Answer:
a
[tex]k = 457333.3 N/m[/tex]
b
[tex]x_a =0.09\ m[/tex]
Explanation:
From the question we are told that
The total mass of three people is [tex]M = 2.00*10^{2} \ kg[/tex]
The mass of the car is [tex]m_c = 1.200 *10^{3} \ kg[/tex]
The compression of the car spring is [tex]x = 3 \ cm = 0.03 \ m[/tex]
Generally the spring constant is mathematically represented as
[tex]k = \frac{F}{x}[/tex]
Here F is the force exerted by the mass of three people and that of the car , this is mathematically represented as
=> [tex]F = (M +m_c) *g[/tex]
=> [tex]F = ([2.0*10^{2} ]+[ 1.200*10^{3}]) * 9.8[/tex]
=> [tex]F = 13720 \ N[/tex]
So
[tex]k = \frac{13720}{0.03}[/tex]
=> [tex]k = 457333.3 N/m[/tex]
Generally if the mass which the car is loaded with is [tex]m = 3.00*10^{2} \ kg[/tex]
Then the force experienced by the spring is
=> [tex]F_a = (m +m_c) *g[/tex]
=> [tex]F_a = (3.00*10^{3} + 1.200 *10^{3}) * 9.8[/tex]
=> [tex]F_a = 41160 \ N[/tex]
Generally from the above formula the compression is
[tex]x_a = \frac{F_a}{k}[/tex]
=> [tex]x_a = \frac{41160}{457333.3}[/tex]
=> [tex]x_a =0.09\ m[/tex]
