Josh pushes on a 70 kg box in the positive direction with a force of 50 N. Marissa pushes on the box in the negative direction with a force of 35 N. If the force of friction is 2N, what is the acceleration of the box?

1 Answer
Nam D.
Jul 9, 2018

I get approximately #0.186 \ "m/s"^2#.

Explanation:

We see that Josh's force vector neutralizes all of Marissa's force vector and then gives an additional boost of #50 \ "N"-35 \ "N"=15 \ "N"#. Assuming that the frictional force was opposite to Josh's push, i.e. towards Marissa's direction, then the total force in favor of Josh will be #15 \ "N"-2 \ "N"=13 \ "N"#.

To find the acceleration, we use Newton's second law of motion, which states that,

#F=ma#

where:

  • #F# is the force exerted in newtons

  • #m# is the mass of the object in kilograms

  • #a# is the acceleration in meters per second squared

So, we get:

#a=F/m#

#=(13 \ "N")/(70 \ "kg")#

#=(13color(red)cancelcolor(black)"kg""m/s"^2)/(70color(red)cancelcolor(black)"kg") \ (because 1 \ "N"-=1 \ "kg m/s"^2)#

#~~0.186 \ "m/s"^2#

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