Question

if a fisherman applies a horizontal force with magnitude 50.0 n to the box and produces an acceleration of magnitude 2.60 m/s², what is the mass of the box? express your answer with the appropriate units.

Explanation:

Step1: Recall Newton's Second Law

Newton's second law states that \( F = ma \), where \( F \) is force, \( m \) is mass, and \( a \) is acceleration. We need to solve for \( m \), so we rearrange the formula to \( m=\frac{F}{a} \).

Step2: Substitute the given values

We are given \( F = 50.0\,\text{N} \) and \( a = 2.60\,\text{m/s}^2 \). Substituting these into the formula, we get \( m=\frac{50.0\,\text{N}}{2.60\,\text{m/s}^2} \).

Step3: Calculate the mass

Performing the division, \( \frac{50.0}{2.60}\approx19.23 \). The unit of mass when force is in Newtons (\( \text{N} \)) and acceleration in \( \text{m/s}^2 \) is kilograms (\( \text{kg} \)) because \( 1\,\text{N}=1\,\text{kg}\cdot\text{m/s}^2 \), so when we divide \( \text{N} \) by \( \text{m/s}^2 \), we get \( \text{kg} \).

Answer:

Value: \( 19.2 \) (or more precisely \( 19.23 \))
Units: \( \text{kg} \)

(If we use more precise calculation: \( \frac{50.0}{2.60}=\frac{500}{26}=\frac{250}{13}\approx19.23 \), so the mass is approximately \( 19.2\,\text{kg} \) or \( 19.23\,\text{kg} \) depending on significant figures. The given values have three significant figures, so \( 19.2\,\text{kg} \) or \( 19.23\,\text{kg} \) is appropriate.)