An object attached to a spring is pulled across a horizontal frictionless surface. If the force constant (spring constant)of the spring is 45 N/m and the spring is stretched by 0.88 m when the object is accelerating at $1.4 \mathrm {~m} / \mathrm { s } ^ { 2 }$ what is the mass of the object?
A)28 kg
B)24 kg
C)31 kg
D)36 kg

Question

Quizplus · Accepted Answer

Explanation:The force exerted by the spring is given by:$$F = -kx$$where:F is the force exerted by the spring (in newtons)k is the force constant (in newtons per meter)x is the displacement of the spring from its equilibrium position (in meters)The acceleration of the object is given by:$$a = \frac{F}{m}$$where:a is the acceleration of the object (in meters per second squared)m is the mass of the object (in kilograms)Substituting the given values into the above equations, we get:$$-45 \mathrm {~N} / \mathrm {~m} 	imes 0.88 \mathrm {~m} = 1.4 \mathrm {~m} / \mathrm {~s} ^ { 2 } 	imes m$$Solving for m, we get:$$m = \frac{-45 \mathrm {~N} / \mathrm {~m} 	imes 0.88 \mathrm {~m}}{1.4 \mathrm {~m} / \mathrm {~s} ^ { 2 }} = 28 \mathrm {~kg}$$Therefore, the mass of the object is 28 kg.

An Object Attached to a Spring Is Pulled Across a Horizontal