A particle moves in a circular path of 0.3 m radius. Calculate the magnitude a of the acceleration of the particle in m/s2 (a) if its speed is constant at 0.6 m/s and (b) if its speed is 0.6 m/s but is increasing at the rate of 0.9 m/s .

Question

A particle moves in a circular path of 0.3 m radius. Calculate the magnitude a of the acceleration of the particle in m/s2  (a) if its speed is constant at 0.6 m/s and (b) if its speed is 0.6 m/s but is increasing at the rate of 0.9 m/s .

BlackTom AI · Accepted Answer

The problem asks for the magnitude of the acceleration of a particle moving in a circle of radius 0.3 m under two scenarios: (a) constant speed 0.6 m/s, (b) speed 0.6 m/s with a tangential acceleration of 0.9 m/s^2. For circular motion with constant speed, the acceleration is purely centripetal, given by a_c = v^2 / r. For non-constant speed, the total acceleration combines centripetal and tangential components: a = sqrt(a_c^2 + a_t^2), where a_t is the tangential acceleration dv/dt.

Option 1: (a) 1.2 (b) 1.9
- In scenario (a), compute a_c = v^2 / r = (0.6)^2 / 0.3 = 0.36 / 0.3 = 1.2 m/s^2, which matches the first value here. For scenario (b), this option would imply a resulting magnitude of 1.9 m/s^2. If we combine a_c = 1.2 with a_t = 0.9 using a = sqrt(a_c^2 + a_t^2), we get sqrt(1.44 + 0.81) = sqrt(2.25) = 1.5 m/s^2, not 1.9. So this option fails the second part.

Option 2: (a) 1.8 (b) 1.9
- The centripetal component a_c with v = 0.6 and r = 0.3 remains 1.2 m/s^2, not 1.8, so the first part is inconsistent with the given data. Even without checking the second part, this already indicates a mismatch with (a). For (b), the combination would still yield 1.5 m/s^2 as shown earlier, not 1.9. Overall, this option is incorrect due to both parts not aligning with the calculated values.

Option 3: (a) 1.2 (b) 1.5
- For (a), a_c = v^2 / r = (0.6)^2 / 0.3 = 1.2 m/s^2, which is consistent with this option’s first value. For (b), tangential acceleration a_t = 0.9 m/s^2 and centripetal a_c = 1.2 m/s^2. The total acceleration magnitude is a = sqrt(a_c^2 + a_t^2) = sqrt(1.44 + 0.81) = sqrt(2.25) = 1.5 m/s^2, matching the second value shown. This option aligns with both parts of the problem.

Option 4: (a) 1.6 (b) 1.5
- The first part would require a_c = 1.6 m/s^2, which would demand v^2 / r = 1.6. With r = 0.3, that would require v^2 = 0.48, so v ≈ 0.693 m/s, which disagrees with the given speed of 0.6 m/s. Hence (a) is inconsistent. The second part, while it coincidentally yields 1.5 m/s^2, relies on an incorrect centripetal value from (a), so this option cannot be correct overall.

In summary, evaluate each option by checking the centripetal calculation for part (a) and, if speed changes in part (b), combining centripetal and tangential components as a = sqrt(a_c^2 + a_t^2) to verify the (b) value. The only choice that satisfies both parts consistently with the given data is the one where (a) matches 1.2 m/s^2 and (b) matches 1.5 m/s^2.

A particle moves in a circular path of 0.3 m radius. Calculate the magnitude a of the acceleration of the particle in m/s2 (a) if its speed is constant at 0.6 m/s and (b) if its speed is 0.6 m/s but is increasing at the rate of 0.9 m/s .单项选择题

类似问题

A satellite is orbiting a planet with an orbital radius r. Which of the following diagrams represents the direction of the velocity and acceleration of the satellite?

A 77.71 kg passenger is in a cabin of a Ferris wheel rotating in a vertical circular path with a uniform speed of 1.37 m/s. If the Ferris wheel has a radius of 69 m, find the normal reaction (in Newtons) exerted on the passenger by the cabin floor at the bottom of the circular path.

0.66 kg object attached to a 6.64 m string is moving in a circular motion on a vertical plane with 80 m/s uniform speed. What is the tension of the string at the highest point of the circle?

Assume that I am on a Ferris wheel that is rotating. We know that my apparent weight will be smallest at the top of the wheel. For which of the following Ferris wheel speeds will that apparent weight be the smallest?

It is possible for an object to be apparently weightless when moving in a horizontal circle.

If you are moving in a vertical circle at constant speed, like on a Ferris wheel, your apparent weight is greatest at the ...

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