a 0.30 kg mass attached to a spring is pulled back horizontally across a table so that the potential energy of the system is increased from zero to 120 J. Ignoring friction what is the kinetic energy of the system after the mass is released and has moved to a point where the potential energy has decreased to 70 J.
KE=120-70
Well, isn't this springing into action! Let's hop right into it.
First, we need to calculate the change in potential energy. We know that the initial potential energy is zero and the final potential energy is 70 J. So, the change in potential energy is 70 J - 0 J, which gives us 70 J.
Now, we need to remember that the change in potential energy is equal to the change in kinetic energy. So, the change in kinetic energy is also 70 J.
Since the initial kinetic energy is zero (the mass is pulled back horizontally), we can conclude that the final kinetic energy is also 70 J.
Voila! The kinetic energy of the system after the mass is released and has moved to a point where the potential energy has decreased to 70 J is 70 J.
Keep on springing forward with those physics questions!
To find the kinetic energy of the system after the mass is released and has moved to a point where the potential energy has decreased to 70 J, we need to use the conservation of mechanical energy.
The total mechanical energy of the system remains constant when there is no external work done on the system, so we can equate the initial potential energy to the final kinetic energy.
Potential Energy (initial) + Kinetic Energy (initial) = Potential Energy (final) + Kinetic Energy (final)
The initial potential energy is 120 J, and the final potential energy is 70 J. The initial kinetic energy is zero as the mass is at rest.
120 J + 0 = 70 J + Kinetic Energy (final)
Now we can calculate the final kinetic energy:
Kinetic Energy (final) = 120 J - 70 J
Kinetic Energy (final) = 50 J
Therefore, the kinetic energy of the system after the mass is released and has moved to a point where the potential energy has decreased to 70 J is 50 J.
To find the kinetic energy of the system after the mass is released, we need to consider the conservation of mechanical energy. The total mechanical energy of the system remains constant when there is no external work done on the system (ignoring friction). It can be stated as:
Initial potential energy + Initial kinetic energy = Final potential energy + Final kinetic energy
Given:
Initial potential energy (Ui) = 120 J
Final potential energy (Uf) = 70 J
We need to find the final kinetic energy (Kf).
Initial kinetic energy (Ki) can be assumed to be zero because the mass is pulled back horizontally across the table, implying no initial velocity.
Using the conservation of mechanical energy equation, we have:
Ui + Ki = Uf + Kf
Since Ki is zero:
Ui = Uf + Kf
Rearranging the equation to isolate Kf, we have:
Kf = Ui - Uf
Substituting the given values:
Kf = 120 J - 70 J
Kf = 50 J
Therefore, the kinetic energy of the system after the mass is released and has moved to a point where the potential energy has decreased to 70 J is 50 J.