What is the kinetic energy in J of a 60.0 g tennis ball approaching a tennis racket at 32.0 m/s?

Question

BlackTom AI · Accepted Answer

Kinetic energy is given by KE = 1/2 m v^2. Convert the mass to SI units and plug into this formula.

1. Relevant concepts:
- Kinetic energy (scalar) formula: KE = (1/2) m v^2.
- Mass must be in kilograms and speed in m/s; KE unit is joules (J).
- Use appropriate significant figures.

2. Step-by-step calculation:
- Given mass = 60.0 g. Convert to kg:
  m = 60.0 g × (1 kg / 1000 g) = 0.0600 kg.
- Given speed v = 32.0 m/s.
- Compute v^2:
  v^2 = (32.0 m/s)^2 = 1024.0 (m^2/s^2).
- Compute 1/2 m:
  1/2 m = 0.5 × 0.0600 kg = 0.0300 kg.
- Multiply:
  KE = (0.0300 kg) × (1024.0 m^2/s^2) = 30.72 kg·m^2/s^2 = 30.72 J.
- With three significant figures (inputs have three sig figs), round to 30.7 J.

3. Why the correct answer is correct:
- All unit conversions and the KE formula were applied correctly; the resulting unit kg·m^2/s^2 equals joules.
- The numeric result 30.72 J rounds properly to 30.7 J, matching option c.

4. Why the other choices are incorrect:
- a. 1920 J: wrong magnitude (would correspond to a much larger mass); not consistent with m = 0.0600 kg.
- b. 960 N: wrong unit (newtons are units of force, not energy) and the numeric value does not match the KE calculation.
- d. 30.7 N: although the number matches, the unit is incorrect—energy must be in joules, not newtons.

Conclusion: The kinetic energy is 30.7 J, which confirms choice c (30.7 J).

What is the kinetic energy in J of a 60.0 g tennis ball approaching a tennis racket at 32.0 m/s?单项选择题

类似问题

A 20.7 kg shopping trolley full of groceries, with frictionless wheels, starting from rest is pushed 13 cm in 0.05 s with a constant acceleration. How much work is done on it? Give your answer to two significant figures.

A car which has a mass of m, needs 27 kJ of energy to travel at a velocity of [math: v]. How much energy is needed for the same car to travel at a speed of 6[math: v] ?*Hint: work out the energies at each velocity separately.

A car which has a mass of m, needs 32 kJ of energy to travel at a velocity of [math: v]. How much energy is needed for the same car to travel at a speed of 5[math: v] ?*Hint: work out the energies at each velocity separately.

A 30% efficient car engine accelerates the 1700 kg car from rest to 15 m/s. How much energy is transferred to the engine by the burning gasoline?

Which has more kinetic energy?

What is the kinetic energy of a proton moving with speed 3.4 × 103 m s−1, in electronvolts?

What is the definition of kinetic energy?

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