# Applied Sciences

Unit V Problem Solving Worksheet

This assignment will allow you to demonstrate the following objectives:

• Identify the building blocks of matter to include their influence on physical properties. o Identify the atomic mass and number of atoms in elements by utilizing the periodic table. o Find the relation between mass, density, and volume. o Distinguish applied force, spring constant, and displacement using Hooke’s law.

Instructions: Choose 8 of the 10 problems below. Show your work in detail. Answer the questions directly in this template. Before doing this, it is highly recommending that you thoroughly review the three examples in the Unit Lesson.

1. Consider two stable isotopes, helium-3 and helium-4. How many neutrons and protons are there in each isotope? What are the mass numbers? Hint: Do not confuse mass number with atomic mass. Review the definition of them.

2. If two protons and two neutrons are added to the nucleus of a carbon atom, what nucleus does it become? Hint: The proton number equals to the atomic number. See the periodic table of Figure 11.9 on. p. 216 in the textbook.

3. Calculate the molecular mass of hydrogen sulfide, H2S in atomic mass unit u. Use the periodic table of Figure 11.9 on. p. 216 in the textbook. Hint: The molecular mass of a molecule is the sum of the atomic masses of its atoms. For instance, hydrogen and oxygen have atomic masses of 1.0079u and 15.999u respectively (See Figure 11.9 on. page 216 in the textbook). Thus, the molecular mass of a water molecule (H2O) is (2×1.0079u+15.999u=18.0148u). In order to express enormous numbers of atoms or molecules, the gram-mole, or, more simply, the mole, is used.

4. Which has the greater density: 100 kg of ice or 10 kg of gold? Consult the Table 12.1 on p. 230 in the textbook. Hint: Be careful about the unit of density, mass, and volume.

5. What is the volume of 1,000 kg of ice? Consult the Table 12.1 on p. 230 in the textbook. Hint: Use the relationship between density, mass, and volume. Mass=density x volume.

6. How many gold atoms are in a 1 kg gold bar? The chemical symbol of gold is Au. Consult The Periodic Table in Figure 11.9 on p. 216 in the textbook. Hint: Remember 1u=1.66×10-27kg. 1 mole= 6.022×1023, which is Avogadro’s number

7. There are two water containers: a cube and a sphere. The length of the side of the cube is 3 m and the radius of the sphere is 3 m. When the two containers are full of water, which container contains more mass? Hint: Use the relationship between density, mass, and volume. Mass=density x volume. If the length of the side of a cube is r m, the volume of the cube is r3 m3. If the radius of a sphere is r, the volume of the sphere is 4/3 xπ x r3 m3. Here x r3 =r x r x r.

8. A force of 100 N is required to squeeze a hand exerciser that has a coiled spring. The spring is compressed by 0.02 meters. Determine the spring constant. Hint: Use Hooke’s law. The restoring force of an ideal spring is F=-kx, where k is the spring constant and x is the displacement of the spring from its original length.

Unit V Problem Solving Worksheet

9. A slingshot has a spring constant of 50 N/m. If you apply a force of 10 N, how far does it stretch? Hint: Use Hooke’s law. The restoring force of an ideal spring is F=-kx, where k is the spring constant and x is the displacement of the spring from its original length.

10. A spring has a spring constant of 300 N/m. Find the magnitude of the force needed to compress the spring by 0.03 m. Hint: Use Hooke’s law. The restoring force of an ideal spring is F=-kx, where k is the spring constant and x is the displacement of the spring from its original length.