Answer:
a) 40,000 N/m
b) f = 6.37 Hz
c) v = 4,8 m/s
Explanation:
part a)
First in order to estimate the spring constant k, we need to know the expression or formula to use in this case:
k = ΔF / Δx
Where:
ΔF: force that the men puts in the car, in this case, the weight.
Δx: the sinking of the car, which is 2 cm or 0.02 m.
With this data, and knowing that there are four mens, replace the data in the above formula:
W = 80 * 10 = 800 N
This is the weight for 1 man, so the 4 men together would be:
W = 800 * 4 = 3200 N
So, replacing this data in the formula:
k = 3200 / 0.02 = 160,000 N/m
This means that one spring will be:
k' = 160,000 / 4 = 40,000 N/m
b) An axle and two wheels has a mass of 50 kg, so we can assume they have a parallel connection to the car. If this is true, then:
k^n = 2k
To get the frequency, we need to know the angular speed of the car with the following expression:
wo = √k^n / M
M: mass of the wheel and axle, which is 50 kg
k = 40,000 N/m
Replacing the data:
wo = √2 * 40,000 / 50 = 40 rad/s
And the frequency:
f = wo/2π
f = 40 / 2π = 6.37 Hz
c) finally for the speed, we have the time and the distance, so:
V = x * t
The only way to hit bumps at this frequency, is covering the gaps of bumping, about 6 times per second so:
x: distance of 80 cm or 0.8 m
V = 0.8 * 6 =
V = 4.8 m/s
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