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

The magnitude of Keith’s push is 230 N

Step-by-step 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* 100* 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* 2\\3f=200+490\\3f=690\\f=(690)/(3)=230\textrm{ N}`

Keith applies a force of
`f` towards left.

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