ScholarshipMechanicsFree

Loop-the-Loop in an Electric Field

Circular motion and gravitation

In a physics laboratory a small conducting sphere of mass

m = 2.00\ \text{g}

carries a charge

q = +3.00 \times 10^{-7}\ \text{C}

. It is tied to a light insulating thread of length

L = 0.250\ \text{m}

and set moving in a vertical circle about a fixed point. The whole apparatus sits between large horizontal plates that produce a uniform vertical electric field of strength

E = 2.50 \times 10^{4}\ \text{V m}^{-1}

directed upward. Air resistance is negligible.

Data: g = 9.81 m s⁻²

(a)

show that2 marks

By considering the forces acting on the sphere at the top of the circle, show that the minimum speed at the top for the thread to stay taut is

v_{\text{top}} = \sqrt{L\left(g - \dfrac{qE}{m}\right)}

, and calculate it.

(b)

calculate2 marks

Calculate the minimum speed the sphere must have at the bottom of the circle to complete the loop.

(c)

show that2 marks

Show that, for any speed large enough to complete the loop, the tension at the bottom exceeds the tension at the top by

6(mg - qE)

, and calculate the tension at the bottom for the motion in (b).

(d)

discuss2 marks

The plate voltage is now slowly increased so that

E

increases. Discuss how the motion and the thread tension change, considering the special case where

qE = mg

and the case

qE > mg

. Calculate the field strength at which the special case occurs, and state what remains constant around the loop in that case.

Your score: 0 / 8(0 of 4 parts marked — open “Mark it” on each part)