Does the Velocity of the Center of Mass Consider the Spring and m2?

Thread starter Zamarripa
Start date Jun 7, 2019
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Spring Two masses

In summary, the relationship between two masses and one spring is described by Hooke's Law, which states that the force applied by a spring is directly proportional to the displacement of the spring from its equilibrium position. The spring constant, represented by the symbol k, determines the stiffness of the spring and affects the system by determining the magnitude of the force applied for a given displacement. Two masses attached to a spring can have different displacements, as the displacement is determined by individual mass and the force applied by the spring. The motion of the two masses differs when the spring is compressed versus stretched, with opposite directions of motion when compressed and the same direction when stretched. The system can also be affected by external forces such as gravity or friction, which can

Jun 7, 2019

Zamarripa

Homework Statement: Two masses m1 and m2 are at rest and joined by a spring of length l = 0.5m, as shown in the figure. There is no friction with the surface. In a given moment, an impulse with velocity v0 = 0.2m /s is given to the mass m1 only.

Relevant Equations: Calculate the velocity of the center of mass immediately after m1 has moved
Calculate the position of the center of mass after a time t = 4.0s

I want to know if my solution is correct:

The velocity of the center of mass immidiately after m1 has moved is just
v_cm=m₁v₁ /(m1+m2)

I thing that i have to consider the spring and the m2

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Jun 7, 2019

haruspex

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Zamarripa said:

The velocity of the center of mass immidiately after m1 has moved is just
vcm=m1v1 /(m1+m2)

Yes.

Zamarripa said:

I thing that i have to consider the spring and the m2

For the second part? Maybe... or perhaps not.

1. What is the relationship between two masses and one spring?

The relationship between two masses and one spring is described by Hooke's Law, which states that the restoring force of a spring is directly proportional to the displacement of the spring from its equilibrium position. In other words, the more a spring is stretched or compressed, the greater the force it exerts.

2. How does the mass affect the spring's behavior?

The mass of an object affects the behavior of a spring by changing the force required to stretch or compress the spring. Heavier masses will require a greater force to displace the spring, while lighter masses will require less force. This is because the mass of an object is directly related to its inertia, or resistance to change in motion.

3. What is the equation for the motion of two masses connected by a spring?

The equation for the motion of two masses connected by a spring is given by Newton's Second Law of Motion: F = ma. In this case, the force (F) is the restoring force of the spring, the mass (m) is the combined mass of the two masses, and the acceleration (a) is the rate of change of velocity of the masses.

4. How does the spring constant affect the system of two masses and one spring?

The spring constant, denoted by k, is a measure of the stiffness of a spring. A higher spring constant means that a greater force is required to displace the spring, resulting in a stronger restoring force. This means that a higher spring constant will result in a faster oscillation of the two masses connected by the spring.

5. Can two masses connected by a spring have different amplitudes?

Yes, two masses connected by a spring can have different amplitudes. The amplitude of an oscillation is the maximum displacement from the equilibrium position. The amplitude of a mass-spring system is affected by factors such as the initial displacement of the masses, the spring constant, and the mass of the objects. Therefore, it is possible for the two masses to have different amplitudes depending on these factors.