Questions: Does the 10.0 kg block move across the top of the slab? (Is is static friction or kinetic friction? Justify your answer.

Solution Steps

We need to determine whether a 10.0 kg block moves across the top of a slab. This involves understanding whether the friction between the block and the slab is static or kinetic.

The provided equations are:

1. \( t = \sqrt{\frac{2 \cdot \Delta x_{r}}{a_{r}}} \)
2. \( \Delta x_{\text{girl}} = v_{i} t + \frac{1}{2} a_{g} t^{2} \)
3. \( \Delta x_{g} = \frac{1}{2} a_{g} t^{2} \)

These equations relate to the motion of objects under constant acceleration. However, they do not directly address friction.

To determine if the block moves, we need to compare the force of static friction \( f_s \) with the applied force \( F \). The static friction force is given by: \[ f_s = \mu_s N \] where \( \mu_s \) is the coefficient of static friction and \( N \) is the normal force.

If the applied force \( F \) exceeds \( f_s \), the block will move, and kinetic friction \( f_k = \mu_k N \) will apply.

The normal force \( N \) for the block is: \[ N = mg \] where \( m = 10.0 \, \text{kg} \) and \( g = 9.81 \, \text{m/s}^2 \).

\[ N = 10.0 \times 9.81 = 98.1 \, \text{N} \]

Assume we have the coefficients of static and kinetic friction, \( \mu_s \) and \( \mu_k \). The static friction force is: \[ f_s = \mu_s \times 98.1 \]

If the applied force \( F \) is greater than \( f_s \), the block will move, and kinetic friction will apply.

Final Answer