Question

1. a student used 85 n of force to raise a box up to a shelf that was 0.75 m above the ground. what was the mass of the box? (hint: $w = e_p$)

Explanation:

Step1: Recall the formula for weight and gravitational potential energy

We know that \( W = E_p \), and the formula for gravitational potential energy is \( E_p = mgh \), where \( W \) is weight, \( m \) is mass, \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)), and \( h \) is height. Also, weight \( W \) can be related to the force used (since the force to raise the box at constant velocity is equal to its weight), so \( W = 85 \, \text{N} \), \( h = 0.75 \, \text{m} \), and we need to find \( m \). From \( W = mgh \), we can solve for \( m \) as \( m=\frac{W}{gh} \).

Step2: Substitute the known values into the formula

Substitute \( W = 85 \, \text{N} \), \( g = 9.8 \, \text{m/s}^2 \), and \( h = 0.75 \, \text{m} \) into the formula \( m=\frac{W}{gh} \).
\[
m=\frac{85}{9.8\times0.75}
\]
First, calculate the denominator: \( 9.8\times0.75 = 7.35 \). Then, \( m=\frac{85}{7.35}\approx11.56 \, \text{kg} \) (rounded to two decimal places).

Answer:

The mass of the box is approximately \( \boldsymbol{11.6 \, \text{kg}} \) (or more precisely \( \approx11.56 \, \text{kg} \)).