If an automobile engine delivers 45.2 hp of power, how much time will it take for the engine to do 5.40 105 J of work? (Hint: Note that one horsepower, 1 hp, is equal to 746 watts.) in seconds
P = 45.2hp * 746W/hp = 33,719. Watts =
33,719 Joules/s.
t=(5.4*10^5J/3.3719*10^4J) * 1s.=16.0s.
To solve this problem, we can use the formula:
work = power × time
We are given that the power is 45.2 hp and the work is 5.40 × 10^5 J. We need to find the time.
First, let's convert the power from horsepower to watts using the conversion factor given in the hint.
1 hp = 746 watts
So, 45.2 hp = 45.2 × 746 watts.
Substituting the values into the formula:
5.40 × 10^5 J = (45.2 × 746 watts) × time
Now, let's solve for time.
time = (5.40 × 10^5 J) / (45.2 × 746 watts)
time = (5.40 × 10^5 J) / (33839.2 watts)
time ≈ 15.95 seconds
Therefore, it will take approximately 15.95 seconds for the engine to do 5.40 × 10^5 J of work.
To find the time it will take for the engine to do 5.40 x 10^5 J of work, we can use the formula:
Work = Power x Time
Given:
Power of the engine = 45.2 hp
Work to be done = 5.40 x 10^5 J
First, let's convert the power from horsepower to watts using the conversion factor given in the hint.
1 hp = 746 watts
Power in watts = 45.2 hp x 746 watts/hp (using the conversion factor)
Power in watts = 33699.2 watts
Now, we can rearrange the formula to solve for time:
Time = Work / Power
Substituting the given values:
Time = (5.40 x 10^5 J) / (33699.2 watts)
Calculating this, we find:
Time = 16.04 seconds (rounded to two decimal places)
Therefore, it will take approximately 16.04 seconds for the engine to do 5.40 x 10^5 J of work.