The diagram below shows a 3.7 kg object being spun around in a circle from a 1.0 m long massless string. The angle [math: θ] is 33.8 degrees. The object is sped up such that the angle is 10 degrees larger. Determine the magnitude of the tension (N) in the string. Give your answer correct to 2 decimal places without units.

Question

BlackTom AI · Accepted Answer

For a conical pendulum the vertical component of the string tension supports the weight, so T cosθ = mg; this gives the tension directly once θ is known.

1) Relevant concepts
- Conical pendulum equilibrium: vertical forces sum to zero, so T cosθ = mg.
- Horizontal component T sinθ provides the centripetal force m v^2 / r, with r = L sinθ, but that horizontal relation is not needed to find T because vertical equilibrium already determines T.

2) Step-by-step reasoning
- Vertical equilibrium: T cosθ = mg → T = mg / cosθ.
- Plug in the given mass m = 3.7 kg, g = 9.8 m/s^2, and the increased angle θ = 33.8° + 10° = 43.8°.

3) Calculations (all intermediate steps)
- Compute weight: mg = 3.7 × 9.8 = 36.26 N.
- Compute cos(43.8°). Using a calculator: cos(43.8°) ≈ 0.72128.
- Solve for T: T = 36.26 / 0.72128 ≈ 50.29 N.

4) Why this is correct
- The mass has no vertical acceleration, so the string’s vertical component must exactly equal the weight. That yields T = mg / cosθ independently of the speed; increasing the angle increases the required tension because cosθ becomes smaller.

5) Why other plausible answers would be incorrect
- Using T = mg (ignoring the angle) gives 36.26 N and underestimates T because it neglects the need for a larger tension to provide the horizontal centripetal component.
- Using T = mg · cosθ (the inverse relation) is algebraically wrong and would give an even smaller number.
- Using only the centripetal formula without the vertical balance cannot produce T uniquely without also enforcing T cosθ = mg.

6) Conclusion
- Applying T = mg / cos(43.8°) yields T ≈ 50.29, which confirms the provided correct answer 50.29.

类似问题

A man is moving in a horizontal circular motion in the air. The man is tied by a rope that is angled at 60 to the vertical. If the man weighs 71 kg, find the tension of the rope in Newtons (N).

Question at position 18 Establishing a wholly-owned subsidiary provides the quickest access to a new market.TrueFalse

Question at position 17 Leading companies should recognize that a firm based in a country with a national competitive advantage is not guaranteed ............................ as it implements its chosen international business-level strategy.dominanceplansuccessNone of the Above

Question at position 16 Costs associated with the issues firms face when entering foreign markets, including unfamiliar operating environments, economic, administrative, and cultural differences, are known as regionalization costs.TrueFalse

Question at position 14 Which of the following is NOT an incentive for firms to become multinational?To gain access to consumers in emerging marketsTo gain easier access to raw materialsTo avoid high domestic taxation on corporate incomeOpportunities to integrate operations on a global scale

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