Relationship between mass and spring constant unit

Motion of a Mass on a Spring

relationship between mass and spring constant unit

The units of the mass m is kg and the units of the period T is s. We can ignore the 4 π 2, since it is a dimensionless (unitless) constant. Its SI unit is Newton per meter (N/m). The spring constant can also be explained as the ratio of the restoring force to the deviation from the Cart 2 has a mass of kg (a) If the total momentum of the system is to be zero, what is the in A. After watching this video, you will be able to explain what Hooke's Law is and Force vs. Time & Force vs. Distance Graphs. Calculating the Velocity of the Center of Mass . One important number that relates to elasticity is the spring constant. The relationship could be almost anything -- linear, quadratic.

In words, the mass first moves away from equilibrium in one direction we'll call that the positive directionreaches a maximum displacement from equilibrium where it changes its direction of motion instantaneously coming to restspeeds up as it moves back towards the equilibrium position going in the opposite direction compared to when we tapped itslows down as it passes the equilibrium position until it reaches its maximum negative displacement the same distance from the origin as the maximum positive displacement and then heads back to the origin.

What we've described is one cycle of its oscillation. The oscillation cycles repeat.

physics - Units for spring constant - Mathematics Stack Exchange

Quantitatively we can measure the time to complete one cycle. This is called the period of the motion generally abbreviated as T. We could also count the number of cycles that occur in each second. That number, in general, will be a fraction: This measure is called the frequency of the motion abbreviated as f.

These two measures of the motion are clearly interrelated: The units of f are cycles per second. In honor of Heinrich Hertz, we use the units of Hertz abbreviated Hz: We can also easily measure the maximum displacement of the mass in both the positive and negative directions.

We find that both of these points are the same distance from the equilibrium position. This quantity is called the amplitude of the motion. There is a simple correspondence between the terms we've used to describe simple harmonic oscillations and those we use to describe sound.

The frequency of oscillations is related to the pitch of sound. The amplitude of oscillation is related to the loudness of sound. We'll discuss this in more detail later in the semester. Sound generally involves the superposition of many different pitches, corresponding to describing general oscillations as a superposition of simple oscillations at different frequencies.

The motion of a simple harmonic oscillator is related to a pure tone single frequency in sound. We can quantitatively measure the position of the mass versus time.

relationship between mass and spring constant unit

This strong fit lends credibility to the results of the experiment. This relationship between the force applied to a spring and the amount of stretch was first discovered in by English scientist Robert Hooke. As Hooke put it: Ut tensio, sic vis.

relationship between mass and spring constant unit

Translated from Latin, this means "As the extension, so the force. If we had completed this study about years ago and if we knew some Latinwe would be famous! The spring constant is a positive constant whose value is dependent upon the spring which is being studied. A stiff spring would have a high spring constant. This is to say that it would take a relatively large amount of force to cause a little displacement. The negative sign in the above equation is an indication that the direction that the spring stretches is opposite the direction of the force which the spring exerts.

For instance, when the spring was stretched below its relaxed position, x is downward.

Determine the Spring Constant

The spring responds to this stretching by exerting an upward force. The x and the F are in opposite directions. A final comment regarding this equation is that it works for a spring which is stretched vertically and for a spring is stretched horizontally such as the one to be discussed below.

Force Analysis of a Mass on a Spring Earlier in this lesson we learned that an object that is vibrating is acted upon by a restoring force. The restoring force causes the vibrating object to slow down as it moves away from the equilibrium position and to speed up as it approaches the equilibrium position. It is this restoring force which is responsible for the vibration. So what is the restoring force for a mass on a spring? We will begin our discussion of this question by considering the system in the diagram below.

Is the spring constant k changed when you divide a spring into parts? - Physics Stack Exchange

The diagram shows an air track and a glider. The glider is attached by a spring to a vertical support. There is a negligible amount of friction between the glider and the air track. As such, there are three dominant forces acting upon the glider. These three forces are shown in the free-body diagram at the right. The force of gravity Fgrav is a rather predictable force - both in terms of its magnitude and its direction.

The support force Fsupport balances the force of gravity. It is supplied by the air from the air track, causing the glider to levitate about the track's surface. The final force is the spring force Fspring. As discussed above, the spring force varies in magnitude and in direction.

The frequency is how many oscillations there are per second, having units of hertz Hz ; the period is how long it takes to make one oscillation.

Forces and elasticity - AQA

Velocity in SHM In simple harmonic motion, the velocity constantly changes, oscillating just as the displacement does. When the displacement is maximum, however, the velocity is zero; when the displacement is zero, the velocity is maximum. It turns out that the velocity is given by: Acceleration in SHM The acceleration also oscillates in simple harmonic motion. If you consider a mass on a spring, when the displacement is zero the acceleration is also zero, because the spring applies no force.

When the displacement is maximum, the acceleration is maximum, because the spring applies maximum force; the force applied by the spring is in the opposite direction as the displacement.

The acceleration is given by: Note that the equation for acceleration is similar to the equation for displacement. The acceleration can in fact be written as: All of the equations above, for displacement, velocity, and acceleration as a function of time, apply to any system undergoing simple harmonic motion.