Questions: Un corpo è in equilibrio su un piano inclinato. La forza equilibrante ha modulo 122 N e la forza premente perpendicolare al piano ha modulo 212 N. - Calcola il modulo della forza-peso. - Quanto vale la massa del corpo? [245 N, 25 kg]

Solution Steps

We are given a body in equilibrium on an inclined plane. The equilibrant force (parallel to the plane) is 122 N, and the normal force (perpendicular to the plane) is 212 N. We need to find the weight of the body and its mass.

The weight of the body can be found using the Pythagorean theorem since the equilibrant force and the normal force are perpendicular components of the weight.

\[ F_{\text{weight}} = \sqrt{(F_{\text{equilibrant}})^2 + (F_{\text{normal}})^2} \]

Substituting the given values:

\[ F_{\text{weight}} = \sqrt{(122 \, \text{N})^2 + (212 \, \text{N})^2} \]

\[ F_{\text{weight}} = \sqrt{14884 + 44944} \]

\[ F_{\text{weight}} = \sqrt{59828} \]

\[ F_{\text{weight}} \approx 244.6 \, \text{N} \]

The mass of the body can be found using the relationship between weight and mass:

\[ F_{\text{weight}} = m \cdot g \]

where \( g \approx 9.81 \, \text{m/s}^2 \). Solving for \( m \):

\[ m = \frac{F_{\text{weight}}}{g} \]

Substituting the calculated weight:

\[ m = \frac{244.6 \, \text{N}}{9.81 \, \text{m/s}^2} \]

\[ m \approx 24.93 \, \text{kg} \]

Final Answer