Two identical marbles are dropped in a classroom. Marble A is dropped from 1.00m, and marble B is dropped from 0.50m. Compare the kinetic energies of the two marbles just before they strike the ground.

Question

BlackTom AI · Accepted Answer

Question restatement: Two identical marbles are dropped from different heights, 1.00 m (A) and 0.50 m (B). Compare their kinetic energies just before they strike the ground. Answer options: a) A and B have the same KE. b) A has 1.4 times as much KE as B. c) A has 2.0 times as much KE as B. d) A has 4.0 times as much KE as B.

Initial analysis: For an object dropped from rest, mechanical energy is conserved, so the kinetic energy just before impact equals the loss of gravitational potential energy: KE = m g h, where m is mass, g is gravity, and h is height dropped. Since the marbles are identical, their masses are the same, so KE scales directly with height h. Therefore, A (h = 1.00 m) should have KE larger than B (h = 0.50 m) by a factor of h_A/h_B = 1.00/0.50 = 2.0. In other words, A should have twice the KE of B.

Option-by-option analysis:
- Option a: 'A and B have the same KE.' This would be true only if the heights were equal or if some other compensating factor canceled the height difference. Since h_A ≠ h_B and KE ∝ h, this statement is incorrect.
- Option b: 'A has 1.4 times as much KE as B.' The factor 1.4 ≈ sqrt(2) arises if one confuses kinetic energy with something proportional to velocity (or places emphasis on speed ratios). Specifically, the speed ratio v_A/v_B = sqrt(h_A/h_B) = sqrt(2) ≈ 1.414, which is not the same as the KE ratio. KE depends on h, not on velocity alone, so this option misidentifies the correct quantity. Therefore this statement is incorrect for kinetic energy.
- Option c: 'A has 2.0 times as much KE as B.' This matches the correct KE relation KE ∝ h, yielding a 2:1 ratio since h_A/h_B = 2.0. Given the energy conservation argument, this would be the correct statement if we are talking about KE.
- Option d: 'A has 4.0 times as much KE as B.' This would imply h_A/h_B = 4, which would require A to be at 2.0 meters higher than B, not the case here. So this is incorrect.

Additional note on potential confusion: If someone calculates the speed ratio instead of energy, they would obtain v_A/v_B = sqrt(h_A/h_B) = sqrt(2) ≈ 1.414, which corresponds to a 1.4× ratio in speed, not energy. This is a common source of mix-ups between velocity and kinetic energy, since KE involves the square of speed: KE ∝ v^2.

Synthesis: Based on the physics principle KE = m g h for an object dropped from rest, the correct energy-based comparison yields A having twice the kinetic energy of B. The option stating 1.4× corresponds to a speed ratio, not to a kinetic-energy ratio, and thus is not correct for KE. The 2.0× option correctly reflects KE ∝ height, while the 4.0× option does not match the given height difference.

SPH4U - Physics 12 (2025-26) - A

Two identical marbles are dropped in a classroom. Marble A is dropped from 1.00m, and marble B is dropped from 0.50m. Compare the kinetic energies of the two marbles just before they strike the ground.

查看解析

登录即可查看完整答案

类似问题

Where is the potential energy the greatest?

What is gravitational potential energy?

What is the potential energy of a soccer ball given it's mass and height from the Earth's surface as depicted on the figure below? Provide your answer to three (3) significant figures and correct SI unit symbol must be provided.

True or false? The gravitational potential energy of an object 5m above the ground in Ontario is the same as an indentical object 5m above the ground on the Moon.

True or false? The amount of gravitational potential energy depends on where the reference height y = 0 is set.

Which of the following statements correctly describes the relationship between an object's gravitational potential energy and its height above the ground?

Consider Sun’s total gravitational potential energy as its power source to maintain its current luminosity. How long would it take to radiate all of it away? (Hint: t = Energy/Luminosity; 1 W = 1 J/s, 1 J = 1 kg 1 m2 s-2)

A 444 g soccer ball is 5.1 m above the ground. How much gravitational energy does it have? Give your answer to the nearest whole number.

更多留学生实用工具

考试浏览器助手

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