Motion in a vertical circle
- A bob of heavy mass m is suspended by a light string of length l. The bob is given a horizontal velocity v_0 as shown in figure. If the string gets slack at some point P making an angle θ from the horizontal, the ratio of the speed v of the bob at po… Answer: 4. (sinθ/2+3sinθ)^(1/2) Key idea: the string goes slack when the tension becomes zero, and energy is conserved along the way. At P (... 1
- A mass m is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when : Answer: 3. the mass is at the lowest point The wire breaks where its tension is largest. At the lowest point: T-mg=mv²/r , so T=mg+mv²/r . H... 1
- A body initially at rest and sliding along a frictionless track from a height h (as shown in the figure) just completes a vertical circle of diameter AB = D. The height h is equal to Answer: 4. 5/4 D To just complete the vertical circle of radius R=D/2 , the speed at the top B must satisfy v_B²=gR . Energy conservation fr... 1
- What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop ? Answer: 4. √(5gR) Key idea: at the top the minimum speed satisfies mg=mv_t²/R , so v_t²=gR . Energy conservation from bottom to top (height... 1