Answer to Question #255632 in Physics for jenny

Question

2. Shayna owns a jewel store. She handed you a golden-colored cube for you to buy it. Out of curiosity for the element, you search on the internet about geology and look up gold in the material table, and read that its density is 19.3 g/cm3. You measure the cube and find that it is 2 cm on each side, and weighs 40 g. What is its density? Is it gold?

3. What is the mass of a cylinder of lead that is 2.50 cm in diameter, and 5.50 cm long. The density of lead is 11.4 g/mL .

4. A barber raises his customer’s chair by applying a force of 150N to a hydraulic piston of area 0.01 m2. If the chair is attached to a piston of area 0.1 m2, how massive a customer can the chair raise? Assume the chair itself has a mass of 5 kg.

Answer 1

2) Let's first find the volume of the cube:

$$V=a^3=(2\ cm)^3=8\ cm^3.$$

Finally, we can find the density of the cube:

$$\rho=\dfrac{m}{V}=\dfrac{40\ g}{8\ cm^3}=5\ \dfrac{g}{cm^3}.$$

As we can see from the calculations, it is not a gold.

3) Let's first find the volume of the cylinder:

$$V=\pi r^2 h=\pi\times(0.0125\ m)^2\times0.055\ m=2.7\times10^{-5}\ m^3.$$

Finally, we can find the mass of the cylinder:

$$m=\rho V,$$ $$m=11.4\ \dfrac{g}{mL}\times\dfrac{1\ kg}{1000\ g}\times\dfrac{1000\ mL}{1\ L}\times\dfrac{1\ L}{0.001\ m^3}\times2.7\times10^{-5}\ m^3,$$ $$m=0.3078\ kg=307.8\ g.$$

4) Let's first find the force applied to the larger piston from the hydraulic press formula:

$$\dfrac{F_1}{A_1}=\dfrac{F_2}{A_2},$$ $$F_2=\dfrac{A_2F_1}{A_1}=\dfrac{0.1\ m^2\times150\ N}{0.01\ m^2}=1500\ N.$$

Then, we can find the maximum mass that can be lifted:

$$F_2 = m_{max}g,$$ $$m_{max}=\dfrac{F_2}{g}=\dfrac{1500\ N}{9.8\ \dfrac{m}{s^2}}=153\ kg.$$

Finally, we can find  the maximum mass of the customer in the chair:

$$m_{customer, max}=m_{max}-m_{chair}=153\ kg-5\ kg=148\ kg.$$