The fly-press shown below is used by a jeweller to punch shapes out of a thin metal sheet.
The frame holds a screw and punch. Two arms are attached to the screw, each loaded with a heavy steel ball. The screw is driven downwards when the arms are rotated.
Kinetic energy is stored in the rotating parts: the balls, arms, screw and punch. This energy is used to punch the shape out of the metal sheet.
Q)For thicker or stiffer metal sheets the rotational kinetic energy at 2.9 rev s–1 is not enough to punch out the shape.
The distance from the axis of rotation to the centre of each ball is y.
The radius of each ball is R.
The stored energy can be increased by
either
• increasing y by 15% without changing R
or
• increasing R by 15% without changing y.
Deduce which of these would produce the greater increase in stored energy.
- I got to the right conclusion that increasing R by 15% without changing y would produce the greater increase in stored energy I just used the logic of I=mr^2 and r=R+y so is R is bigger increasing R would obviously do more.
-However the mark scheme says:
(I = 2 mr2 and Ek = ½ I ω2)
Increasing y by 15% gives new I = 1.15^2 × original I (or 1.32) ✔
Increasing R by 15% increases I by 1.15^3 (or 1.52) ✔
Second option gives greater increase in I, and Ek
also increased (by same ratio). ✔
Accept answers without calculation:
I prop to y^2 ✔
I prop to R^3 ✔
I don't understand how they got
>I prop to y^2 ✔
>I prop to R^3 ✔