Position of glider on an air track

• brunettegurl
In summary, an air-track glider attached to a spring is pulled to the right and released from rest at t=0.00 s. It then oscillates with a period of 11.1 s and a maximum speed of 44.7 cm/s. The amplitude of the oscillation is 7.90e-01 m and the glider's position at t=0.555 s can be solved by setting the phase constant to zero in the equation x(t)= Acos (\omegat+\phi). This is the only way to solve for the position, as it was released with no initial velocity and was not at its equilibrium point.
brunettegurl

Homework Statement

An air-track glider is attached to a spring. The glider is pulled to the right and released from rest at t=0.00 s. It then oscillates with a period of 11.1 s and a maximum speed of 44.7 cm/s. What is the amplitude of the oscillation? (answer A= 7.90e-01 m)
What is the glider's position at t=0.555 s?

Homework Equations

x(t)= Acos ($$\omega$$t+$$\phi$$)

The Attempt at a Solution

so i solved this question already and got it right by assuming that the phase constant to be zero and solving for x. I was wondering if there was another way to solve for the position??

brunettegurl said:

Homework Statement

An air-track glider is attached to a spring. The glider is pulled to the right and released from rest at t=0.00 s. It then oscillates with a period of 11.1 s and a maximum speed of 44.7 cm/s. What is the amplitude of the oscillation? (answer A= 7.90e-01 m)
What is the glider's position at t=0.555 s?

Homework Equations

x(t)= Acos ($$\omega$$t+$$\phi$$)

The Attempt at a Solution

so i solved this question already and got it right by assuming that the phase constant to be zero and solving for x. I was wondering if there was another way to solve for the position??

No, that's the only way to do it.
Do you see why it is correct to set the phase constant equal to zero here?

i'm assuming it had to with the fact that when the glider was released it waas not at it's equilibrium point..is that a correct assumption??

brunettegurl said:
i'm assuming it had to with the fact that when the glider was released it waas not at it's equilibrium point..is that a correct assumption??

It's part of it but that's not sufficient.
We have to know that it was released from the right of its equilibrim position *and* that it was released with no initial velocity (it was not kicked one way or another). That tells us that it starts with x equal to the maximum amplitude, so x(t) is a pure cosine curve, with no phase constant.

For example, it it had been released from rest but at the left of the equilibrium position, we would have needed to use pi (or -pi) for the phase constant. If it had had an initial velocity, the phase constant wold be some other value.

if it was released from rest at the left of the equilibrium how can we determine if it is pi or -pi without any additional information??..and thank you for answering my questions

brunettegurl said:
if it was released from rest at the left of the equilibrium how can we determine if it is pi or -pi without any additional information??..and thank you for answering my questions

You are welcome.

I said pi or -pi because it makes no difference (since a difference of 2pi in the phase constant does not change anything to a cosine function). Any calculation done with pi or -pi would give the same answer.

Last edited:
ok thanks

1. What is the purpose of an air track?

The purpose of an air track is to study the motion of objects with minimal friction. This allows for more accurate measurements and observations of an object's position and velocity.

2. How does the position of a glider on an air track affect its motion?

The position of a glider on an air track can affect its motion in several ways. If the glider is placed at an angle, it will experience a component of gravity pulling it down the track. If the glider is placed at different points on the track, it may experience different amounts of air resistance, affecting its velocity and acceleration.

3. Can the position of a glider on an air track be changed?

Yes, the position of a glider on an air track can be changed. This can be done manually by physically moving the glider, or by adjusting the angle or starting point of the track. It can also be changed through external forces, such as applying a force to the glider or changing the air pressure in the track.

4. How is the position of a glider on an air track measured?

The position of a glider on an air track can be measured using a variety of tools, such as a motion detector or photogate. These devices use sensors to track the position of the glider as it moves along the track, providing real-time data on its position, velocity, and acceleration.

5. Why is the position of a glider on an air track important in scientific experiments?

The position of a glider on an air track is important in scientific experiments because it allows for more precise and controlled measurements of an object's motion. By minimizing friction and external forces, scientists can isolate and study the effects of different variables on an object's position and motion, leading to a better understanding of the laws of physics.

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