Question
An automobile delivers 30.0 hp to its wheels when moving at a constant speed of \( 22.0 \mathrm{~m} / \mathrm{s} \). What is the resistance force on the automobile at this speed? ( \( \mathrm{hp}=746 \) watts) 1) 18600 N 2) 410000 N 3) 1020 N 4) 848 N 5) 763 N
Ask by Ray Barber. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The resistance force on the automobile is approximately 1020 N.
Solution
We start with the relationship between power (P), force (F), and velocity (v):
P = F × v
Given the problem:
Power delivered = 30.0 hp
Conversion: 1 hp = 746 watts, so
P = 30.0 × 746 W = 22,380 W
The car is moving at a constant speed of 22.0 m/s. Solving for F:
F = P / v = 22,380 W / 22.0 m/s ≈ 1017.3 N
Rounded to three significant figures, the resistance force is about 1020 N.
Thus, the correct answer is option 3) 1020 N.
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Simplify this solution Extra Insights
To find the resistance force on the automobile, we need to convert horsepower to watts and then calculate the force using the relationship between power, force, and velocity. First, convert 30.0 hp to watts: \[ 30.0 \, \text{hp} = 30.0 \times 746 \, \text{W} = 22380 \, \text{W} \] Next, use the formula for power: \[ P = F \cdot v \] where \( P \) is the power (in watts), \( F \) is the force (in newtons), and \( v \) is the velocity (in m/s). Rearranging the formula gives us: \[ F = \frac{P}{v} \] Substituting in the values: \[ F = \frac{22380 \, \text{W}}{22.0 \, \text{m/s}} \approx 1017.27 \, \text{N} \] Rounding it, the closest answer is: \( 3) \, 1020 \, \text{N}. \)
