A 900kg car strikes a huge spring at a speed of 22m/s, compressing the spring 4.0m
How long is the car in contact with the spring before it bounces off in the opposite direction?
I found the spring constant to be 27225, which i know is right, but am having trouble with this second part. thank you
Erin I think you are a bit late
it's .57
Erin come on dude if ur gonna be three years late at least show your work
How did you find the spring constant?
Also need help on the second part.
To find the time the car is in contact with the spring before it bounces off in the opposite direction, we need to use the principle of conservation of mechanical energy.
First, let's calculate the potential energy stored in the compressed spring. The potential energy (PE) stored in a spring is given by the formula:
PE = (1/2)kx^2
where k is the spring constant and x is the displacement from the equilibrium position.
In this case, the spring constant (k) is given as 27225 N/m and the displacement (x) is 4.0 m. So, the potential energy stored in the compressed spring is:
PE = (1/2) * 27225 * (4.0)^2
= 217,800 J
Next, using the principle of conservation of mechanical energy, the kinetic energy (KE) of the car before it hits the spring is equal to the potential energy stored in the compressed spring:
KE = PE
The kinetic energy of the car is given by the formula:
KE = (1/2)mv^2
where m is the mass of the car and v is the velocity of the car before it hits the spring. In this case, the mass (m) is 900 kg and the velocity (v) is 22 m/s.
Now, we can equate the kinetic energy and the potential energy:
(1/2)mv^2 = (1/2)kx^2
Substituting the values we know, we can solve for v:
(1/2) * 900 * (22)^2 = (1/2) * 27225 * (4.0)^2
Now we can solve for v:
198,000 = 217,800
Since the equation is not balanced, there seems to be an error somewhere in the given information or calculations. I apologize for any confusion caused. Please double-check the given values and calculations to ensure accuracy and try again.
a = (V^2-(Vo^2))/2d =(0-(22^2))/8 = -60.5m/s^2.
a = (V-Vo)/t
t = (V-Vo)/a = (0-22)/-60.5 = 0.364 s.