Question

What is the formula to calculate the force required to start moving a 30kg box across a wooden floor with a coefficient of static friction of 0.55?

Answer 1

To calculate the force required to start moving a box across a surface, we use the formula for static friction. The force of static friction can be calculated using the formula:

\[
F_s = \mu_s \cdot N
\]

where:
- \( F_s \) is the force of static friction,
- \( \mu_s \) is the coefficient of static friction,
- \( N \) is the normal force.

For a box resting on a flat horizontal surface, the normal force \( N \) is equal to the weight of the box, which is calculated as:

\[
N = m \cdot g
\]

where:
- \( m \) is the mass of the box (in kg),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)).

Now, substituting the values into the equations:

1. First, calculate the normal force \( N \):

\[
N = 30 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 = 294.3 \, \text{N}
\]

2. Now, calculate the force of static friction \( F_s \):

\[
F_s = \mu_s \cdot N
\]
\[
F_s = 0.55 \cdot 294.3 \, \text{N}
\]
\[
F_s \approx 162.865 \, \text{N}
\]

Therefore, the force required to start moving the 30 kg box across the wooden floor is approximately **162.87 N**.