For the exercises in this chapter (and subsequent chapters), use the more accurate value of \( g=9.8 \mathrm{~m} / \mathrm{s}^{2} \) for the acceleration due to gravity. E1. A horizontally directed force of 40 N is used to pull a box a distance of 1.5 m across a tabletop. How much work is done by the \( 40-\mathrm{N} \) force?

To calculate the work done by the force, you can use the formula for work, which is \( \text{Work} = \text{Force} \times \text{Distance} \times \cos(\theta) \). In this case, since the force is applied horizontally and the movement is also horizontal, \( \theta = 0 \) degrees, and \( \cos(0) = 1 \). Thus, the work done is: \[ \text{Work} = 40 \, \text{N} \times 1.5 \, \text{m} \times 1 = 60 \, \text{J} \] So, the work done by the \( 40 \, \text{N} \) force is \( 60 \, \text{J} \). Visionaries in physics like James Prescott Joule, after whom the unit of work (joule) is named, discovered that work isn’t just about applying force; it’s all about the movement that results. Joule's experiments with mechanical energy laid the groundwork for energy conservation principles, illustrating how energy can transfer and transform—a delightful dance of forces in action! If you're calculating work, remember that only the component of the force parallel to the direction of movement contributes to work done. So, even if you're pulling with a mighty force, any angle other than zero could mean less work done than expected! Watch out for this common slip, especially when forces aren't aligned!