Calcu[ate the weight of a body in lb if it has a kinetic energy of 38.6 ft-Ib when moving at 19.5 mi/h
19.5 miles/h = 28.6 ft/s
(1/2) M V^2 = (M/2*818) ft^2/s^2 = 38.6 ft-lb
M = 0.0944 slugs = 3.04 lb mass
To calculate the weight of a body in pounds (lb) using kinetic energy and velocity, we need to use the formula:
Kinetic energy (KE) = 1/2 * mass * velocity^2
First, we need to convert the given values to the appropriate units:
Convert kinetic energy from ft-Ib to lb-ft:
1 lb-ft = 1.3558 ft-Ib
38.6 ft-Ib = 38.6 / 1.3558 = 28.485 lb-ft (rounded to three decimal places)
Convert velocity from miles per hour (mi/h) to feet per second (ft/s):
1 mi/h = 1.4667 ft/s
19.5 mi/h = 19.5 * 1.4667 = 28.6165 ft/s (rounded to four decimal places)
Let's substitute the known values into the formula and solve for mass:
28.485 lb-ft = 1/2 * mass * (28.6165 ft/s)^2
Multiply both sides by 2:
56.97 lb-ft = mass * (28.6165 ft/s)^2
Divide both sides by (28.6165 ft/s)^2:
56.97 lb-ft / (28.6165 ft/s)^2 = mass
Calculate the mass:
mass = 56.97 lb-ft / (28.6165 ft/s)^2 = 56.97 lb-ft / 820.9847 ft^2/s^2 = 0.0694 lb-s^2/ft
(rounded to four decimal places)
Finally, we need to convert the mass from lb-s^2/ft to pounds (lb):
1 lb = 1 lb-s^2/ft
0.0694 lb-s^2/ft = 0.0694 lb (rounded to four decimal places)
Therefore, the weight of the body is approximately 0.0694 pounds.
To calculate the weight of a body in pounds (lb) based on its kinetic energy and speed, we need to use the formula for kinetic energy and convert the units appropriately. Here are the steps to get the answer:
1. Convert the given kinetic energy from foot-pounds (ft-lb) to pound-feet (lb-ft) since the formula for kinetic energy uses pound-feet:
- 1 lb-ft = 1.35582 ft-lb
- So, 38.6 ft-lb = 38.6 / 1.35582 lb-ft ≈ 28.49 lb-ft (rounded to two decimal places)
2. Convert the given speed from miles per hour (mi/h) to feet per second (ft/s) since the formula for kinetic energy uses feet per second:
- 1 mi = 5280 ft
- 1 h = 3600 s
- So, 19.5 mi/h = (19.5 * 5280) ft / 3600 s ≈ 28.6 ft/s (rounded to one decimal place)
3. Now, we can use the formula for kinetic energy to calculate the weight (W):
- Kinetic energy = (1/2) * W * velocity^2
- Rearranging the formula gives us: W = (2 * kinetic energy) / velocity^2
Substituting the given values:
- W = (2 * 28.49 lb-ft) / (28.6 ft/s)^2
4. Calculate the weight:
- W = 1.993 lb (rounded to three decimal places)
Therefore, the weight of the body is approximately 1.993 lb when it has a kinetic energy of 38.6 ft-lb while moving at 19.5 mi/h.