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Definition: This calculator computes the mass of a second body (\( m_2 \)) based on the mass and acceleration of a first body (\( m_1 \), \( a_1 \)) and the acceleration of the second body (\( a_2 \)), assuming equal forces are applied to both bodies.
Purpose: It is used in classical mechanics to determine the unknown mass of one body when the force applied to two bodies is the same, applicable in physics problems involving Newton’s second law.
The calculator uses the relationship:
Where:
Explanation: Enter the acceleration of body 1, mass of body 1, and acceleration of body 2 in the chosen units, and the calculator computes the mass of body 2. Results are displayed with 5 decimal places, using scientific notation if the value exceeds 100,000 or is less than 0.0001. For default inputs (\( a_1 = 2 \, \text{m/s}^2 \), \( m_1 = 5 \, \text{kg} \), \( a_2 = 4 \, \text{m/s}^2 \)), the calculated mass \( m_2 \) is 2.50000 kg.
Details: Calculating the mass from equal force helps in understanding the relationship between mass, force, and acceleration, aiding in solving physics problems involving multiple objects under the same force, such as in mechanics and dynamics.
How do I find the mass of a body using equal force?
Measure the mass and acceleration of one body and the acceleration of the second body. Compute the mass of the second body using the formula \( m_2 = \frac{m_1 \cdot a_1}{a_2} \). The result will be in kilograms.
What does equal force imply in this context?
Equal force implies that the same force is applied to both bodies. According to Newton’s second law (\( F = m \cdot a \)), if the force is the same, the product of mass and acceleration must be equal for both bodies, leading to the given formula.
What is the formula for mass from equal force?
The formula for mass from equal force is \( m_2 = \frac{m_1 \cdot a_1}{a_2} \), where \( m_1 \) and \( a_1 \) are the mass and acceleration of the first body, and \( a_2 \) is the acceleration of the second body. The standard unit for mass is kilograms (kg).