Is it reasonable that a 3030-kg child could run fast enough to have 100100 J of kinetic energy?

Ch 06: Work & Kinetic Energy

Young & Freedman Calc - University Physics 14th Edition

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Young & Freedman Calc 14th Edition

Ch 06: Work & Kinetic Energy

문제 18c

6장, 문제 18c

Is it reasonable that a $30$ -kg child could run fast enough to have $100$ J of kinetic energy?

검증된 단계별 안내

Step 1: Recall the formula for kinetic energy, which is $ KE = \frac{1}{2} m v^2 $, where $ KE $ is the kinetic energy, $ m $ is the mass of the object, and $ v $ is its velocity.

Step 2: Substitute the given values into the formula. The mass of the child is $ m = 30 \, \text{kg} $, and the kinetic energy is $ KE = 100 \, \text{J} $. Rearrange the formula to solve for velocity $ v $: $ v = \sqrt{\frac{2 \cdot KE}{m}} $.

Step 3: Perform the substitution: $ v = \sqrt{\frac{2 \cdot 100}{30}} $. This will give the velocity of the child in meters per second.

Step 4: Compare the calculated velocity to typical running speeds for a child. Typical running speeds for children are usually in the range of 3 to 5 m/s. If the calculated velocity is within this range, it is reasonable for the child to have 100 J of kinetic energy.

Step 5: Conclude whether the calculated velocity is realistic based on the comparison to typical running speeds. If the velocity is significantly higher than typical speeds, it may not be reasonable for the child to achieve 100 J of kinetic energy.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion, calculated using the formula KE = 0.5 * m * v^2, where m is mass and v is velocity. In this context, the kinetic energy of the child is given as 100 J, which can be used to determine the necessary speed for the child to achieve this energy level.

Mass and Weight

Mass is a measure of the amount of matter in an object, typically measured in kilograms. In this scenario, the child's mass is 30 kg, which is essential for calculating kinetic energy. Understanding the relationship between mass and energy helps in assessing whether the child can reach the required speed to have 100 J of kinetic energy.

Velocity

Velocity is the speed of an object in a specific direction and is a vector quantity. To find out if the child can achieve 100 J of kinetic energy, we need to calculate the velocity using the kinetic energy formula. This involves rearranging the formula to solve for v, which will indicate if the child's running speed is feasible.