Broom Push Force Calculator

Acceleration (\( a \)):

Mass of Broom (\( m \)):

Friction Coefficient (\( \mu_k \)):

Broom Angle (\( \theta \)):

Acceleration due to Gravity (\( g \)):

Horizontal Force (\( F_H \)) in newtons (N):

Horizontal Force (\( F_H \)) in pound-force (lbf):

Horizontal Force (\( F_H \)) in dynes (dyn):

Horizontal Force (\( F_H \)) in kilogram-force (kgf):

1. What is the Broom Push Force Calculator?

Definition: This calculator determines the horizontal force (\( F_H \)) required to push a broom, based on its acceleration (\( a \)), mass (\( m \)), friction coefficient (\( \mu_k \)), broom angle (\( \theta \)), and acceleration due to gravity (\( g \)).

Purpose: It assists in understanding the force needed to move a broom across a surface, accounting for friction and the angle of the broom handle.

2. How Does the Calculator Work?

The calculator uses the relationship:

\[ F_H = m \left( \frac{a + \mu_k \cdot g}{\cos(\theta) + \mu_k \cdot \sin(\theta)} \right) \]

Where:

\( F_H \) — Horizontal force (in various units)
\( a \) — Acceleration of the broom
\( m \) — Mass of the broom
\( \mu_k \) — Kinetic friction coefficient
\( \theta \) — Broom angle
\( g \) — Acceleration due to gravity

Explanation: Enter the acceleration, mass, friction coefficient, broom angle, and gravity in the chosen units, and the calculator computes the horizontal force. Results use scientific notation (5 decimal places) if the force in newtons is greater than 10000 or less than 0.00001, otherwise 2 decimal places. For the image inputs (\( a = 22 \, \text{m/s}^2 \), \( m = 33 \, \text{kg} \), \( \mu_k = 0.56 \), \( \theta = 55^\circ \), \( g = 9.80665 \, \text{m/s}^2 \)), the calculated force is 878.84 N.

3. Importance of Horizontal Force

Details: Calculating the horizontal force is crucial for ergonomic design and understanding the effort required to move objects like a broom, considering friction and angular effects, applicable in physics and engineering.

4. Using the Calculator

Tips: Enter positive values for acceleration, mass, friction coefficient, and angle, and ensure \( \cos(\theta) + \mu_k \cdot \sin(\theta) \neq 0 \), then click "Calculate." Results show the horizontal force in newtons, pound-force, dynes, and kilogram-force (scientific notation with 5 decimal places if > 10000 or < 0.00001 N, otherwise 2 decimal places).

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