A 25 kg box is released on a 27° inclined plane with a coefficient of kinetic friction of 0. Calculate the acceleration of the box as it slides down the inclined plane. You must dr... A 25 kg box is released on a 27° inclined plane with a coefficient of kinetic friction of 0. Calculate the acceleration of the box as it slides down the inclined plane. You must draw the FREE-BODY DIAGRAM and follow the procedure discussed in class to receive full credit. Read more

Steps to Solve

1. Identify Forces Acting on the Box

The forces acting on the box include gravitational force, normal force, and frictional force. The gravitational force can be calculated as:

$$ F_g = m \cdot g $$

where:

• ( m = 25 \text{ kg} )
• ( g = 9.81 \text{ m/s}^2 )

2. Calculate the Gravitational Force

Using the values from the previous step:

$$ F_g = 25 \text{ kg} \cdot 9.81 \text{ m/s}^2 = 245.25 \text{ N} $$

3. Resolve the Gravitational Force Along the Incline

The component of the gravitational force acting down the incline is:

$$ F_{\text{parallel}} = F_g \cdot \sin(\theta) $$

where ( \theta = 27^\circ ).

Calculate:

$$ F_{\text{parallel}} = 245.25 \text{ N} \cdot \sin(27^\circ) $$

4. Calculate Normal Force

The normal force acts perpendicular to the incline and can be calculated as:

$$ F_{\text{normal}} = F_g \cdot \cos(\theta) $$

Calculate:

$$ F_{\text{normal}} = 245.25 \text{ N} \cdot \cos(27^\circ) $$

5. Determine the Frictional Force

With the coefficient of kinetic friction (( \mu_k = 0 )), the frictional force is:

$$ F_{\text{friction}} = \mu_k \cdot F_{\text{normal}} $$ $$ F_{\text{friction}} = 0 \cdot F_{\text{normal}} = 0 $$

6. Calculate the Net Force Acting on the Box

The net force (( F_{\text{net}} )) acting on the box is:

$$ F_{\text{net}} = F_{\text{parallel}} - F_{\text{friction}} $$

Since ( F_{\text{friction}} = 0 ):

$$ F_{\text{net}} = F_{\text{parallel}} $$

7. Calculate the Acceleration of the Box

Using Newton's second law, the acceleration (( a )) can be expressed as:

$$ a = \frac{F_{\text{net}}}{m} $$

Substitute ( F_{\text{net}} = F_{\text{parallel}} ):

$$ a = \frac{F_{\text{parallel}}}{25 \text{ kg}} $$

8. Final Calculation

After substituting ( F_{\text{parallel}} ) values, calculate the final acceleration.