SAMPLE PROBLEMS1. Calculate the kinetic energy of a 1000-kg cartraveling at 60km/h?2. If a 0.2-kg ball is thrown with a velocity of6m/s, what is its KE?3. What is the potential energy of a 0.3-kg balllifted to a height of 5.0 m above the ground?4. A 1.5-kg book on top a shelf has a PE of 29.4J. How high is the shelf?Q
Answer (1)
1. SOLUTION:Step 1: List the given values.[tex]\begin{aligned} & m = \text{1,000 kg} \\ & v = \text{60 km/h} \end{aligned}[/tex]Step 1.1: Convert the given velocity into SI units (m/s).[tex]\begin{aligned} v & = 60 \: \frac{\text{km}}{\text{h}} \times \frac{\text{1,000 m}}{\text{1 km}} \times \frac{\text{1 h}}{\text{3,600 s}} \\ & = \text{16.6666667 m/s} \end{aligned}[/tex]Step 2: Calculate the kinetic energy.[tex]\begin{aligned} KE & = \frac{1}{2}mv^2 \\ & = \frac{1}{2}(\text{1,000 kg})(\text{16.6666667 m/s})^2 \\ & = \boxed{\text{138,888.89 J}} \end{aligned}[/tex]Hence, the kinetic energy is 138,888.89 J.2. SOLUTION:Step 1: List the given values.[tex]\begin{aligned} & m = \text{0.2 kg} \\ & v = \text{6 m/s} \end{aligned}[/tex]Step 2: Calculate the kinetic energy.[tex]\begin{aligned} KE & = \frac{1}{2}mv^2 \\ & = \frac{1}{2}(\text{0.2 kg})(\text{6 m/s})^2 \\ & = \boxed{\text{3.6 J}} \end{aligned}[/tex]Hence, the kinetic energy is 3.6 J.3. SOLUTION:Step 1: List the given values.[tex]\begin{aligned} & m = \text{0.3 kg} \\ & h = \text{5.0 m} \end{aligned}[/tex]Step 2: Calculate the potential energy.[tex]\begin{aligned} PE & = mgh \\ & = (\text{0.3 kg})(\text{9.8 m/s}^2)(\text{5.0 m}) \\ & = \boxed{\text{14.7 J}} \end{aligned}[/tex]Hence, the potential energy is 14.7J.4. SOLUTION:Step 1: List the given values.[tex]\begin{aligned} & m = \text{1.5 kg} \\ & PE = \text{29.4 J} \end{aligned}[/tex]Step 2: Calculate the height.[tex]\begin{aligned} PE & = mgh \\ \frac{PE}{mg} & = \frac{mgh}{mg} \\ \frac{PE}{mg} & = h \\ h & = \frac{PE}{mg} \\ & = \frac{\text{29.4 J}}{(\text{1.5 kg})(\text{9.8 m/s}^2)} \\ & = \boxed{\text{2 m}} \end{aligned}[/tex]Hence, the shelf is 2 m high.
