A friend claims that her car can accelerate from a stop to 60 mi/h (26.8 m/s)in

Question

A friend claims that her car can accelerate from a stop to 60 mi/h (26.8 m/s)in 4.7 s , but the speedometer is broken. You decide to test her claim by riding with her, and you bring along a small metal washer, a short length of string, a protractor, and a pen that can write on glass. Sitting in the passenger seat, you tie the washer to one end of the string and then let the string-washer combination hang straight down by rolling up the passenger-door window to pinch the free end of the string. While the car is stationary, you draw a line on the window alongside the vertical string

1. How large is the angle the string makes with the line you drew if the car accelerates at the rate your friend claims?

2. If an identical washer does not slide on the horizontal dashboard while this is happening, what is the ratio of the frictional force to the gravitational force exerted on this washer?

Explanation / Answer

The acceleration of the car,
a = v / t = 26.8 m/s / 4.7 s = 5.7 m/s^2
If the acceleration of the car were equal to the acceleration of gravity, 9.81 m/s^2, the horizontal acceleration would balance the vertical acceleration, due to gravity, and the pendulum would be at 45 degrees (tangent = 1)
Therefore tangent of the angle from vertical
tan = a / g = 5.7 / 9.81 = 0.58
angle = atan(0.53) = 30.11 degrees from vertical

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.