which formula would be used to directly calculate the kinetic energy of an object with mass m bouncing up and don on a spring with spring constant k?
is it KE=1/2kx^2?
or...KE=1/2mv^2?
The correct formula to directly calculate the kinetic energy of an object bouncing up and down on a spring with mass 'm' and spring constant 'k' is KE = 1/2kx^2.
To understand why this formula is used, let's break it down step by step:
1. The potential energy of a spring is given by the formula PE = 1/2kx^2, where 'k' represents the spring constant and 'x' represents the displacement from the equilibrium position.
2. When the object is at the equilibrium position or bouncing up and down (considering no external forces like gravity), all of the potential energy is converted into kinetic energy.
3. Therefore, the kinetic energy at any given point can be equated to the potential energy at that point. So, KE = PE.
4. Since the potential energy of the spring is given by PE = 1/2kx^2, the kinetic energy can also be expressed as KE = 1/2kx^2.
Therefore, the correct formula for the kinetic energy of an object bouncing up and down on a spring is KE = 1/2kx^2. The formula KE = 1/2mv^2 represents the kinetic energy of an object in general, but when dealing specifically with a spring, the first formula is more appropriate.
Neither.
KE + (1/2) kx^2 = constant, or
(1/2 m V^2 + (1/2) k X^2 = constant, or
(1/2) k Xmax^2 = (1/2) M Vmax^2 is the consnant
The Vmax and Xmax will not occur at the same time. Maximum deflection Xmax occurs when V = 0, and vice versa