A spring (k = 600 N/m) is placed in a vertical position with its lower end supported by a horizontal surface. A 2.0-kg block that is initially 0.40 m above the upper end of the spring is dropped from rest onto the spring. What is the kinetic energy of the block at the instant it has fallen 0.50 m (compressing the spring 0.10 m)?
A) 5.3 J
B) 6.8 J
C) 6.3 J
D) 5.8 J
E) 6.5 J

Question

Quizplus · Accepted Answer

The kinetic energy of the block can be found by calculating the difference between the initial potential energy and the sum of the spring potential energy and gravitational potential energy at the point of 0.50 m descent. Initially, the block has gravitational potential energy $U_g = mgh = 2.0 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 0.50 \, \text{m} = 9.8 \, \text{J}$. The spring potential energy when compressed by 0.10 m is $U_s = \frac{1}{2}kx^2 = \frac{1}{2} \times 600 \, \text{N/m} \times (0.10 \, \text{m})^2 = 3.0 \, \text{J}$. The gravitational potential energy at the new height (0.10 m lower than the original position due to spring compression) is $U_g' = mgh' = 2.0 \, \text{kg} \times 9.8 \, \text{m/s}^2 \times 0.10 \, \text{m} = 1.96 \, \text{J}$. The kinetic energy is then $KE = U_g - (U_s + U_g') = 9.8 \, \text{J} - (3.0 \, \text{J} + 1.96 \, \text{J}) = 4.84 \, \text{J}$. However, given the options provided do not match this calculation, it appears there was a mistake in the calculation process or interpretation of the options. The correct approach involves considering the total mechanical energy conservation, but without the exact steps leading to the options provided, there's a discrepancy in the calculation presented here. The correct approach should involve calculating the initial potential energy and subtracting the energy stored in the spring and the remaining gravitational potential energy to find the kinetic energy at the point of interest.

A Spring (K = 600 N/m) Is Placed in a Vertical