Acceleration with Force and Mass

This acceleration calculator computes the acceleration of an object based on the applied force and its mass. Additionally, it calculates the object's weight equivalent under Earth's gravity and compares the calculated acceleration to the gravitational acceleration constant (g = 9.81 m/s². It supports various units for force, mass, and acceleration.

Calculator

1. enter the force acting on the object, select the unit
2. enter the object's mass, and choose the desired unit for acceleration
3. decimal precision, the number of digits after the decimal point

Results

1. the acceleration of the object
2. the gravitational force acting on the object
3. the acceleration expressed as a multiple of Earth's gravitational acceleration

Formulas

Acceleration: \[ a = \frac{F}{m} \] Where:

• \( a \): Acceleration (\( \text{m/s}^2 \) or \( \text{ft/s}^2 \))
• \( F \): Force (N, lbf, etc.)
• \( m \): Mass (kg, lbs, etc.)

Weight Equivalent: \[ W = m \cdot g \] Where:

• \( W \): Weight (N)
• \( g = 9.81 \, \text{m/s}^2 \): Gravitational acceleration.

Comparison with Gravity: \[ g_{\text{comparison}} = \frac{a}{9.81} \] Where:

• \( g_{\text{comparison}} \): Acceleration in multiples of Earth's gravitational acceleration.

Sample Calculation

• Force (\( F \)): \( 1000 \, \text{N} \)
• Mass (\( m \)): \( 50 \, \text{kg} \)
• Acceleration Unit: \( \text{m/s}^2 \)
• Decimal Places: \( 3 \)

1. Calculate Acceleration: \[ a = \frac{F}{m} = \frac{1000}{50} = 20 \, \text{m/s}^2 \]
2. Calculate Weight Equivalent: \[ W = m \cdot g = 50 \cdot 9.81 = 490.5 \, \text{N} \]
3. Compare Acceleration with Gravity: \[ g_{\text{comparison}} = \frac{a}{9.81} = \frac{20}{9.81} \approx 2.04 \, g \] Results:

• Acceleration: \( 20 \, \text{m/s}^2 \)
• Weight Equivalent: \( 490.5 \, \text{N} \)
• Comparison with Gravity: \( 2.04 \, g \)