Question

A 215 N box is placed on an inclined plane that makes a 35.0 degree angle with the horizontal.  What applied force is needed to accelerate box up the incline at 0.470 m/s2 if the force of friction is 75.0 Newtons?​

Answer 1

The applied force that is needed to accelerate box up the incline is 208.66 N.

The net force on the box

The net force on the box is calculated by applying Newton's second law of motion.

$\Sigma F = ma\\\\F - mgsin(\theta) - F_f = ma\\\\F = ma+ mgsin(\theta) + F_f$

where;

m is the mass of the box

The mass of the box is calculated as follows;

$W = mg\\\\m = \frac{W}{g} \\\\m = \frac{215}{9.8} \\\\m = 21.94 \ kg$

The applied force that is needed to accelerate box up the incline is calculated as follows;

$F = 21.94(0.47) \ + \ 215sin(35) \ + \ 75\\\\F = 208.6 6 \ N$

Thus, the applied force that is needed to accelerate box up the incline is 208.66 N.

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