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The coiled spring of a toy supports the weight of a child. The spring is compressed a distance of 1.9 inches by the weight of a 25-pound child. The toy will not work properly if its spring is compressed more than 3 inches. What is the maximum weight for which the toy will work properly

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oladayoademosu

The maximum weight for which the toy will work properly is 39.5 lb

Spring force

The spring is compressed a distance of 1.9 inches by the weight of a 25-pound child, the spring force, F = kx where

  • k = spring constant and
  • x = compression.

Spring constant

Making k subject of the formula, we have

k = F/x

Now F = weight of child = mg where

  • m = pound weight of child = 25 lb and
  • g = acceleration due to gravity = 32 ft/s²

and x = compression = 1.9 in

So, k = F/x

k = mg/x

k = 25 lb × 32 ft/s²/1.9 in

k = 800 lbft/s²/1.9 in

k = 421.1 lb-f/in

The maximum force

The maximum force for a compression of 3 inches is

F = kx where

  • k = 421.1 lb-f/in and
  • x = 3 in

So, F = 421.1 lb-f/in × 3 in

F = 1263.3 lb-f

The maximum weight

Since F = mg

The maximum weight m = F/g

= 1263.3 lb-f ÷ 32 ft/s²

= 39.48 lb

≅ 39.5 lb

So, the maximum weight for which the toy will work properly is 39.5 lb

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