A 3200 lb car traveling at 30 mi/hr speeds up to 60 mi/hr. How much useful work was supplied by the engine?
what is the change in Ke of the car? 1/2 m (vf^2-vi^2) v in m/s, mass in kg
To calculate the amount of useful work supplied by the engine, we need to first calculate the change in kinetic energy of the car.
Given data:
Mass of the car (m) = 3200 lb
Initial velocity (v1) = 30 mi/hr
Final velocity (v2) = 60 mi/hr
We need to convert the mass from pounds to the standard unit of kilograms. 1 lb is approximately equal to 0.4536 kg.
Mass of the car (m) = 3200 lb × 0.4536 kg/lb
Now, we convert the velocities from miles per hour to meters per second. 1 mi/hr is approximately equal to 0.44704 m/s.
Initial velocity (v1) = 30 mi/hr × 0.44704 m/s
Final velocity (v2) = 60 mi/hr × 0.44704 m/s
Next, we can calculate the change in kinetic energy:
Change in kinetic energy (ΔKE) = 0.5 × m × (v2^2 - v1^2)
Now, let's substitute the known values into the equation:
ΔKE = 0.5 × (3200 × 0.4536) kg × ((60 × 0.44704 m/s)^2 - (30 × 0.44704 m/s)^2)
Simplifying the equation, we get:
ΔKE ≈ 0.5 × (1451.52) kg × ((26.82 m/s)^2 - (13.41 m/s)^2)
Calculating the values inside the parentheses first:
ΔKE ≈ 0.5 × (1451.52) kg × (720.1924 m^2/s^2 - 179.6881 m^2/s^2)
Next, simplify the equation further:
ΔKE ≈ 0.5 × (1451.52) kg × (540.5043 m^2/s^2)
Finally, calculate the product:
ΔKE ≈ 393,670.86 kg m^2/s^2
Since joule (J) is the unit for work, we can convert the unit by multiplying by the conversion factor:
ΔKE ≈ 393,670.86 kg m^2/s^2 × (1 J / 1 kg m^2/s^2)
Therefore, the amount of useful work supplied by the engine is approximately 393,670.86 J.
To determine the amount of useful work supplied by the engine, we need to consider the change in kinetic energy of the car.
The formula for kinetic energy is given by:
KE = 1/2 * m * v^2
Where
KE is the kinetic energy,
m is the mass of the car, and
v is the velocity of the car.
First, let's convert the car's mass from pounds to kilograms. We know that 1 pound is approximately equal to 0.4536 kilograms. Therefore, the mass of the car is:
m = 3200 lb * 0.4536 kg/lb = 1451.52 kg
Next, we calculate the initial and final kinetic energies of the car.
Initial kinetic energy (KE1) at 30 mi/hr:
KE1 = 1/2 * m * v1^2 = 1/2 * 1451.52 kg * (30 mi/hr)^2
Final kinetic energy (KE2) at 60 mi/hr:
KE2 = 1/2 * m * v2^2 = 1/2 * 1451.52 kg * (60 mi/hr)^2
The change in kinetic energy (ΔKE) is the difference between KE2 and KE1:
ΔKE = KE2 - KE1
Finally, the useful work supplied by the engine is equal to the change in kinetic energy:
Useful work = ΔKE
You can plug in the values to calculate the specific amounts for KE1, KE2, ΔKE, and the useful work.