III. Problem Solving: Kinetic Linergy, Potential Energy and Power.12. Calculate the kinetic energy of a 5.2 kg object moving at 2.4 m/s.13. Calculate the speed of a 5.2 kg object that possesses 26.1 J of kinetic energy.14. Calculate the potential energy of a 5.2 kg object positioned 5.8 m above theground.15. A person weighing 600 N gets on an elevator. The elevator lifts the person6 m in 10 seconds. How much power was used?
Answer (1)
12. SOLUTION:Step 1: List the given values.[tex]\begin{aligned} & m = \text{5.2 kg} \\ & v = \text{2.4 m/s} \end{aligned}[/tex]Step 2: Calculate the kinetic energy.[tex]\begin{aligned} KE & = \frac{1}{2}mv^2 \\ & = \frac{1}{2}(\text{5.2 kg})(\text{2.4 m/s})^2 \\ & = \boxed{\text{14.976 J}} \end{aligned}[/tex]Hence, the kinetic energy is 14.976 J.13. SOLUTION:Step 1: List the given values.[tex]\begin{aligned} & m = \text{5.2 kg} \\ & KE = \text{26.1 J} \end{aligned}[/tex]Step 2: Calculate the speed.[tex]\begin{aligned} KE & = \frac{1}{2}mv^2 \\ 2KE & = mv^2 \\ mv^2 & = 2KE \\ \frac{mv^2}{m} & = \frac{2KE}{m} \\ v^2 & = \frac{2KE}{m} \\ \sqrt{v^2} & = \sqrt{\frac{2KE}{m}} \\ v & = \sqrt{\frac{2KE}{m}} \\ & = \sqrt{\frac{2(\text{26.1 J})}{\text{5.2 kg}}} \\ & = \boxed{\text{3.168 m/s}} \end{aligned}[/tex]Hence, the speed is 3.168 m/s.14. SOLUTION:Step 1: List the given values.[tex]\begin{aligned} & m = \text{5.2 kg} \\ & h = \text{5.8 m} \end{aligned}[/tex]Step 2: Calculate the potential energy.[tex]\begin{aligned} PE & = mgh \\ & = (\text{5.2 kg})(\text{9.8 m/s}^2)(\text{5.8 m}) \\ & = \boxed{\text{295.568 J}} \end{aligned}[/tex]Hence, the potential energy of an object is 295.568 J.15. SOLUTION:Step 1: List the given values.[tex]\begin{aligned} & F = \text{600 N} \\ & d = \text{6 m} \\ & t = \text{10 s} \end{aligned}[/tex]Step 2: Calculate the work done.[tex]\begin{aligned} W & = Fd \\ & = \text{(600 N)(6 m)} \\ & = \text{3,600 J} \end{aligned}[/tex]Step 3: Calculate the power[tex]\begin{aligned} P & = \frac{W}{t} \\ & = \frac{\text{3,600 J}}{\text{10 s}} \\ & = \boxed{\text{360 W}} \end{aligned}[/tex]Hence, 360 W of power was used.
