated using the formula:
Force = Mass * Acceleration
Since the angle of the treadmill is given, we can calculate the net force acting on the patient along the incline. The net force will be equal to the weight of the patient (mass * gravity) multiplied by the sine of the angle:
Net Force = (Mass * Gravity) * sin(angle)
Now we can calculate the work done:
Work = Force * Distance
Work = ((Mass * Gravity) * sin(angle)) * Distance
Finally, we can calculate power by dividing the work done by the time:
Power = Work / Time
Now you're all set! Just plug in the values and you'll find the power required from the patient. Remember, laughter is the best medicine, especially for treadmills in therapy!
To estimate the power required from a patient during a stress test, we can start by calculating the work done, and then dividing it by the time taken to find the power.
1. First, let's calculate the work done. The work done is equal to the force applied multiplied by the distance traveled. In this case, the force is the force against gravity due to the slope of the treadmill, and the distance traveled is the vertical distance covered.
2. To calculate the force against gravity, we use the equation: force = mass * gravitational acceleration. The mass of the patient is given as 70 kg, and the acceleration due to gravity is approximately 9.8 m/s^2.
force = 70 kg * 9.8 m/s^2
3. Next, we need to calculate the vertical distance traveled. This can be determined using the angle of inclination and the horizontal distance traveled. We are given the velocity as 3.10 km/h. We need to convert it to meters per second to maintain consistent units:
velocity = 3.10 km/h * (1000 m / 1 km) * (1 h / 3600 s)
4. The horizontal distance traveled can be found using trigonometry. Since we know the angle of inclination, we can use the following equation:
horizontal distance = vertical distance / tan(angle of inclination)
Note: The tangent of an angle is equal to the ratio of the opposite side to the adjacent side in a right triangle.
5. Combining steps 3 and 4, we can calculate the horizontal distance traveled.
6. Now, we can calculate the work done by multiplying the force against gravity by the vertical distance traveled.
7. Finally, to find the power, we divide the work done by the time taken.
F = m*g = 70kg * 9.8N/kg = 686 N.
V=3.1km/h * 1000m/km * 1h/3600s=0.86 m/s
P = F*V = 686 * 0.86 = 590.7 Joules/s.=
590.7 Watts.