Question

Starting with one of Newton's laws and your free body diagram, derive an expression for the normal force exerted on the block by floor. Starting with one of Newton's laws and your free body diagram, derive an expression for the coefficient of kinetic friction Create a qualitative graph of the speed v of the block as a function of time t. Create a qualitative graph of the position x of the block as a function of time t. Derive and expression for the magnitude of the force F1 when the block loses contact with the surface. Call this quantity Derice an expression for the magnitude of the greatest acceleration Image the mass of the block doubles. What does this do to your answers for Remember to answer with:

1. Starting with one of Newton's laws and your free body diagram, derive an expression for the normal force exerted on the block by floor.

  - Assess you answer in the following way: If you let       \(\theta\)   = 0, what does your solution predict for the normal force? Does this make physical sense?

2. Starting with one of Newton's laws and your free body diagram, derive an expression for the coefficient of kinetic friction       \(\mu_{k}\)    between the block and the floor.

   - Assess your answer by determining its units. Are these the correct units for the coefficient of friction?

3. Create a qualitative graph of the speed v of the block as a function of time t.

4. Create a qualitative graph of the position x of the block as a function of time t.

    

5.Derive and expression for the magnitude of the force F1 when the block loses contact with the surface. Call this quantity       \(F_{1max}\)      \(\theta\)   , and fundamental constants.

6. Derice an expression for the magnitude of the greatest acceleration       \(a_{max}\)    that the block will have the instant it loses contact with the ground. Express it in terms of       \(\theta\)   and fundamental constants.

7. Image the mass of the block doubles. What does this do to your answers for       \(F_{1max}\)    and       ? Does this make physical sense?

Remember to answer with:

Model %u2013 Simplify the situation with a model that captures the essential features.

Visualize %u2013 Draw sketches, diagrams, graphs, etc. to visualize the problem.

Solve %u2013 Starting with basic physics principles, work step-by-step to the solution.

Assess %u2013 Clearly state your answer, and find a way to assess if it is reasonable.

Answer 1