A 45.0-kg crate of tools rests on a horizontal floor. You exert a gradually increasing horizontal push on it, and the crate just begins to move when your force exceeds 313 N. Then you must reduce your push to 208 N to keep it moving at a steady 25.0 cm/s. (b) What push must you exert to give it an acceleration of 1.10 m/s2?

Video transcript

Welcome back everybody. We have a piece of luggage that is resting on the floor of your house. We are told that its mass is 29 kg. And we're told a couple other things too. A constant horizontal force, we're sorry, an increasing horizontal force is applied to it in the positive X direction. And we are also told that there is a force due to friction on the other side. And it's going to be kinetic friction since the box is going to be moving after a certain point. Now, with all objects to, we are also going to have a normal force and a force due to gravity. Now we are told that when the velocity is constant at 1.8 m/s, the force that is being applied at this constant velocity equal to newtons. And we want to figure out what the force is when the acceleration of the box is 1.5 m per second squared first. Let's look at this scenario right here. Right, let's let let's break this down. And we're going to use one of newton's laws for this. Newton's second law states that the sum of all forces in the extraction is equal to mass times the acceleration in the X direction. Right? So the forces acting in the extraction are this F. And this friction force in the opposite direction. Now, when we are looking at the F, that uh corresponds to the constant velocity, our acceleration is going to equal zero. This means that our force with corresponding to the constant velocity is equal to our friction force, which we are told is 147 newtons. Now we can use this to find the force when the acceleration is not zero. So let's go and do that using newton's second law. Again, we have that. The force minus the friction force is equal to mass times acceleration, adding our friction force to both sides. This cancels out and we get that our force is equal to this so let's go ahead and plug in. Some numbers are mass is 29. Our acceleration that we want to achieve is 1.5. The friction force which we just found to be 147 newtons. This summation equals 191 newtons corresponding to answer choice. C Thank you all so much for watching. Hope this video helped. We will see you all in the next one.