A horse pulls a cart with a force of 180.0 N at and angle of 33.0° with respect to the horizontal and moves along at a speed of 11.0 km/hr. How much work does the horse do in 8.6 min?
What is the average power of the horse?
Vo = 11km/h = 11,000m/3600s = 3.056 m/s.
d=r*t=3.056m/s * 8.6min * 60s/min=1577 m
Work = F*d = 180*cos33 * 1577 = 238 J.
Power = F*V = 180*cos33 * 3.056 =
461.3 J./s = 461.3 Watts.
Correction:
Work = 180*cos33 * 1577 = 238,065 J.
To find the work done by the horse, we can use the formula:
Work = Force × Distance × cosine(theta)
where:
- Work is the amount of work done by the horse
- Force is the magnitude of the force applied by the horse, which is 180.0 N
- Distance is the distance covered by the horse
- Theta (θ) is the angle between the force and the direction of motion
First, let's calculate the distance covered by the horse:
To find the distance covered in 8.6 minutes, we need to convert the speed from km/hr to m/s:
Speed = 11.0 km/hr = 11.0 × 1000 / 3600 = 3.06 m/s
Distance = Speed × Time = 3.06 m/s × 8.6 min × 60 s/min = 1478.56 m
Now, let's calculate the work done by the horse:
Work = 180.0 N × 1478.56 m × cosine(33.0°)
For the average power of the horse, we can use the formula:
Power = Work / Time
where:
- Power is the average power of the horse
- Work is the amount of work done by the horse
- Time is the time taken to do the work, which is 8.6 min
Let's calculate the average power:
Power = Work / (8.6 min × 60 s/min)
Now we can substitute the values into the formulas and solve for Work and Power.
To find the work done by the horse, we can use the formula:
Work = Force x Distance x Cos(angle)
First, let's convert the speed of the horse from km/hr to m/s:
11.0 km/hr = 11.0 x 1000 m / 3600 s = 3.06 m/s (approx)
Now, we need to find the distance traveled by the horse in 8.6 min:
8.6 min = 8.6 x 60 s = 516 s
To find the distance, we can use the formula:
Distance = Speed x Time
Distance = 3.06 m/s x 516 s = 1578.96 m (approx)
Now, we can calculate the work done by the horse:
Work = 180.0 N x 1578.96 m x Cos(33.0°)
Using a scientific calculator:
Work = 180.0 N x 1578.96 m x 0.8387
Work ≈ 233,931.45 J
Therefore, the horse does approximately 233,931.45 Joules of work in 8.6 minutes.
To find the average power of the horse, we can use the formula:
Power = Work / Time
Since the time is given in minutes, let's convert it to seconds:
8.6 min = 8.6 x 60 s = 516 s
Now, we can calculate the average power:
Power = 233,931.45 J / 516 s
Power ≈ 453.06 W
Therefore, the average power of the horse is approximately 453.06 Watts.