Question

Many medical devices use a footswitch to toggle important functions (like turning a laser ON). The footswitch is affixed in metal housing to prevent accidental use and possible damage. See the figure. The housing is required to withstand at least 300 lb force before failure. A failure is a complete collapse of the housing such that the switch is affected 3. To test the housing strength a 20 kg mass is dropped onto the housing from a height of 2 m. We assume that the 20 kg mass slows down linearly upon impact. At impact, the top of the housing buckles 5.5 cm. From energy considerations, calculate the impact force needed to buckle the housing a. b. Does the housing meet requirements?

Answer 1

ka) From conservation of energy, 1 mv mgh 2 (9.8 m/s2)(2 m = . 39.2 m/s From kinematic equations 2 0-v22as -39.2 m/s 2a(5.5x10 m) a-356.36 m/s Force is F ma 20 kg (356.36 m/s2 =7127.3 N (b) Needed force is F 300 lb 4.4482 N =300 1b 1 lb =1334.466 N This is clearly much less than 7127.3 N, the house does actually meet the requirements

Answer 2

Apply the conservation of energy on the mass. 1 mgh-mv 2 Here mis mass of the block, h is dropped height, v is the speed of the mass just before tough the housing and g is gravitational acceleration Substitute the known values in the above expression 1V (9.81m/s')(2m)= 2 v239.24m2/s2 Use the second equation of motion. 2 = v 2aS Here, v is the final speed of the mass, a is an acceleration of the mass and s is housing buckles distance Substitute the known values in the above expression 0=(39.24m2/s2)+2a(5.5cm) 1m -(39.24 m2/ 2a (5.5cm 100cm a-356.72m/s2

The negative sign of the acceleration indicates de-acceleration (the speed of the mass decreases) Consider the force applied by the mass on the housing is (F). Apply Newton's second law of motion F = ma =(20kg)(356.72m/s) =7134.545 N Thus, the impact force needed to buckle the housing is 7134.545N The minimum required force to withstand the housing is Fin300 lb 4.4482 N (300 lb) 1 lb = 1334.466N From the above calculation (F>> F so the housing does meet the requirements. min