A 0.30kg soccer ball is released from the top of a 10m building. The ball strikes the ground with a speed of 12m/s. Use the conservation of energy to determine the energy lost due to the work done by air resistance.

Question

BlackTom AI · Accepted Answer

Question restatement: A 0.30 kg soccer ball is released from a height of 10 m. It strikes the ground with a speed of 12 m/s. Using conservation of energy, determine the energy lost to air resistance.

Option analysis:
- a) 21.6 J: This value matches the final kinetic energy of the ball at impact, calculated as KE = 1/2 m v^2 = 1/2 × 0.30 kg × (12 m/s)^2 = 0.15 × 144 = 21.6 J. However, this is not the energy lost to air resistance; it is the portion of energy remaining as kinetic energy at impact.
- b) 7.8 J: This is the energy dissipated by air resistance. Start with the initial gravitational potential energy: U_i = m g h = 0.30 kg × 9.8 m/s^2 × 10 m = 29.4 J. If there were no air resistance, all this potential energy would convert to kinetic energy at ground, K_ground = 29.4 J. But the actual kinetic energy at impact is 21.6 J, so the difference is E_lost = 29.4 J − 21.6 J = 7.8 J. This is the energy that went into overcoming air resistance (heat, sound, deformation, etc.).
- c) 13.2 J: This value does not correspond to any standard energy partition in this setup. It could arise from a miscalculation, such as taking KE_final as 16.2 J or misapplying the energy balance, but it does not match the actual energy lost to drag.
- d) 29.4 J: This would imply that all the initial potential energy was lost to air resistance, leaving zero kinetic energy at impact, which contradicts the given final speed of 12 m/s. Therefore this choice is inconsistent with the stated impact velocity.

Summary: The correct energy loss due to air resistance is the difference between the initial potential energy and the final kinetic energy, 29.4 J − 21.6 J = 7.8 J. The other options misidentify the final kinetic energy, miscalculate the energy dissipated, or ignore the nonzero final speed.

A 0.30kg soccer ball is released from the top of a 10m building. The ball strikes the ground with a speed of 12m/s. Use the conservation of energy to determine the energy lost due to the work done by air resistance.单项选择题

类似问题

Figure caption: A puck sliding to the right with a velocity of 4 meters per second. The puck approaches an incline that rises up 1 meter before leveling off again. A hockey puck sliding on smooth ice at 4.5 m/s comes to a 1-m high hill. How fast is the puck going at the top of the hill?

True or False: Energy can be created.

What should the height of a slide in a park be so that a child will reach the bottom of the slide with a speed of 15.0 m/s? Use g = 10.0 m/s2.

A simple pendulum of length 2.00 m is made with a mass of 2.00 kg. The mass has a speed of 3.00 m/s when the pendulum is 30.0° above its lowest position. What is the maximum angle (in degrees) away from the lowest position the pendulum will reach?

A ball can be rolled down one of four different ramps, as shown below. The final elevation loss of each of the ramps is the same. Neglecting friction, for which ramp will the speed of the ball be the highest at the bottom?

Question at position 9 True or False. The energy of the universe can be created.TrueFalse

What happens when energy is changed from one form to another?

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单