Final answer:
The spring stiffness constant of the spring is 14400 N/m. The car is in contact with the spring for approximately 4.04 seconds before bouncing off in the opposite direction.
Step-by-step explanation:
To find the spring stiffness constant of the spring, we can use Hooke's Law, which states that the force exerted by a spring is proportional to the displacement from its equilibrium position. The formula for Hooke's Law is F = -kx, where F is the force, k is the spring constant, and x is the displacement.
Using the given information, we know that the car has a mass of 900 kg and a speed of 24 m/s before striking the spring. The spring compresses by 6.0 m under this force.
So, we can calculate the spring constant as follows:
- F = m * v2 / (2 * x) = 900 kg * (24 m/s)2 / (2 * 6.0 m) = 86400 N
- k = F / x = 86400 N / 6.0 m = 14400 N/m
Therefore, the spring stiffness constant of the spring is 14400 N/m.
To find how long the car is in contact with the spring before bouncing off, we can use the principle of conservation of energy. The kinetic energy of the car before hitting the spring will be equal to the potential energy of the compressed spring at maximum compression.
The formula for the potential energy of a compressed spring is PE = (1/2) * k * x^2, where PE is the potential energy, k is the spring constant, and x is the displacement of the spring.
Setting the initial kinetic energy of the car equal to the potential energy of the compressed spring, we have:
- (1/2) * m * v^2 = (1/2) * k * x^2
- (1/2) * 900 kg * (24 m/s)^2 = (1/2) * 14400 N/m * (6.0 m)^2
- 259200 J = 129600 J
Since the energies are equal, we can conclude that the car is in contact with the spring for the time it takes to compress and decompress the spring, which is known as the period T.
Therefore, the time the car is in contact with the spring before bouncing off in the opposite direction can be calculated using the formula T = 2 * pi * sqrt(m / k), where T is the period, m is the mass of the car, and k is the spring constant.
Plugging in the values, we have:
- T = 2 * 3.14 * sqrt(900 kg / 14400 N/m) = 4.04 s
So, the car is in contact with the spring for approximately 4.04 seconds before bouncing off in the opposite direction.