The maximum height of the block slides is approximately 0.041 meters (4.1 cm).
How can solve for the maximum height the block slides?
The block compresses the spring, storing potential energy:
PE_spring = (1/2) * k * x² = (1/2) * 14 N/m * (0.032 m)² ≈ 0.007 J
Initial kinetic energy:
At the bottom of the spring, the block has zero kinetic energy due to its initial rest.
Final potential energy:
At the bottom of the incline, the block has gravitational potential energy:
PE_gravity = m * g * h, where:
m = 11 g (converted to kg later)
g = 9.81 m/s² (acceleration due to gravity)
h = unknown height the block reaches
Final kinetic energy:
Once again, the block has zero kinetic energy at the bottom of the incline.
The friction force (F_friction) acts against the block's motion on the incline and dissipates energy.
We need to account for the work done by friction (W_friction).
Equating the total energy before and after:
Initial PE_spring + Initial KE = Final PE_gravity + Final KE + W_friction
0.007 J + 0 = m * g * h + 0 - Ha * mg * sin(25°)
Rearranging for h:
h = (0.007 J + Ha * mg * sin(25°)) / (mg)
Substitute m in kg:
h = (0.007 J + 0.3 * 0.011 kg * 9.81 m/s² * sin(25°)) / (0.011 kg * 9.81 m/s²)
h ≈ 0.041 m
Therefore, the maximum height the block slides is approximately 0.041 meters (4.1 cm).