A box of bananas weighing 40.0 N rests on a horizontal surface. The coefficient of static friction between the box and the surface is 0.40, and the coefficient of kinetic friction is 0.20. (c) What minimum horizontal force must the monkey apply to start the box in motion?

Video transcript

Everyone in this problem. We have a 31 Newton crate of feed resting on a horizontal floor. The coefficient of static and kinetic friction between the crate and the floor are 0.52 and 0.34, respectively. The goat is pushing against the crate, applying a horizontal force on the crate. Okay, horizontal force. And were asked to determine the least horizontal force applied by that goat to move the crate. Alright, so let's draw a little diagram. We have this horizontal floor, we have this crate, and then we have our goat, and I'm just gonna draw it as a circle with four legs. Um You can pretend that that's a goat, my bad drawing skills, okay? And he's gonna be pushing against that block. So converting this to a free body diagram, we have our crate drawn in the middle here, can we know that we have the normal force pointing up, always acting perpendicular early to the surface, we have the weight w pointing down. Okay? And now this goat is going to be pushing the crate, and the way we've drawn it in our diagram is going to be pushing the crate to the right, Okay, so we have our applied force f acting to the right, and we're told some information about friction. Okay, We have friction between the crate on the floor, so the friction force is going to oppose the motion or resist the motion. So it's gonna be acting in the opposite direction, that's going to be pointing to the left with the friction force F. Okay, Alright, we're gonna take up into the right as positive in our coordinate system. You could do it the opposite way if you want it. Okay. Alright, so if we want to figure out the least horizontal force applied in order to move the crate, Okay, We're thinking about F. S. Max the maximum force of static friction. Okay, that's that force that once you overcome it, the crate is gonna start to move. Okay? So if we look at F. S. Max, recall that this is equal to mu s coefficient of static friction times and the normal force. Okay, well, we know the coefficient of static friction. We were given in the problem but we don't know the normal force yet, and we see that the normal force acts in the y direction. Ok, so let's look at the forces in the Y direction to try to figure out and we see that the sum of the forces in the Y direction, according to Newton's second law is going to be equal to the mass times the acceleration in the y direction. And we know that this crate is not moving up or down, It's just resting on the floor. So the acceleration, the y direction is zero, which makes us some of the forces in the Y direction zero. The sum of the forces is what while we have the normal force acting up in the positive Y direction, so we have N. And then we have the weight acting in the negative y direction of pointing down, we have n minus W is equal to zero, which tells us that the normal force N is equal to the weight W. And the weight of the crate we're told in the problem is 31 Nunes. Okay, and just watch here, in this case we're given the weight of the crate, okay, we're given 31 newtons were not given the mass of the crate in kg. Okay, so that can be an easy place to mess up. So just pay attention to whether you're given the weight or the mass of an object. Alright, so now we know our normal force and we can get back to our maximum force of static friction um us the coefficient of static friction is 0.52 Times The normal force. We just found 31 newtons. And this is gonna give us A maximum force of static friction of 16.12 Newtons. Okay. Alright, so what this means is that if you were to apply a force, Okay, more than 16.12 newtons. The block is going to start to move. Okay? Up until 16.12 newtons, The force of static friction is going to be greater than the applied force. Okay, so the block is not going to be moving but once you pass that threshold, that maximum static friction, the block is gonna start to move. Okay? And so if we round to the nearest decimal we get, the answer is going to be d. The least horizontal force is going to be 16.1 newtons. Thanks everyone for watching. I hope this video helped see you in the next one.