1. You are tasked to design a car park on the top floor of a condominium that can accommodate 10 cars, each car has a maximum mass of 2000 kg. The material you are using can withstand a pressure of 500 N/m^2. Calculate how large your park must be?
2. Cheryl filled a measuring cylinder with 30 cm^3 of H2O. When she dropped a piece of metal pipe of mass 50 g in to the water, it sank to the bottom and the water level rose to 95cm^3 graduation
a. What is the density of the metal pipe?
b. The metal pipe was removed from the liquid and cut carefully into two pieces of equal size. What is density of one such place?
c. Explain why it would not be possible for her to use the above method to determining the density of a piece of wood which floats in the liquid.
1. To calculate how large the car park must be, we need to determine the total weight or force exerted by the cars on the park.
Since each car has a maximum mass of 2000 kg, we can assume that the weight of each car is equal to its mass multiplied by the acceleration due to gravity (9.8 m/s^2). Therefore, the weight of each car is 2000 kg * 9.8 m/s^2 = 19600 N.
To accommodate 10 cars, we need to calculate the total weight that the car park must withstand. 10 cars * 19600 N = 196000 N.
The pressure exerted on the car park can be calculated by dividing the force exerted (196000 N) by the area the force is applied on. In this case, the area is the size of the car park.
Assuming a square car park, let's denote the side length of the square as "x." The area of the square is then x^2.
Now, we can calculate the pressure: pressure = force/area. In this case, the force is 196000 N, and the area is x^2. So, pressure = 196000 N/x^2.
Given that the material can withstand a pressure of 500 N/m^2, we can set up an equation:
196000 N/x^2 = 500 N/m^2.
Simplifying the equation, we get:
x^2 = 196000 N/500 N/m^2
x^2 = 392 m^2
x = sqrt(392) = 19.8 m
Therefore, the car park must be at least 19.8 meters on each side to accommodate the 10 cars.
2. a. To calculate the density of the metal pipe, we need to use the formula:
Density = Mass/Volume
Given that the mass of the metal pipe is 50 g and the volume of the pipe submerged in water is the difference in water levels (95 cm^3 - 30 cm^3 = 65 cm^3), we need to convert the volume to liters (1 cm^3 = 1 mL = 0.001 L):
Volume = 65 cm^3 * 0.001 L/cm^3 = 0.065 L
Now we can calculate the density:
Density = 50 g / 0.065 L ≈ 769.2 g/L or 769.2 kg/m^3
Therefore, the density of the metal pipe is approximately 769.2 g/L or 769.2 kg/m^3.
b. If the metal pipe is cut into two equal pieces, each piece will have half the mass of the original pipe. The volume of each piece remains the same (0.065 L). Therefore, the density of one such piece would be half of the density of the original pipe:
Density = (50 g / 2) / 0.065 L ≈ 384.6 g/L or 384.6 kg/m^3
Therefore, the density of one such piece is approximately 384.6 g/L or 384.6 kg/m^3.
c. Cheryl's method to determine the density of the metal pipe relies on it sinking in water. However, wood generally floats in water due to its lower density compared to water. Therefore, if Cheryl were to try the same method with a piece of wood, it would not sink to the bottom, and the volume change in the measuring cylinder would be different. This method is not suitable for determining the density of a piece of wood that floats in the liquid. Other methods, such as displacement or direct measurements, would need to be used to determine the density of a floating object.