A fisherman lifts a fish of mass 250 g from rest through a vertical height of 1.8 m. The fish gains a speed of 1.1 m/s. What is the energy gained by the fish?
Correct answer: D. 4.6 J
- A. 0.15 J
- B. 4.3 J
- C. 4.4 J
- D. 4.6 J
Explanation
Potential Energy Gain:The fish gains potential energy due to its change in height. Potential energy (PE) = mgh, where: m = mass (in kg) g = acceleration due to gravity (approximately 9.8 m/s²) h = height (in m) Convert the mass to kilograms: 250 g = 0.25 kg Calculate the potential energy gain:PE = (0.25 kg) * (9.8 m/s²) * (1.8 m) PE = 4.41 J2. Kinetic Energy Gain:The fish also gains kinetic energy due to its speed.Kinetic energy (KE) = 1/2 mv², where: m = mass (in kg) v = speed (in m/s) Calculate the kinetic energy gain:KE = 1/2 * (0.25 kg) * (1.1 m/s)²KE = 1/2 * 0.25 * 1.21KE = 0.15125 J3. Total Energy Gain:The total energy gained is the sum of the potential and kinetic energy gains.Total Energy = PE + KETotal Energy = 4.41 J + 0.15125 JTotal Energy ≈ 4.56 J
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About Potential Energy
Potential energy is energy stored because of position or configuration, including gravitational potential energy near Earth's surface and elastic energy in a stretched or compressed spring. Questions use changes in potential energy and conservation of mechanical energy, while distinguishing a chosen reference level from an absolute zero of energy.
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