A factory worker pushes a 30.0-kg crate a distance of 4.5 m along...

Question

A factory worker pushes a 30.0-kg crate a distance of 4.5 m along a level floor at constant velocity by pushing horizontally on it. The coefficient of kinetic friction between the crate and the floor is 0.25. (e) What is the total work done on the crate?

Accepted Answer

Hey everyone. So today we're dealing with the problem about the force of friction and network. So in this problem we're being told that James is pulling a 65 kg fridge along a 10 m horizontal straight path. Now the motion of this fridge is assumed to be uniform with this information. We're being asked to calculate how much work is done on the fridge, assuming the coefficient of coefficient of kinetic friction is 0.4. So before going into any other calculations, I actually like to take a look at the force diagram for this problem. So let's draw this out. We have a horizontal straight path With a distance of 10 m. Let's just say this is 10 m. We have our protagonist James and let's just say that he is pulling a fridge by rope because I think that makes the most sense. This is our fridge, It is. Let me try that a little better. This is our fridge, it is 65 kg. And with that in mind. Now let's go ahead and sort of work out what force actually being acted on here. So we have the force of gravity, the force due to gravity, which is simply the weight. It is the that's where this out force due to gravity, Z equal to MG. The opposing force. The normal force which also helps prevent the the fridge from sinking into the ground. Uh points in the opposite direction, it is perpendicular. If I was to actually draw this down, let me draw this in a different color. Let me draw this in green, The normal force. If I was to draw it down like so we would see that it forms a 90° angle with the horizontal or a straight path. And so does the uh force of gravity. But due to its opposing nature to the force of gravity, the normal force is also equal to MG. So that makes a pretty good sense so far. Now let's take a closer look at the force due to uh James is push or James pull rather and the force due to friction. Now in the question, it says that the path of motion by the fridge is assumed to be uniform. Well, what does this mean? Exactly? Well this means that the force that James is exerting the force via James must be equal to James must be equal to the force due to kinetic friction because to assume a uniform horizontal velocity, a constant velocity. While there's also friction. If there is a constant force this way, a constant velocity rather due to the uniformity that is mentioned, that must mean that the opposing force due to friction because the force of friction always opposes the direction of motion. The force due to friction must also be equal to the force James is exerting and we know that the force due to friction is nothing but the coefficient of kinetic friction multiplied by the normal force. So with that in mind we can go back and we know that network network is equal to and at force times distance. The distance traveled multiplied by Kassian data where theta is the angle between the direction of the force and the plane upon which the force is being exerted on which the distance we're measuring is on. So let's expand that a little. We have the net force. Or the network must be equal to the work done by James plus to work done by gravity plus the work done by the normal force plus the work done by the force of friction expanding this out. We know that the force due to James right is equal to the uh coefficient of friction multiplied by the normal force which is simply just the coefficient of friction multiplied by M G. So this will be the friction multiplied by M. G. Multiplied by the distance. And since this is the direction of travel, if we assume that the horizontal goes this way, then the direction or the angle theta between James's force. The force due to James and they work therefore due to James and the direction of travel will be zero. This will just be multiplied by Kassian zero, which is one. We add this to the work gravity work to to gravity. Mg. Multiplied by the distance. Again, distance traveled multiplied by Kassian. Now, as we recall both the normal force and the Uh force due to gravity will have an angle of 90° with the horizontal. So this will be 90 degrees. Now the force due to the normal force rather my bad. The normal force will be an ape will be an opposing force to the force of excuse me, it'll be a opposing force to the force due to gravity. So if we are to write that out well we're adding but it is a negative term, it is M. G. T co sign 90. It is essentially the same in magnitude as the force due to gravity but it is inherently opposing. So we'll say let me write that a little better. It's a negative quantity and finally we have to look at the force due to friction. No, the force due to friction is again another negative quantity it is opposing. However, while it's opposing, the easier way to describe this would be the coefficient of friction. The definition of the force of friction of kinetic friction. My man multiplied by the distance and since its direction of motion is directly opposite to James and therefore the opposite to the horizontal, it will have a angle data Data will be equal to 180°. So Kassian 180°. And for those of you who don't know the Kassian of 180° is simply -1. So, if we actually some all of this up well, the magnitudes of both James's work and the work done by friction will cancel out and the magnitudes of the work done by gravity and the normal force will also cancel out. So therefore the network done on the system is simply zero jewels. It is answer choice B and now this may be confusing because well, James is clearly pulling the fridge. He's doing work on the fridge, so how can the network zero? Well, even though he is doing work on the fridge, there's also opposing work being done as well that leads to a net force of zero. So even though the fridge moves a distance, there is work that is done on it. The network applied onto the fridge is still zero. I hope this helps. And I look forward to seeing you all in the next one.

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