Two geekie physics students with a combined mass of 131 kg jump into their old car to run out for some late night pizza. The distance between the front and back axles of the car is 2.9 m. When they get in the car, the springs compress a total of 9.3 cm. On their way to the Pizza Hut, when they go over a bump, the car oscillates up and down with a period of 1.6 seconds.

(a) What is mass of the car?

completely lost for this one

To determine the mass of the car, we need to use the given information about its oscillation and the compression of the springs.

First, let's use the period of oscillation to calculate the angular frequency (ω):
T = 2π/ω

Given that the period (T) is 1.6 seconds:
1.6 = 2π/ω

Now, solve for ω:
ω = 2π / 1.6

ω ≈ 3.93 rad/s

Next, we can use Hooke's Law to relate the compression of the springs to the restoring force. Hooke's Law states that the restoring force (F) is directly proportional to the displacement (x) from the equilibrium position:

F = -kx

Where:
F is the force
k is the spring constant
x is the displacement

Given that the springs compress a total of 9.3 cm (or 0.093 m), and the force is caused by the mass of the car (m) times the acceleration due to gravity (g), we can rewrite Hooke's Law as:

mg = kx

Now, let's calculate the spring constant (k):

k = (mg) / x

The distance between the front and back axles of the car, which is 2.9 m, can be approximated as the amplitude (A) of the oscillation:

A = x

Now, we'll use the relation between the angular frequency (ω) and the spring constant (k):

k = mω^2

Now substitute the value of k:

mg = mω^2

We can now solve for the mass of the car (m):

m = g / ω^2

Substituting the values for g (approximately 9.8 m/s^2) and ω (approximately 3.93 rad/s):

m ≈ 9.8 / (3.93^2)

m ≈ 0.65 kg

Therefore, the mass of the car is approximately 0.65 kg.

To determine the mass of the car, we need to consider the physics principles involved in the given situation. Let's break down the problem into smaller steps:

Step 1: Understanding the physics principles involved
In this problem, we are dealing with oscillations, specifically related to the springs and their compression. The period of oscillation (T) can be related to the mass (m) and the spring constant (k) through the equation:
T = 2π√(m/k)

Step 2: Determining the spring constant (k)
To find the spring constant, we need to use the information provided about the compression of the springs. When the students get in the car, the springs compress a total of 9.3 cm, which can be converted to meters as 0.093 m. We can use Hooke's law to find the spring constant:
F = kx
where F is the force applied by the springs, k is the spring constant, and x is the displacement. In this case, F is the weight of the students, which is equal to their combined mass multiplied by the acceleration due to gravity (9.8 m/s^2).
F = mg
where g is the acceleration due to gravity. Rearranging the equation, we can find k:
k = F/x = mg/x

Step 3: Substituting values and finding the mass of the car
Now that we have the spring constant (k), we can substitute it into the equation for the period of oscillation and solve for the mass of the car (m). The equation becomes:
T = 2π√(m/k)
Rearranging the equation to solve for m:
m = (T^2 * k) / (4π^2)

By substituting the given period (T = 1.6 s) and the previously calculated spring constant (k), we can find the mass of the car.

Note: Ensure that all units are consistent throughout the calculations to obtain accurate results.

Once you have performed these calculations, the result will provide you with the mass of the car.