Energy Calculations: Step 3C

1. Initial Gravitational Potential Energy (U_g,initial)

Using the formula: U_g = mgh

• Mass (m): 0.257 kg
• Gravity (g): 10 m/s2
• Initial Height (h): 0.09 m

Calculation: U_g,initial = 0.257 ¡Ñ 10 ¡Ñ 0.09 = 0.2313 J

2. Final Gravitational Potential Energy (U_g,final)

As the cart returns to the same height, U_g,final = U_g,initial = 0.2313 J.

3. Spring Potential Energy (U_s,final)

Using the formula: U_s = ? k (£Gx)2

• Change in Spring Length (£Gx): 0.041 m
• Spring Constant (k): (To be calculated in Step 3D)

Substitute k into the formula once known.

4. Work by Friction (W_friction)

Using the formula: W_friction = U_g,initial - (U_s,final + U_g,final)

Substitute:
W_friction = 0.2313 - (U_s,final + 0.2313)