When a 3600 lb automobile runs out of gas, it is pushed by its unhappy driver and a friend a quarter of a mile (0.250 mi). To keep the car rolling, they must exert a constant force of 175 lb. (a.) How much work do they do? (b.) If it takes them 15 minutes, how much power do they develop? (c.)Expressed in horsepower, how much power do they develop?
work=force*distance
if you are allowed to use ft-lbs, you can do it directly with the given units.
b. work/time=power.
change 15 min to seconds, and note
1 HP, = 550 ft.lb./sec.
259.11
To solve these questions, we will use the following formulas:
(a) Work = Force × Distance
(b) Power = Work / Time
(c) 1 horsepower (hp) = 550 foot-pounds per second
Given:
Mass of the automobile (m) = 3600 lb
Distance (d) = 0.250 mi = 0.250 mi × 5280 ft/mi = 1320 ft
Force (F) = 175 lb
Time (t) = 15 minutes = 15 minutes × 60 sec/min = 900 seconds
(a) To find the work done:
Work = Force × Distance
Work = 175 lb × 1320 ft
Work = 231,000 ft-lb
Therefore, the work they do is 231,000 foot-pounds.
(b) To find the power developed:
Power = Work / Time
Power = 231,000 ft-lb / 900 sec
Power = 257.33 ft-lb/sec
Therefore, the power they develop is 257.33 foot-pounds per second.
(c) To express power in horsepower:
Power (in horsepower) = Power (in foot-pounds per second) / 550
Power (in horsepower) = 257.33 ft-lb/sec / 550
Power (in horsepower) ≈ 0.468 hp
Therefore, they develop approximately 0.468 horsepower.
To answer these questions, we can use the formulas for work, power, and horsepower.
(a) The work done is equal to the force applied multiplied by the distance over which the force is exerted. In this case, the force is 175 lb and the distance is 0.250 miles. The work is calculated as:
Work = Force * Distance
Work = 175 lb * 0.250 mi
Work = 43.75 lb·mi
Therefore, the amount of work done is 43.75 pound-miles.
(b) Power is defined as the rate at which work is done, or the work done divided by the time taken. In this case, the work done is 43.75 lb·mi and the time taken is 15 minutes. However, it is important to convert minutes to hours to maintain consistent units. There are 60 minutes in an hour, so we divide 15 minutes by 60 to get the time in hours:
Time (in hours) = 15 min / 60 min/hour
Time (in hours) = 0.25 hours
Now we can calculate the power:
Power = Work / Time
Power = 43.75 lb·mi / 0.25 hours
Power = 175 lb·mi/hour
Therefore, the power developed is 175 pound-miles per hour (lb·mi/h).
(c) To express the power in horsepower, we need to convert pound-miles per hour to horsepower. One horsepower is equivalent to 550 foot-pounds per second. To convert pound-miles per hour to foot-pounds per second, we can use the following conversion factors:
1 mile = 5280 feet
1 hour = 3600 seconds
First, we convert the distance from miles to feet:
Distance (in feet) = 0.250 mi * 5280 ft/mi
Distance (in feet) = 1320 ft
Then, we convert the time from hours to seconds:
Time (in seconds) = 0.25 hours * 3600 s/hour
Time (in seconds) = 900 s
Now we can convert the power:
Power (in foot-pounds per second) = Power (in lb·mi/h) * 5280 ft/mi * 3600 s/hour
Power (in foot-pounds per second) = 175 lb·mi/h * 5280 ft/mi * 3600 s/hour
Power (in foot-pounds per second) = 1,662,000 ft·lb/s
Finally, we divide the power in foot-pounds per second by 550 to convert to horsepower:
Power (in horsepower) = Power (in foot-pounds per second) / 550
Power (in horsepower) = 1,662,000 ft·lb/s / 550
Power (in horsepower) = 3,021.82 hp
Therefore, the power developed is approximately 3,021.82 horsepower.