Answer:
0.505 m
Explanation:
From the question,
The kinetic energy of the car = energy stored in the spring
1/2mv² = 1/2ke²...................... Equation 1
Where m = mass of the car, v = velocity of the car, k = spring constant of the car, e = extension/compression
make e the subject of the equation
e = v√(m/k)............... Equation 2
We can calculate the value of v, by applying,
v² = u²+2gH...................... Equation 3
Where u = initial velocity of the car, H = height of the car, g = acceleration due to gravity.
Given: u = 0 m/s (from rest), H, 10 m, g = 9.8 m/s²
Substitute into equation 2
v² = 2(10×9.8)
v² = 196
v = √196
v = 14 m/s
Also given: m = 1300 kg, e = 1.0×10⁶ N/m =1000000 N/m
Substitute into equation 2
e = 14√(1300/1000000)
e = 14√(0.00013)
e = 14(0.036)
e = 0.505 m
Hence the maximum distance of the spring is compressed = 0.505 m
