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Beginning at time t = 0, a student exerts a horizontal force on a box of mass 30 kg, causing it to move at 1.2 m/s toward an elevator door located 16 m away, as shown above. The coefficient of kinetic friction μk between the box and the floor is 0.20. Calculate the magnitude of the horizontal force the student must exert on the box in order to keep it moving at 1.2 m/s.

User Kggoh
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2 Answers

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First of all, let's draw a FBD:
We notice that the box is moving in the horizontal direction (x-direction). So let's see what else is happening here. The force that we applied is to the right and can be defined as Fx=ma x
Next we need to look at the normal force; however, we only need it to find the frictional force (you'll see why later). The normal force is always the force opposite of the force into the surface. In this case, the force into the surface (floor) is just the weight, which is −mg. Therefore, N=mg Next we have the frictional force, which is always defined as:
Ff=μN
which for our situation means that Ff=μmg
Now let's sum what we have!
∑F=FxFf=max−μmg
Now, here comes the tricky part.. If I am correct, the question says that the velocity remains constant (1.2m/s before and 1.2m/s after). What happens when velocity is constant? Position increases linearly, BUT acceleration is ZERO. This would mean that our term for maxis = 0 since a is 0. So ∑F=−Ff=−μmg Plug in your numbers and you should get your answer! Now here's the other trick... the FRICTIONAL force is acting in the leftward direction, which means that, according to our convention we made that right is positive, that the frictional force is negative. But what we're calculating here needs to be rightward (positive) because we need to keep pushing it at the same force as the force due to the kinetic friction. So I think the final answer should be positive
User Nikos Alexandris
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Since the initial and the final velocity are just equal, it is implied that the acceleration is zero. This means that the net force acting on the body is also zero. The horizontal force should be equal to the force of friction. The force of friction is equal to the product of the coefficient and the normal force.
Ff = (coefficient of friction) x Fn
The normal force is equal to the object's weight if the surface is horizontal.
Ff = (0.20) x (30 kg) x (9.8 m/s²) = 58.8 N
Thus, the horizontal force exerted must be 58.8 N.
User Dwilkins
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