An object attached to a vertical spring is displaced 16.4 cm from rest and then released. If the mass oscillates 14.0 times in 8.60 s and the spring constant in the spring is 20.0 N/m, what is the mass of the object? 0.0101 kg 0.102 kg 53.0 kg 0.191 kg
Question
An object attached to a vertical spring is displaced 16.4 cm from rest and then released. If the mass oscillates 14.0 times in 8.60 s and the spring constant in the spring is 20.0 N/m, what is the mass of the object? 0.0101 kg 0.102 kg 53.0 kg 0.191 kg
Solution
To solve this problem, we need to use the formula for the period of a mass-spring system, which is T = 2π√(m/k), where T is the period of oscillation, m is the mass, and k is the spring constant.
First, we need to find the period of oscillation. We know that the mass oscillates 14.0 times in 8.60 s, so the period of one oscillation is T = 8.60 s / 14.0 = 0.614 s.
Next, we can rearrange the formula to solve for m: m = k(T/2π)^2.
Substituting the given values into the formula, we get m = 20.0 N/m * (0.614 s / 2π)^2 = 0.191 kg.
So, the mass of the object is 0.191 kg.
Similar Questions
A 0.450 kg mass attached to a horizontal spring is displaced 11.4 cm from rest and then released. If the mass oscillates 7.00 times in 11.5 s, what is the spring constant in the spring? 0.167 N/m 6.58 N/m 0.134 N/m 14.6 N/m
A 3.4-kg object rests on a horizontal frictionless surface. It is in a position such that it is compressing a spring a distance 11.8 cm.If the object is released, the object leaves the spring at a speed of 18.3 cm/s.What is the spring constant of the spring?Express your answer in N/m, to at least one digit after the decimal point.
A 1.13-kg mass attached to a spring is displaced 7.87 cm from the equilibrium position. It is released and then oscillates with a frequency of 4.05 Hz. What is the speed of the mass when it is 2.63 cm from the equilibrium position?
A 1.13-kg mass attached to a spring is displaced 7.87 cm from the equilibrium position. It is released and then oscillates with a frequency of 4.05 Hz. What is the energy of the motion when the mass passes through the equilibrium
A 7 kg mass is attached to a very light ideal spring hanging vertically and hangs at rest in the equilibrium position. The spring constant of the spring is 1.7 N/cm. The mass is pulled downward 2.8 cm and released. What is the speed of the mass when it is half of the distance above the point from which it was released? For example, if the mass was pulled till 2 cm, then half of the distance is 1 cm.Note: Write your answer in normal format up to 4 decimal points. Example: 12.3456. Please DO NOT write the units in the electronic format. Definitely, write the units on paper. If I don't find the units in your hand-written notes, then marks will be deducted.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.