In Haiti, public transportation is often by taptaps, small pickup trucks with se

Question

In Haiti, public transportation is often by taptaps, small pickup trucks with seats along the sides of the pickup bed and railings to which passengers can hang on. Typically they carry two dozen or more passengers plus an assortment of chickens, goats, luggage, etc. Putting this much into the back of a pickup truck puts quite a large load on the truck springs.

A truck has springs for each wheel, but for simplicity assume that the individual springs can be treated as one spring with a spring constant that includes the effect of all the springs. Also for simplicity, assume that all four springs compress equally when weight is added to the truck and that the equilibrium length of the springs is the length they have when they support the load of an empty truck.

Part A

A 69 kg driver gets into an empty taptap to start the day's work. The springs compress 1.5×102 m . What is the effective spring constant of the spring system in the taptap?

Enter the spring constant numerically in newtons per meter using two significant figures.

k= 4.5x10^4 N/m *ALREADY SOLVED PART (A)*

Part B

After driving a portion of the route, the taptap is fully loaded with a total of 27 people including the driver, with an average mass of 69 kg per person. In addition, there are three 15-kg goats, five 3-kg chickens, and a total of 25 kg of bananas on their way to the market. Assume that the springs have somehow not yet compressed to their maximum amount. How much are the springs compressed?

Enter the compression numerically in meters using two significant figures.

x= _________ m

I just need Part B

Explanation / Answer

As we know that the all spring are in the parallel connection therefore we have to calcualte effective or net equivalent spring constant
K = K1 +K2 +K3+K4
K1=K2= K3 = K4 = k
K = 4k = 4*4.5*104 = 18*104 N/m
(b) Now when forces =
27 person of average mass 69 kg then total mass = 69*27 = 1863 kg
Goat mass = 15 kg
5 chickens of mass 3 kg = 5*3 = 15 kg
Bananas of = 25 kg
total mass = 1863 +15+15 +25 = 1918 kg
Hence the force = 1918*9.81 = 18815.58 N
Now we know that
Force = spring constant*sprig compression
F = KX
X = F/K = 18815.58/(18*104) = 0.1045 m

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