Questions: 2. A block has a mass of 40.0 kg . The coefficient of static friction between the block and the level floor on which it rest is 0.781 . A horizontal force of 424 N is applied to the block to the right. Will the block move?

Solution Steps

The normal force (\( F_N \)) is the force exerted by a surface to support the weight of an object resting on it. For a block of mass \( m = 40.0 \) kg on a level floor, the normal force is equal to the weight of the block, which is given by:

\[ F_N = m \cdot g \]

where \( g \) is the acceleration due to gravity (\( 9.81 \, \text{m/s}^2 \)).

\[ F_N = 40.0 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 392.4 \, \text{N} \]

The maximum static friction force (\( F_{\text{friction, max}} \)) can be calculated using the coefficient of static friction (\( \mu_s \)) and the normal force (\( F_N \)):

\[ F_{\text{friction, max}} = \mu_s \cdot F_N \]

Given \( \mu_s = 0.781 \):

\[ F_{\text{friction, max}} = 0.781 \times 392.4 \, \text{N} = 306.4 \, \text{N} \]

The applied horizontal force (\( F_{\text{applied}} \)) is 424 N. To determine if the block will move, we compare \( F_{\text{applied}} \) to \( F_{\text{friction, max}} \):

\[ F_{\text{applied}} = 424 \, \text{N} \]

Since \( F_{\text{applied}} > F_{\text{friction, max}} \):

\[ 424 \, \text{N} > 306.4 \, \text{N} \]

Final Answer