Question

The spring in a pinball machine has a spring constant

k
kk of
2
,
130

N
m
2,130
m
N
​
2, comma, 130, start fraction, start text, N, end text, divided by, start text, m, end text, end fraction.
What is the magnitude of the force required to compress this spring
4.5

cm
4.5cm4, point, 5, start text, c, m, end text?
Write your answer using two significant figures.

Answer 1

The magnitude of the force required to compress a spring with a spring constant of 2130 N/m by 4.5 cm is 95 N.

Step-by-step explanation:

To calculate the magnitude of the force required to compress a spring, we can use Hooke's Law which states that the force is directly proportional to the displacement of the spring from its equilibrium position. The formula is given by F = -kx, where F is the force, k is the spring constant, and x is the displacement. In this case, the spring constant is given as k = 2,130 N/m and the spring is compressed by 4.5 cm.

Converting the displacement to meters, we have x = 0.045 m. Plugging these values into the formula, we get:

F = -(2,130 N/m)(0.045 m) = -95.85 N

Rounding to two significant figures, the magnitude of the force required to compress the spring by 4.5 cm is 95 N.