Question

A 175 g glider on a horizontal, frictionless air track is attached to a fixed ideal spring with force constant 155 n/m . at the instant you make measurements on the glider, it is moving at 0.815 m / s and is 3.00 cm from its equilibrium point. use energy conservation to find (a) the amplitude of the motion and (b) the maximum speed of the glider. (c) what is the angular frequency of the oscillations?

Answer 1

To find the amplitude of the motion, use the equation of energy conservation. The maximum speed of the glider can be found using the equation v = sqrt(2*(PE/m)). The angular frequency of the oscillations can be calculated using the equation omega = sqrt(k/m).

Step-by-step explanation:

To find the amplitude of the motion, we can use the equation of energy conservation. At its maximum displacement, all of the initial kinetic energy of the glider will have been converted to potential energy stored in the spring. The potential energy of the spring at maximum displacement is given by 0.5k(A^2), where k is the force constant and A is the amplitude. Therefore, A = sqrt((2KE)/k), where KE is the initial kinetic energy.

To find the maximum speed of the glider, we can use the equation v = sqrt(2*(PE/m)), where v is the velocity of the glider, PE is the potential energy of the spring at maximum displacement, and m is the mass of the glider. Plugging in the values, we can find the maximum speed.

The angular frequency of the oscillations can be calculated using the equation omega = sqrt(k/m), where omega is the angular frequency, k is the force constant, and m is the mass of the glider. Plugging in the values, we can find the angular frequency.