An engineer must design a hand-operated lever system that can supply a torque of to a…

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

An engineer must design a hand-operated lever system that can supply a torque of

40\,\text{N}\cdot\text{m}

to a shaft. The straight lever handle can be manufactured at any length between

0.20\,\text{m}

and

0.40\,\text{m}

. During operation, the user will pull on the handle with a force that makes an angle

\theta

with the handle. (a) Derive an expression for the required pulling force

F

in terms of the desired torque

\tau

, the handle length

r

, and the angle

\theta

. (b) Calculate the force the user must exert if the handle length is fixed at

0.30\,\text{m}

and the pulling angle is

20^{\circ}

. (c) The maximum comfortable force a user can apply is

120\,\text{N}

. If the user must pull at an angle of

45^{\circ}

, determine the minimum handle length (within the allowable range) that will still deliver the required

40\,\text{N}\cdot\text{m}

torque. State whether this length is feasible given the manufacturing constraints.