Question

Drew bill and kieth push horizontally on chuck (100kg). Drew and bill each push to the right with force 2f and Keith pushes to the left with a force of f. Chuck moves and accelerates to the right at 2 m/s^2 across the floor where coefficient of friction is 0.5. What is the magnitude of Keith’s push?

Answer 1

Answer:

The magnitude of Keith’s push is 230 N

Explanation:

Given:

Mass of chuck, $m=100$ kg

Acceleration of the chuck, $a=2$ m/s².

Coefficient of friction, $\mu =0.5$

Frictional force acts to left as motion is to right.

Frictional force is given as:

$Friction=\mu N=\mu mg=0.5\times 100\times 9.8=490\textrm{ N}$

$N = mg$ as net force in vertical direction is zero.

Total force to the right, $F_r=2f+2f=4f$

Total force to the left, $F_l=f+490$

Net force acting on the chuck, $F_{net}=F_r-F_l=4f-f-490=3f-490$

According to Newton's second law,

$F_{net}=ma\\3f-490=100\times 2\\3f=200+490\\3f=690\\f=\frac{690}{3}=230\textrm{ N}$

Keith applies a force of $f$ towards left.

Therefore, the magnitude of Keith’s push is 230 N.