If an automobile engine delivers 40.2 hp of power, how much time will it take for the engine to do 5.90 ✕ 105 J of work? (Hint: Note that one horsepower, 1 hp, is equal to 746 watts.)
P = 40.2hp * 746W/hp = 29,989 Watts. =
29,989 Joules/s.
T = 5.9*10*5J/(2.9989*10^4J/s=19.67 s.
To solve this problem, we need to find the time it takes for the engine to do 5.90 x 10^5 J of work using the given power of 40.2 hp.
Step 1: Convert 40.2 horsepower (hp) to watts (W).
Given: 1 hp = 746 W
Calculation: 40.2 hp x 746 W/hp = 29979.2 W
Step 2: Use the formula for power (P) in terms of work (W) and time (t): P = W / t
Given: W = 5.90 x 10^5 J
Calculation: 29979.2 W = 5.90 x 10^5 J / t
Step 3: Rearrange the formula to solve for time (t):
Calculation: t = (5.90 x 10^5 J) / (29979.2 W)
Calculation (simplified): t = 19.68 seconds
Therefore, it will take approximately 19.68 seconds for the engine to do 5.90 x 10^5 J of work.
To solve this problem, we need to use the formula to calculate work done:
Work = Power × Time
Given:
Power = 40.2 hp
Work = 5.90 × 10^5 J
First, let's convert horsepower to watts using the conversion factor provided in the hint:
1 hp = 746 watts
So, the power in watts is:
Power = 40.2 hp × 746 watts/hp
Now, we can calculate the power in watts:
Power = 40.2 × 746 watts
Next, rearrange the formula to solve for time:
Time = Work / Power
Substitute the given values into the equation:
Time = 5.90 × 10^5 J / (40.2 × 746 watts)
Now, we can calculate the time it will take for the engine to do the work:
Time = 5.90 × 10^5 J / (40.2 × 746) seconds
Evaluate the expression:
Time ≈ 0.197 seconds
Therefore, it will take approximately 0.197 seconds for the engine to do 5.90 × 10^5 J of work.