In a physics lab, you attach a 0.200-kg air-track glider to the end of an ideal spring of negligible mass and start it oscillating. The elapsed time from when the glider first moves through the equilibrium point to the second time it moves through that point is 2.60 s. Find the spring's force constant.

검증된 단계별 안내

First, understand that the problem involves simple harmonic motion (SHM) of a glider attached to a spring. The time given is the period of half an oscillation, so the full period (T) is twice this time: T = 2 * 2.60 s.

Recall the formula for the period of a mass-spring system in SHM:

T = \frac{2 π}{\sqrt{\frac{m}{k}}}

, where T is the period, m is the mass, and k is the spring constant.

Rearrange the formula to solve for the spring constant k:

k = \frac{m}{\frac{4 π^2}{T^{2}}}

Substitute the known values into the equation: m = 0.200 kg and T = 5.20 s (since T is twice the given time).

Calculate the spring constant k using the rearranged formula and the substituted values. This will give you the spring's force constant.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Simple Harmonic Motion

Simple Harmonic Motion (SHM) describes the oscillatory motion of systems like springs and pendulums, where the restoring force is proportional to the displacement from equilibrium. In this problem, the glider's motion through the equilibrium point indicates SHM, characterized by sinusoidal oscillations and a constant period.

Period of Oscillation

The period of oscillation is the time taken for one complete cycle of motion in SHM. It is crucial for determining the properties of the system, such as the spring constant. In this scenario, the time from the first to the second equilibrium point passage is half the period, helping calculate the full period and subsequently the spring constant.

Spring Constant

The spring constant, denoted as k, measures the stiffness of a spring and is defined by Hooke's Law, F = -kx, where F is the restoring force and x is the displacement. It can be derived from the period of oscillation using the formula T = 2π√(m/k), where T is the period and m is the mass of the glider.