A compact car has a mass of 1400kg. Assume that the car has one spring on each wheel, that the springs are identical, and that the mass is equally distributed over the four springs.
What is the spring constant of each spring if the empty car bounces up and down 1.9 times each second?
What will be the car's oscillation frequency while carrying four 68kg passengers?
Physics is soo not my subject, I've tried this problem three times and cant get it. Help?
need this soon!
http://www.jiskha.com/display.cgi?id=1312075943
See answer to falcon306 question posted later today.
http://www.jiskha.com/display.cgi?id=1312075943#1312075943.1312083926
My links to previous posts don't seem to be working
To find the spring constant, we can use Hooke's law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.
The formula for the frequency of a mass-spring system is given by:
f = 1 / (2π) * sqrt(k / m)
Where:
- f is the frequency in Hz
- k is the spring constant in N/m
- m is the mass in kg
Let's solve the first problem:
1. The car bounces up and down 1.9 times each second, which represents the frequency (f) of oscillation.
2. Rearranging the formula, we have: (2πf)^2 = k / m
3. Assuming that the car has a mass of 1400 kg equally distributed over the four springs, each spring will bear a quarter of the total mass. So the mass (m) for each spring will be 1400 kg / 4 = 350 kg.
4. Substitute the known values into the formula:
(2π * 1.9)^2 = k / 350
5. Rearrange the formula to solve for k:
k = (2π * 1.9)^2 * 350
Calculating this, we get the spring constant (k) for each spring.
Now let's move on to the second problem:
1. The car is carrying four 68 kg passengers. So the total mass (m) will be the mass of the empty car (1400 kg) plus the mass of the passengers (4 * 68 kg).
2. Calculate the total mass (m).
3. Substitute the new total mass into the frequency formula, and solve for f using the same spring constant (k) calculated above.
By following these steps, you should be able to find the spring constant and the oscillation frequency for the given scenarios. If you encounter any issues during the calculation, feel free to ask for further assistance.