To determine the force of friction experienced by the crate, we can follow these steps:
1. Identify the Given Values:
- The weight of the crate, [tex]\( W \)[/tex], is given as 343 Newtons (N).
- The coefficient of kinetic friction, [tex]\( \mu_k \)[/tex], is provided as 0.30.
2. Understand the Relevant Formula:
The formula to calculate the force of friction, [tex]\( f_k \)[/tex], is:
[tex]\[
f_k = \mu_k \times N
\][/tex]
where:
- [tex]\( f_k \)[/tex] is the force of kinetic friction.
- [tex]\( \mu_k \)[/tex] is the coefficient of kinetic friction.
- [tex]\( N \)[/tex] is the normal force.
3. Compute the Normal Force:
In this scenario, the normal force [tex]\( N \)[/tex] is equal to the weight of the crate since the crate is on a horizontal surface with no additional vertical forces acting on it. Thus:
[tex]\[
N = W = 343 \text{ N}
\][/tex]
4. Substitute the Values into the Formula:
We can plug the given values into the formula for the force of kinetic friction:
[tex]\[
f_k = \mu_k \times N = 0.30 \times 343 \text{ N}
\][/tex]
5. Calculate the Force of Friction:
Performing the multiplication gives:
[tex]\[
f_k = 0.30 \times 343 \text{ N} = 102.90 \text{ N}
\][/tex]
Hence, the force of friction experienced by the crate is approximately [tex]\( 102.90 \)[/tex] Newtons.
