Final answer:
To calculate the work done by friction during the block's descent on a spring, the potential energy lost due to gravity and the elastic potential energy when the spring is stretched are considered. The difference between the two should give the work done by friction, which comes out as -0.45 J. None of the provided answer choices match the calculated value, suggesting there could be an error in the question or answer options.
Step-by-step explanation:
To find out how much work is done by friction during the block's descent, we need to consider the energy changes in the system. The potential energy lost by the block due to gravity is transformed into elastic potential energy in the spring and work done by friction.
The potential energy lost (PE) is given by PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height. Using m = 2.0 kg, g = 9.81 m/s², and h = 17 cm = 0.17 m, we get:
PE = 2.0 kg * 9.81 m/s² * 0.17 m ≈ 3.34 J
The elastic potential energy stored in the spring (EPE) when the spring is stretched by x is given by EPE = 0.5 * k * x², where k is the spring constant. With k = 200 N/m and x = 0.17 m, we get:
EPE = 0.5 * 200 N/m * (0.17 m)² ≈ 2.89 J
Since the total mechanical energy is conserved if there is no friction, any difference between the initial potential energy and elastic potential energy must be the work done by friction (Wf). Thus:
Wf = PE - EPE ≈ 3.34 J - 2.89 J ≈ 0.45 J
However, we must consider the direction of work done by friction. Since friction acts to oppose motion, the work done by friction is negative. Therefore, the correct answer is:
Wf = -0.45 J
None of the options given match the correct calculation. Therefore, based on the information and calculations presented, there might be an error in the question or the options provided.