Question

A man pushes an $80N$ crate for a distance of $5.0m$ upward along a frictionless slope that makes an angle of ${30}^o$ with the horizontal. His force is parallel to the slope. If the speed of the crate decreases at a rate of $1.5m/s^2$, then the work done by the man is:

• A. $-140J$
  
• B. $140J$
  
• C. $-200J$
  
• D. $200J$
  

Answer 1

The correct option is B $140J$

The net result is a negative acceleration of 1.5 so...

let F be the man's force

$F=mgsin30$ is the component of gravity parallel to the slope

$80/9.8$ is the crate's mass

$F-gravity=ma$

$F-mgsin30=80/9.8(-1.5)$

$F-80sin30=80/9.8(-1.5)$

$F=40+80/9.8(-1.5)$

Then work is just F*d since the force is parallel to the displacement

$W=(40+80/9.8-1.5)$

$W=140J$