A sled is at rest at the top of a slope 2 m high. The sled has a mass of 45 kg. What is the sled's potential energy? (Formula: [tex]PE=mgh[/tex])
A. 90 J
B. 56.8 J
C. 441 J
D. 882 J
Answer (1)
Identify the given values: mass m = 45 k g , height h = 2 m , and acceleration due to gravity g = 9.8 m / s 2 .
Use the formula for potential energy: PE = m g h .
Substitute the values into the formula: PE = 45 k g × 9.8 m / s 2 × 2 m .
Calculate the potential energy: PE = 882 J . The sled's potential energy is 882 J .
Explanation
Understanding the Problem We are given a sled at the top of a slope with a height of 2 meters. The sled has a mass of 45 kg. We need to find the sled's potential energy (PE). The formula for potential energy is given as PE = m g h , where m is the mass, g is the acceleration due to gravity, and h is the height. We will assume that g = 9.8 m / s 2 .
Identifying Given Values We are given: Mass, m = 45 k g Height, h = 2 m Acceleration due to gravity, g = 9.8 m / s 2 Potential Energy formula: PE = m g h
Substituting Values into the Formula Now, we substitute the given values into the potential energy formula: PE = ( 45 k g ) × ( 9.8 m / s 2 ) × ( 2 m ) PE = 45 × 9.8 × 2
Calculating Potential Energy Calculating the potential energy: PE = 882 k g ⋅ m 2 / s 2 Since 1 J = 1 k g ⋅ m 2 / s 2 , the potential energy is: PE = 882 J
Final Answer The sled's potential energy is 882 J.
Examples
Potential energy is a crucial concept in physics and has many real-world applications. For example, when designing roller coasters, engineers use the principle of potential energy to determine the height of the initial hill. The potential energy at the top of the hill is converted into kinetic energy as the coaster descends, providing the necessary speed and momentum for the rest of the ride. Similarly, in hydroelectric power plants, the potential energy of water stored at a height is converted into electrical energy as the water flows down, turning turbines. Understanding and calculating potential energy helps in designing efficient and safe systems in various engineering applications.
