What do you think? Can you think of an expression for how fast the compression of the spring is growing?ubergewehr273 said:
I think when mass m stops moving relative to the ground is when max compression occurs.Orodruin said:
This is not correct. Can you give an expression for the spring length as a function of the positions of the masses?ubergewehr273 said:
If mass m moves by x1 wrt mass M and mass M moves by x2 wrt ground then spring compression will be x1-x2.Orodruin said:
So compression is maximum when both masses have equal velocities.Orodruin said:
Yes. If the upper block moves faster, the string will be compressing, if it is moving slower it will be decompressing. This should give you enough information to solve your original question.ubergewehr273 said:
An impulse is a force acting over a short period of time, resulting in a change in momentum. In the case of a spring, an impulse can cause the spring to compress or extend, depending on the direction of the force.
An impulse can affect the motion of a spring by changing its velocity and/or position. If the impulse is in the same direction as the current motion of the spring, it will increase the velocity and extend the spring further. If the impulse is in the opposite direction, it will decrease the velocity and compress the spring.
The magnitude of an impulse on a spring is affected by the force applied and the duration of the force. A greater force or a longer duration will result in a larger impulse. The mass of the spring and any external factors, such as friction, may also affect the magnitude of the impulse.
Yes, the elasticity of a spring can affect the impulse. A more elastic spring will be able to absorb and release a greater amount of energy, resulting in a larger impulse. On the other hand, a less elastic spring may not be able to handle as much energy and will have a smaller impulse.
The impulse-momentum theorem states that the change in momentum of an object is equal to the impulse acting on it. This can be applied to the motion of a spring by considering the initial and final momentum of the spring after an impulse is applied. By equating these two values and solving for the unknown variables, the motion of the spring can be accurately modeled.
