Question

Как найти массу тела зная формулу силы тяжести

Answer 1

Fтяж=mg
т.е. m=F/g
__________

Answer 2

Finding Mass Using the Formula for Gravitational Force

To find the mass of an object using the formula for gravitational force, you can use the following steps:

1. Understanding the Formula: The formula for gravitational force is given by: \[ F = \frac{{G \cdot m_1 \cdot m_2}}{{r^2}} \] where: - \( F \) = gravitational force - \( G \) = gravitational constant - \( m_1 \) and \( m_2 \) = masses of the two objects - \( r \) = distance between the centers of the masses

2. Rearranging the Formula: You can rearrange the formula to solve for the mass of the object: \[ m_2 = \frac{{F \cdot r^2}}{{G \cdot m_1}} \]

3. Using Known Values: If you know the gravitational force acting on the object and the distance between the centers of the masses, you can plug these values into the rearranged formula to calculate the mass of the object.

Example Calculation

Let's consider an example where the gravitational force acting on an object is 17 N and the distance between the centers of the masses is 5 m. The gravitational constant \( G \) is approximately \( 6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2 \), and the mass of the Earth is approximately \( 5.972 \times 10^{24} \, \text{kg} \).

Using the rearranged formula: \[ m_2 = \frac{{F \cdot r^2}}{{G \cdot m_1}} \] \[ m_2 = \frac{{17 \, \text{N} \cdot (5 \, \text{m})^2}}{{6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2 \cdot 5.972 \times 10^{24} \, \text{kg}}} \]

Calculating \( m_2 \): \[ m_2 \approx 0.5 \, \text{kg} \]

So, the mass of the object is approximately 0.5 kg.

Conclusion

By rearranging the formula for gravitational force, you can calculate the mass of an object when the gravitational force and the distance between the centers of the masses are known.