The coiled spring of a toy supports the weight of a child.The spring is compressed a distance of 1.6 inches by the weight of a 35-pound child.The toy will not work properly if its spring is compressed more than 6 inches.What is the weight of the heaviest child who should be allowed to use the toy? (Round your answer to two decimal places. )
A)136.25 lb
B)126.25 lb
C)131.25 lb
D)35 lb
E)141.25 lb

Question

The coiled spring of a toy supports the weight of a child.The spring is compressed a distance of 1.6 inches by the weight of a 35-pound child.The toy will not work properly if its spring is compressed more than 6 inches.What is the weight of the heaviest child who should be allowed to use the toy? (Round your answer to two decimal places. ) ​
A)136.25 lb
B)126.25 lb
C)131.25 lb
D)35 lb
E)141.25 lb

Quizplus · Accepted Answer

First, we need to find the spring constant, which relates the force exerted by the spring to its displacement.

Using Hooke's Law, F = -kx, where F is the force, k is the spring constant, and x is the displacement:

k = F/x = 35 lb / 1.6 in = 21.875 lb/in

Now, we can find the weight of the heaviest child using the maximum permitted compression of the spring:

x_max = 6 in

F_max = kx_max = (21.875 lb/in)(6 in) = 131.25 lb

Therefore, any child weighing more than 131.25 lb should not use the toy.

The closest answer choice to this is C, 131.25 lb, rounded to two decimal places.

The Coiled Spring of a Toy Supports the Weight of a Child.The