which of the following formulas would be used to directly calculate the KE of a mass bouncing up and down on a spring?
1) KE = 1/2kx^2
2) KE = -1/2kx^2
3)KE = 1/2mv^2
4)KE= -1/2mv^2
Would the correct answer be 1)?
Yes, the correct answer would be 1) KE = 1/2kx^2.
To understand why, let's break down each option:
1) KE = 1/2kx^2
This formula calculates the kinetic energy (KE) by using the spring constant (k) and the displacement (x) of the mass. It implies that the energy is directly proportional to the square of the displacement of the mass.
2) KE = -1/2kx^2
This formula has a negative sign, which implies that the kinetic energy is negative. In the context of a bouncing mass on a spring, kinetic energy cannot be negative. Therefore, this formula is incorrect.
3) KE = 1/2mv^2
This formula calculates the kinetic energy (KE) by using the mass (m) and the velocity (v). While this formula is commonly used to calculate kinetic energy, it doesn't directly apply to a mass bouncing up and down on a spring. Velocity is not directly linked to the properties of the spring in this case.
4) KE= -1/2mv^2
Similar to option 2, this formula has a negative sign implying negative kinetic energy. Therefore, it is incorrect in the context of a bouncing mass on a spring.
Overall, option 1) is the correct formula as it properly considers the mass and displacement in relation to the spring constant.