What is the frequency of the car's vibration

[saltyload]

Having trouble figuring out these 4 problems. I could use a walk through or an answer. thanks guys.

Homework Statement

1a)When four people with a combined mass of 270 kg sit down in a car, they find that the car drops 1.00 cm lower on its springs. Then they get out of the car and bounce it up and down. What is the frequency of the car's vibration if its mass (when it is empty) is 2.0 103 kg?b)An astronaut on a small planet wishes to measure the local value of g by timing pulses traveling down a wire which has a large object suspended from it. Assume a wire of mass 4.00 g is 1.60 m long and has a 3.00 kg object suspended from it. A pulse requires 38.3 ms to traverse the length of the wire. Calculate gplanet from these data. (You may neglect the mass of the wire when calculating the tension in it.)c)A string is 41.0 cm long and has a mass of 3.00 g. A wave travels at 4.55 m/s along this string. A second string has the same length but one-fourth the mass of the first. If the two strings are under the same tension, what is the speed of a wave along the second string?d)An aluminum clock pendulum having a period of 1.80 s keeps perfect time at 20.0?C. When placed in a room at a temperature of -5?C, it will gain time. How much time will it gain or lose every hour?

The Attempt at a Solution

3) For question d, I used the equation for thermal expansion and got the new length. Then I set up a proportion for 1.8/3600 = 1.794/x. It was wrong :(

 

[Hootenanny]

Having trouble figuring out these 4 problems. I could use a walk through or an answer. thanks guys.

We're more than happy to help you with your problems, but you're going to have to do some work yourself and we certainly won't give you any answers.

1a)When four people with a combined mass of 270 kg sit down in a car, they find that the car drops 1.00 cm lower on its springs. Then they get out of the car and bounce it up and down. What is the frequency of the car's vibration if its mass (when it is empty) is 2.0 103 kg?

Let's start with the first question, which concepts do you think would apply here? Try reading your class notes on SHM and see if it helps.

 

[Moetasim]

For question a, the frequency of the car's vibration can be calculated using the formula f = 1/2π√(k/m), where k is the spring constant and m is the mass of the car. First, we need to find the spring constant by using the given information that the car drops 1.00 cm lower on its springs when four people with a combined mass of 270 kg sit in it. This means that the weight of the four people (270 kg x 9.8 m/s^2 = 2646 N) is balanced by the force exerted by the springs (kx = 2646 N, where x is the displacement of 1.00 cm or 0.01 m). Thus, k = 2646 N/0.01 m = 264600 N/m. Now we can plug in the values into the formula to get the frequency: f = 1/2π√(264600 N/m / 2000 kg) = 0.018 Hz.

For question b, we can use the formula for wave speed v = √(T/μ), where T is the tension in the wire and μ is the mass per unit length. We can find the tension by balancing the weight of the object (3.00 kg x 9.8 m/s^2 = 29.4 N) with the tension in the wire (T = 29.4 N). We can also find the mass per unit length by dividing the mass of the wire (0.004 kg) by its length (1.60 m), giving us μ = 0.0025 kg/m. Plugging these values into the formula, we get v = √(29.4 N / 0.0025 kg/m) = 20.4 m/s. Now we can use the formula for wave speed again to find the local value of g: gplanet = v^2 / L = (20.4 m/s)^2 / 1.60 m = 259.2 m/s^2.

For question c, we can use the formula for wave speed again, but with the new mass per unit length for the second string. Since the second string has one-fourth the mass of the first string, its μ will be 1/4 of the first string's μ. Plugging this into the formula, we get v =