Section 3.6: Problem-Solving Strategies

This section provides strategies to approach work and energy problems effectively. Using systematic methods helps reduce mistakes and improves understanding.

Step 1: Identify the System

Determine the object(s) involved and the forces acting on them.

Step 2: Choose the Appropriate Principle

Decide whether to use work formulas, kinetic energy, potential energy, or the work-energy theorem.

Step 3: Set Up Equations

Express work and energy in mathematical form, and relate initial and final states.

Step 4: Solve for Unknowns

Use algebra to solve for quantities like speed, height, or work done.

Step 5: Check Results

Verify units, order of magnitude, and consistency with physical intuition.

Example 1

A 3 kg object slides down a frictionless 5 m high ramp. Use conservation of energy to find speed at the bottom.

Step 1: System = object (3 kg)

Step 2: Use conservation of energy: \( U_i + K_i = U_f + K_f \)

Step 3: \( K_f = m g h = 3 * 9.8 * 5 = 147 \, \text{J} \)

Step 4: \( K_f = 1/2 m v^2 \Rightarrow v = \sqrt{2*147/3} \approx 9.9 \, \text{m/s} \)

Step 5: Units and magnitude make sense.

Practice Problems

  1. A 2 kg object slides down a frictionless 4 m ramp. Find final speed using energy conservation.
  2. A 5 kg object is lifted 3 m vertically. Compute work done by gravity.
  3. An object of 3 kg accelerates on a horizontal frictionless surface with a 15 N force. Find work done over 2 m.
  4. A 1 kg ball falls from 10 m. Use energy conservation to find speed just before impact.
  5. A 4 kg object slides down a ramp with 2 m height and friction of 5 N. Find speed at bottom.
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