A 900 kg car rolling on a horizontal surface has speed v = 60 km/h when it strikes a horizontal coiled spring and is brought to rest in a distance of 2.2 m. What is the spring stiffness constant of the spring?
I solved this and i had 25826.44629, but i am being told i am wrong. please i need help with this.
1/2 m v^2=1/2 k x^2
k= mv^2/x^2
be certain to change km/hr to m/s
To find the spring stiffness constant (also known as the spring constant or force constant), we can use Hooke's Law which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position.
In this case, the car strikes the spring and is brought to rest, meaning that the spring exerts a force (opposite to the direction of the car's motion) to stop the car. At the point the car comes to rest, the spring is compressed by a certain amount.
We can start by determining the initial kinetic energy of the car before it strikes the spring using the formula:
Kinetic energy = (1/2) * mass * velocity^2
Since the mass is given as 900 kg and the velocity is given as 60 km/h, we need to convert the velocity to m/s:
Velocity = 60 km/h = (60 * 1000 m) / (60 * 60 s) = 16.67 m/s
Now we can calculate the initial kinetic energy:
Kinetic energy = (1/2) * 900 kg * (16.67 m/s)^2 = 125,925 J
Next, we need to determine the work done by the spring in stopping the car. The work done by the spring is equal to the change in potential energy of the spring:
Work = change in potential energy
The potential energy stored in a spring is given by the formula:
Potential energy = (1/2) * k * x^2
Where k is the spring stiffness constant and x is the displacement from the equilibrium position.
Since the car comes to rest, the change in potential energy is equal to the initial kinetic energy:
Work = (1/2) * k * x^2 = 125,925 J
Now we can solve for k. Rearranging the equation, we get:
k = (2 * Work) / x^2
Plug in the values:
k = (2 * 125,925 J) / (2.2 m)^2 = 102,702 N/m
Therefore, the spring stiffness constant of the spring is approximately 102,702 N/m.
It seems that your calculated value of 25,826.44629 N/m is not correct. Please double-check your calculations to ensure you are using the correct formulas and units.