A 68 kg crate is dragged across a floor by pulling on a rope attached to the crate and inclined `15^(@)` above the horizontal.
(a) If the coefficient of static friction is 0.50, what minimum force magnitude is required from the rope to start the crate moving?
(b) If `mu_(k)=0.35`, what is the magnitude of the initial acceleration of the crate?

Explanation

To solve the problem step by step, we will break it down into parts (a) and (b) as given in the question.

### Part (a): Minimum Force to Start Moving the Crate

1. **Identify the Forces Acting on the Crate**:
- Weight of the crate (W) = \( mg = 68 \, \text{kg} \times g \) (where \( g \approx 9.8 \, \text{m/s}^2 \))
- Normal force (N)
- Applied force (F) at an angle of \( 15^\circ \) above the horizontal
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