A block of mass m on a horizontal frictionless tabletop isattached by a swivel t

Question

A block of mass m on a horizontal frictionless tabletop isattached by a swivel to a spring that is attached to the ceiling.The vertical distance between the top of the block and the ceilingis y0, and the horizontal position is x. When the blockis x = 0, the spring, which has force constant k, is completelyunstressed.

a) what is Fx, the x component of the force on the blockdue to the spring, as a function of x?
b) show that Fx is proportional to x3 forsufficiently small values of absolute x.
c) if the block is released from rest at x = x0, whereabsolute x0 is smaller than y0, what is itsspeed when it reaches x = 0?

Explanation / Answer

Let h = y0 F = k ((x2 + h2) - h) sin   where is angle spring makes withvertical sin = x / ((x2 + h2) F = k x [1 - h /  ((x2 +h2)] = k x (1 - cos ) F = k x (1 - (1 - 2 /2))  expanding cos for small F = k x 2 / 2 = x / h   for small F = k x3 / (2 h2)
Integrating F dx (small x) W =  k x4 / (8 h2) =1/2 m v2

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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