a custodian pulls a vacuum 13.5 m with a 33.9 n force at a 55.0° angle, against a 14.2 n friction force…

Explanation:

Step1: Recall work - formula

The work - done formula is $W = Fd\cos\theta$, where $W$ is work, $F$ is force, $d$ is displacement, and $\theta$ is the angle between the force and the displacement.

Step2: Identify values for friction - force work

For the friction force, $F = 14.2\ N$, $d=13.5\ m$, and the angle $\theta = 180^{\circ}$ (since the friction force acts in the opposite direction of the motion).

Step3: Calculate work - done by friction force

Substitute the values into the work - formula: $W = Fd\cos\theta$. $W=(14.2\ N)\times(13.5\ m)\times\cos(180^{\circ})$. We know that $\cos(180^{\circ})=- 1$. So, $W = 14.2\times13.5\times(-1)$. $W=-191.7\ J$.

Answer:

$-191.7\ J$