A 600 kg dragster accelerates from rest to a final speed of 120 m/s in 400 m (about a quarter of a mile) and encounters an average frictional force of 1200 N. What is its average power output in watts and horsepower if this takes 7.30 s?
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To find the average power output of the dragster, we can use the formula:
Power = Work / Time
1. Calculate the work done:
The work done can be calculated as the product of force and displacement:
Work = Force * Displacement
Given:
Force (frictional force) = 1200 N
Displacement = 400 m
Work = 1200 N * 400 m
Work = 480000 J
2. Calculate the time taken:
Given: Time = 7.30 s
3. Calculate the power in watts:
Power = Work / Time
Power = 480000 J / 7.30 s
Power ≈ 65753.4 W
Therefore, the average power output of the dragster is approximately 65753.4 Watts.
4. Calculate the power in horsepower:
To convert watts to horsepower, we use the conversion factor 1 horsepower = 746 Watts.
Power (in horsepower) = Power (in watts) / 746
Power (in horsepower) = 65753.4 W / 746
Power (in horsepower) ≈ 88.08 hp
Therefore, the average power output of the dragster is approximately 88.08 horsepower.
To find the average power output of the dragster, we can use the equation:
Power = Work / time
First, let's find the work done. The work done on an object can be calculated using the formula:
Work = force × distance × cos(theta)
In this case, the force is the frictional force of 1200 N and the distance is 400 m. Since the dragster is moving in the same direction as the force, theta is 0 degrees and cos(0) is equal to 1.
So, the work done on the dragster is:
Work = 1200 N × 400 m × cos(0) = 480,000 J
Next, we'll calculate the time taken to accelerate from rest to a final speed of 120 m/s. It is given as 7.30 s.
Now, let's calculate the average power output using the equation provided earlier:
Power = Work / time = 480,000 J / 7.30 s ≈ 65,753.42 W
So, the average power output of the dragster is approximately 65,753.42 Watts.
To convert this to horsepower, we can use the conversion factor:
1 horsepower (HP) = 745.7 watts
Therefore, the average power output of the dragster is approximately:
65,753.42 W / 745.7 ≈ 88.20 HP
ma=mv²/2s =600•120²/2•400 =10800
P=W/t=[F+F(fr)]s/t = {10800+1200}•400/7.3 = 6.58•10⁵W =894 hp