a 60-kg patient exercise on the treadmill, exerting a constant force of 500N while running at a constant velocity of 4 m/s at an angle of 30 for 5 minutes. the coefficient of kinetic friction of the treadmill os 0.45. determine the work done by the patient.
The coefficient of kinetic friction has nothing to do with the work done. His shoes are not sliding on the treadmill.
Work = (Force exerted) x velocity x time
You don't need to know his mass or the angle of the ramp. Just the force.
The force required is a function of the slope and his weight, but they have already told you what the force is. So use it
To determine the work done by the patient, we need to calculate the distance the patient covers on the treadmill.
Given:
Mass of the patient (m) = 60 kg
Force exerted by the patient (F) = 500 N
Velocity of the patient (v) = 4 m/s
Angle (θ) = 30°
Coefficient of kinetic friction (μk) = 0.45
Time (t) = 5 minutes = 5 × 60 = 300 seconds
First, let's decompose the force exerted by the patient into two components: one acting parallel to the treadmill (F_parallel) and the other perpendicular to the treadmill (F_perpendicular).
F_parallel = F × cos(θ)
F_parallel = 500 × cos(30°)
F_parallel = 500 × √(3)/2
F_parallel ≈ 500 × 0.866
F_parallel ≈ 433 N
F_perpendicular = F × sin(θ)
F_perpendicular = 500 × sin(30°)
F_perpendicular = 500 × 1/2
F_perpendicular = 250 N
The frictional force opposing the motion of the patient can be calculated using the equation:
Frictional force (f) = μk × F_perpendicular
f = 0.45 × 250
f = 112.5 N
The net force acting on the patient in the direction of motion can be calculated as:
Net force (F_net) = F_parallel - f
F_net = 433 - 112.5
F_net = 320.5 N
Now, we can calculate the work done by the patient using the equation:
Work (W) = Force × Distance
The distance covered by the patient can be calculated using the formula:
Distance (d) = velocity × time
d = 4 × 300
d = 1200 m
Work (W) = F_net × d
W = 320.5 × 1200
W = 384,600 Joules
Therefore, the work done by the patient is approximately 384,600 Joules.
To determine the work done by the patient, we first need to calculate the total distance covered by the patient on the treadmill during the 5 minutes.
The patient is running at a constant velocity of 4 m/s, and since velocity is defined as distance divided by time, we can calculate the distance covered in 5 minutes.
Distance = Velocity × Time
Distance = 4 m/s × 5 minutes
However, we need to convert the units of time from minutes to seconds because the velocity is given in meters per second.
Since there are 60 seconds in a minute,
Distance = 4 m/s × 5 minutes × 60 seconds/minute
Distance = 4 m/s × 300 seconds
Distance = 1200 meters
Now that we have the distance covered by the patient, we can calculate the work done using the formula:
Work = Force × Distance × Cosine(angle)
The force exerted by the patient is 500N, and the angle is 30 degrees. The cosine of 30 degrees is approximately 0.866.
Work = 500N × 1200 meters × 0.866
Work = 520,800 Joules
Therefore, the work done by the patient on the treadmill is 520,800 Joules.