A string with length L (m) and mass density ? (kg/m ) hangs over a massless pull

Question

A string with length L (m) and mass density ?                                 (kg/m) hangs over a massless pulley. Each end of the string has a point mass M attached. Initially, the                                 ends of the string are distances x0 above and below their average position.                                 The rope is given an initial speed v0 so that it will NOT eventually fall                                 off the pulley. Calculate the value of this required initial speed, in terms of the given quantities. The acceleration of gravity is 9.8                                 m/s2. How will be required initial speed be affected if both point masses M approach 0 -- the only                                 mass remaining in the string? How will the required initial speed be affected if the mass density of the string approaches 0 -- the only mass                                 remaining at the ends of the string?
                                
                                We have not gone over energy equations. This problem is supposed to involve differential equations.

Explanation / Answer

v^2 - u^2 = 2as

s= x0

u =0

v^2= 2*9.8*x0

hence initial velocity v= sqrt(2*9.8*x0)-----------------> ans

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.