Section 3.8: Advanced Problems
This section presents challenging work and energy problems that combine multiple concepts, forces, and varying conditions. It prepares students for high-level problem-solving and critical thinking.
Example 1
A 2 kg block slides down a ramp with height 3 m and length 5 m. Friction coefficient is 0.1. Find speed at bottom.
Step 1: Identify system and forces (gravity, friction)
Step 2: Use work-energy theorem: \( W_\text{net} = \Delta K \)
Step 3: \( W_\text{gravity} = m g h = 2*9.8*3 = 58.8\,\text{J} \)
Friction work: \( W_f = f_k d = \mu_k m g \cos\theta * 5 \) (calculate θ from ramp geometry)
Step 4: \( K_f = W_\text{net} = 58.8 - W_f \Rightarrow v = \sqrt{2 K_f/m} \)
Advanced Practice Problems
- A 3 kg box slides down a 4 m ramp with friction µk=0.2. Compute final speed.
- A 5 kg object is pulled by a force of 20 N over 6 m at 30°. Find work done and speed if friction is 5 N.
- A roller coaster car of 400 kg starts from 10 m height. Compute speed at 2 m if friction work is 500 J.
- A 2 kg ball rolls down a ramp of height 2 m and radius of curvature 0.5 m. Find speed at bottom and centripetal acceleration.
- A 4 kg block slides down a ramp with varying slope. Friction coefficient changes from 0.1 to 0.2. Determine final kinetic energy.