When a car drives along a “washboard” road, the regular bumps causes the wheels

Question

When a car drives along a “washboard” road, the regular bumps causes the wheels tooscillate on the springs. (What actually oscillates is each axle assembly, comprising the axle and its two wheels. Find the speed of my car at which this oscillation resonates, given thefollowing information:

(a) When four 80-kg men climb into my car, the body sinks by a couple of centimeters. Use this to estimate the spring constant k of each of the four springs.

(b) If an axle assembly (axle plus two wheels) has total mass 50 kg, what is the natural frequency f of the seembly oscillating on its two springs?

(c) If the bumps on a road are 80 cm apart, at about what speed would these oscillations go into resonance?

Explanation / Answer

a)If the body of the car sinks by 5 cm,
F = 4mg = 4kx

k =mg/x=80 × 9.8/0.05
= 15680(N/m)

For such a result, we can simply estimate the spring constant k by 20000N/m

(b)The natural frequency is
0=(m/2K)=(50/(2x20000))
=0.035(Hz)

(c)When the frequency the car goes over bumps is the same as the natural frequency, the oscillations
would go into resonance
=1/0
v=d/=0.035x0.8=0.028m/s

there may be calculation mistake but concept is right

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

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