A med tech student pushes a 30-kg carton of books across the floor of her dormitory by exerting a constant force of 185 N at an angle of 37° with the horizon. If the opposing force of friction is 70 N, how much work does she do as she moves the carton 4 min 15 s? What power in watts has she expended?
To find the work done by the student in pushing the carton of books, we first need to find the component of the force that is in the direction of the displacement. This can be done using the equation:
Work = Force * Distance * cos(theta)
Where:
Force = 185 N
Distance = (4 min 15 s) * (60 s/min) = 255 s
theta = 37°
First, convert the angle to radians:
theta_radians = 37° * (pi/180) = 0.6458 radians
Now, calculate the work done:
Work = 185 N * 255 s * cos(0.6458) = 39961.2 J
Next, to find the power expended by the student, we use the equation:
Power = Work / Time
Time = 255 s
Power = 39961.2 J / 255 s = 156.9 W
Therefore, the student has done 39961.2 J of work and expended 156.9 W of power while pushing the carton of books.