4.28) A. Calculate the horsepower needed for a 1200 kg car to climb to an altitude of 1000 m from sea level in 1 hr.
B. If the useful output of the engine is actually 40 hp, where does the rest of the power go?
C. If the car engine is 20% efficient, calculate the total power consumption of the car in horsepower.
Note: Guys help me..... Provide me an answer with solution/formula. Thanks!
A. To calculate the horsepower needed for the car to climb to an altitude of 1000 m from sea level in 1 hr, we can use the following formula:
Power (in watts) = work (in joules) / time (in seconds)
First, we need to calculate the work done in joules. The work done when lifting an object against gravity is given by the equation:
Work (in joules) = mass (in kg) * gravity (in m/s^2) * height (in meters)
In this case, the mass is 1200 kg, gravity is 9.8 m/s^2, and the height is 1000 m. Plugging these values into the formula, we get:
Work = 1200 kg * 9.8 m/s^2 * 1000 m = 11,760,000 joules
Next, we need to convert the time from hours to seconds. Since there are 3600 seconds in an hour, we have:
Time = 1 hr * 3600 s/hr = 3600 seconds
Now we can calculate the power in watts:
Power = 11,760,000 joules / 3600 seconds = 3266.67 watts
To convert watts to horsepower, we can use the conversion factor:
1 horsepower (hp) = 745.7 watts
So, the horsepower needed for the car to climb to an altitude of 1000 m from sea level in 1 hr is:
Power (in horsepower) = 3266.67 watts / 745.7 = 4.38 hp (rounded to two decimal places)
B. If the useful output of the engine is actually 40 hp, the rest of the power goes into various losses and inefficiencies in the engine and drivetrain. This can include losses due to friction, air resistance, and other mechanical losses. These losses can be caused by factors such as the internal friction of engine components, energy lost as heat, and energy required to overcome drag forces.
C. If the car engine is 20% efficient, we can calculate the total power consumption of the car in horsepower by dividing the useful power output by the efficiency.
Total power consumption (in horsepower) = useful power output (in horsepower) / efficiency
In this case, the useful power output is 40 hp and the efficiency is 20%. Converting the efficiency to a decimal, we get 0.20. Plugging these values into the formula, we have:
Total power consumption = 40 hp / 0.20 = 200 hp
Therefore, the total power consumption of the car is 200 horsepower.
A. To calculate the horsepower needed for the car to climb to an altitude of 1000 m in 1 hour, we can use the following formula:
Power = Work / Time
First, let's calculate the work done by the car:
Work = Force × Distance
The force required to lift the car against gravity can be calculated using:
Force = mass × gravitational acceleration
Where the mass of the car is 1200 kg and the gravitational acceleration is approximately 9.8 m/s².
Force = 1200 kg × 9.8 m/s² = 11,760 N
Next, we need to calculate the distance traveled by the car. Since it climbs to an altitude of 1000 m, the total distance traveled is 1000 m.
Now we can calculate the work:
Work = Force × Distance = 11,760 N × 1000 m = 11,760,000 N·m
Finally, we can calculate the horsepower needed:
Power = Work / Time = 11,760,000 N·m / 3600 s = 3266.67 W
Since 1 horsepower (hp) is approximately 735.5 W, we can convert the power to horsepower:
Horsepower = Power / 735.5 = 3266.67 W / 735.5 = 4.44 hp
Therefore, the horsepower needed for the car to climb to an altitude of 1000 m in 1 hour is approximately 4.44 hp.
B. If the useful output of the engine is actually 40 hp, the rest of the power goes to various forms of energy loss, such as friction, heat, and other inefficiencies within the engine and drivetrain.
C. If the car engine is 20% efficient, we can calculate the total power consumption of the car in horsepower. The efficiency of an engine is given by:
Efficiency = Useful Output Power / Total Input Power
Let's assume the total input power is P. We can rearrange the formula to solve for P:
P = Useful Output Power / Efficiency
Given that the useful output power is 40 hp and the efficiency is 20% (or 0.2), we can calculate the total power consumption:
P = 40 hp / 0.2 = 200 hp
Therefore, the total power consumption of the car is 200 horsepower.