What is the kinetic energy of a 16.1 g ball moving at 42.1 m/s? Report your answer with the correct number of significant figures. Do not include units in your answer.
Answer (2)
Convert the mass from grams to kilograms: m = 16.1 g = 0.0161 kg .
Calculate the kinetic energy using the formula: K E = 2 1 m v 2 = 2 1 ( 0.0161 kg ) ( 42.1 m/s ) 2 .
Compute the kinetic energy: K E = 14.2679005 J .
Round the result to 3 significant figures: K E = 14.3 .
Explanation
Understanding the Problem We are asked to calculate the kinetic energy of a ball given its mass and velocity. We need to use the formula for kinetic energy, which is K E = 2 1 m v 2 , where m is the mass and v is the velocity. We also need to pay attention to the units and significant figures.
Converting Units First, we need to convert the mass from grams to kilograms since the standard unit for mass in physics is kilograms. To convert grams to kilograms, we divide by 1000: m (kg) = 1000 16.1 g = 0.0161 kg
Calculating Kinetic Energy Now we can calculate the kinetic energy using the formula: K E = 2 1 m v 2 = 2 1 ( 0.0161 kg ) ( 42.1 m/s ) 2 K E = 2 1 ( 0.0161 ) ( 1772.41 ) = 0.00805 × 1772.41 = 14.2679005 J
Significant Figures We are given that the mass is 16.1 g and the velocity is 42.1 m/s. Both values have 3 significant figures. Therefore, our final answer should also have 3 significant figures. Rounding 14.2679005 to 3 significant figures, we get 14.3.
Final Answer The kinetic energy of the ball is 14.3 J.
Examples
Understanding kinetic energy is crucial in many real-world applications. For example, when designing vehicles, engineers need to calculate the kinetic energy involved in collisions to improve safety features. Similarly, in sports, understanding the kinetic energy of a ball helps athletes optimize their performance, such as maximizing the impact force in a baseball bat swing or a tennis serve. Even in roller coaster design, engineers use kinetic energy principles to ensure a thrilling yet safe ride.
The kinetic energy of a 16.1 g ball moving at 42.1 m/s is calculated using the formula K E = 2 1 m v 2 . After converting mass to kilograms and calculating, the kinetic energy is approximately 14.3 J. This result is reported with the correct number of significant figures.
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