Friction Practice Problems Solutions | PDF - Free Printable

Problem Statement:

The coefficient of static friction between the surface and a wooden box is \( \mu = 0.55 \). What is the minimum force required to start the block moving?

Solution:

To solve this problem, we need to determine the minimum force required to overcome the static friction acting on the wooden box. Here's the step-by-step reasoning:

#### Step 1: Understand the forces involved
- The static friction force (\( f_s \)) is the force that resists the initiation of motion between two surfaces in contact.
- The maximum static friction force is given by:
\[
f_s^{\text{max}} = \mu_s F_n
\]
where:
- \( \mu_s \) is the coefficient of static friction,
- \( F_n \) is the normal force acting on the object.

- To start the block moving, the applied force (\( F_{\text{applied}} \)) must be at least equal to the maximum static friction force (\( f_s^{\text{max}} \)).

#### Step 2: Relate the normal force to the weight of the block
- The normal force (\( F_n \)) is the force exerted by the surface on the block, which is equal to the weight of the block if the block is on a horizontal surface.
- The weight of the block is given by:
\[
W = mg
\]
where:
- \( m \) is the mass of the block,
- \( g \) is the acceleration due to gravity (\( g = 9.8 \, \text{m/s}^2 \)).

- Therefore, the normal force is:
\[
F_n = mg
\]

#### Step 3: Calculate the maximum static friction force
- Using the formula for maximum static friction:
\[
f_s^{\text{max}} = \mu_s F_n
\]
Substitute \( F_n = mg \):
\[
f_s^{\text{max}} = \mu_s (mg)
\]

#### Step 4: Determine the minimum applied force
- To start the block moving, the applied force must be at least equal to the maximum static friction force:
\[
F_{\text{applied}} \geq f_s^{\text{max}}
\]
Therefore:
\[
F_{\text{applied}} = \mu_s mg
\]

#### Step 5: Plug in the given values
- The coefficient of static friction is given as \( \mu_s = 0.55 \).
- The mass of the wooden box is not explicitly stated in the problem. However, since the problem asks for the minimum force to start the block moving, we can express the answer in terms of the mass \( m \).

#### Final Expression
The minimum force required to start the block moving is:
\[
F_{\text{applied}} = \mu_s mg = 0.55 \cdot m \cdot 9.8
\]
Simplify:
\[
F_{\text{applied}} = 5.39m
\]

Final Answer:

\[
\boxed{5.39m}
\]

This expression gives the minimum force required to start the block moving, where \( m \) is the mass of the wooden box in kilograms. If the mass \( m \) were provided, you could substitute it to get a numerical value.