A horse pulls a cart with a force of 40lb at an angle of 30 degrees above the horizontal and moves along at a speed of 6mi/hr. A) how much work does the force do in 10 min? B) What is the average power (in horsepower) of the force?
A) (Force component along direction of motion) * 5280 ft = ___ ft lb
B) (Force component along direction of motion) * (speed, in ft/s) = ___ ft lb/s
Use the conversion factor 550 ft lb/s per HP. Also convert 6 mi/h to 8.8 ft/s
a-642,648.7029 ft.lb
b- 823.9085934 W
i want 1nd qus
(a)1.8*10^5 ft.lb (b)0.55 hp
Plz give the answer
To solve these questions, we need to understand the formulas for work and power.
A) Work (W) is given by the formula:
W = F * d * cos(theta)
Where F is the force, d is the distance moved, and theta is the angle between the direction of the force and the direction of movement.
B) Power (P) is given by the formula:
P = W / t
Where W is the work done, and t is the time taken.
Now, let's calculate the answers step by step.
A) To find the work done in 10 minutes, we need to find the distance moved in 10 minutes. The distance can be calculated using the formula:
Distance (d) = speed * time
Given that the speed is 6 mi/hr and time is 10 minutes, we convert the time to hours:
10 minutes = 10/60 hours = 1/6 hour
Now, substituting the values into the formula:
d = 6 mi/hr * 1/6 hour = 1 mile
The force acting on the cart is 40 lb, and the angle of 30 degrees. Let's calculate the work:
W = 40 lb * 1 mile * cos(30 degrees)
To calculate the cosine of 30 degrees, we convert it to radians by multiplying by (pi/180):
W = 40 lb * 1 mile * cos(30 degrees) = 40 lb * 1 mile * cos(30 * pi/180)
Now, calculate cos(30 * pi/180) ≈ 0.866:
W = 40 lb * 1 mile * 0.866 ≈ 34.64 lb * mile
Therefore, the work done by the force in 10 minutes is approximately 34.64 lb * mile.
B) To find the average power in horsepower, we need to convert the work into foot-pounds (since power is usually measured in foot-pounds per second) and then convert it into horsepower.
1 horsepower = 550 foot-pounds per second.
We know the work done is 34.64 lb * mile. To convert it into foot-pounds, we need to multiply by the conversion factor:
1 mile = 5,280 feet
1 foot = 0.3048 meters
1 lb = 0.4536 kg
Now, let's calculate the work in foot-pounds:
Work (W) = 34.64 lb * mile * 5,280 feet/mile * 0.3048 meters/foot * 0.4536 kg/lb * 9.8 m/s^2
Simplifying the conversion factors:
W = 34.64 * 5,280 * 0.3048 * 0.4536 * 9.8 foot-pounds
Now, let's convert the work from foot-pounds to horsepower:
Power (P) = W / t
Now, let's substitute the values:
P = (34.64 * 5,280 * 0.3048 * 0.4536 * 9.8) foot-pounds / (10 minutes * 60 seconds/minute)
Simplifying the units:
P = (34.64 * 5,280 * 0.3048 * 0.4536 * 9.8) foot-pounds / (600 seconds)
Now, converting from foot-pounds/second to horsepower, we divide by 550:
P = (34.64 * 5,280 * 0.3048 * 0.4536 * 9.8) foot-pounds / (600 seconds * 550)
Finally, calculate the value:
P ≈ 0.838 horsepower
Therefore, the average power of the force is approximately 0.838 horsepower.