In this question, we're trying to determine the force of friction acting on a block. So first let's draw our free body diagram for our situation. So we gotta force after the right the force of gravity down force of friction opposite that force. And then up we have some force P. And our normal force. Yeah. Okay. So what we can say in this situation up and down has to be balanced to the block is and flying up into the air, breaking down to the table. So please p. Plus the normal force is equal to the force of gravity and left and right. We don't know if they're balanced or unbalanced yet but we really don't care. All we know is that this force is six mm. So we want to figure out the force of friction. So a couple other pieces of information that we need. So the mass of the block Is 2.5 kg. The coefficient of static friction is .4. The coalition of kinetic friction This .25. Mhm. Okay. Yeah. So now we are using three different values for P. To determine our normal force. Let's move this equation around here, I'm gonna subtract peter both sides. So the normal force is equal to F. G minus P. Yeah. Yeah. Mhm. Okay, so let's calculate the force of gravity first. So force of gravity equals 2.5 kg. The force of gravity is mass times gravity Times 9.8 meters per second squared. So our force of gravity acting on the block is always going to be 24.5 mittens. Okay, so now let's calculate our three normal forces for the three situations. So in part A P equals eight newtons. So when we plug into our equation here, F.G. This is going to give me a normal force. Uh 16.5 Newtons in B. He is tendons. This gives me a normal force Of 14 5 Newtons. And see here's 12 movements, which gives me a normal force of 12.5 mittens. Okay, so now how do we figure out the forces of friction? So in each part we'll start with part A. We could have the force of friction static which is less than or equal to the coefficient of static friction comes normal force or the force of friction, kinetic is equal to the coalition of kinetic friction times normal force. So the way that we're going to know which one to use is we're going to start with static friction. Okay. And if static friction, when we calculate here, if the force of friction is less than or equal to a number that's bigger than six because that's our force here, We know it's not going to move. Static friction has to be less than six in order for the back to block to be moving. So let's first calculate for part A. So we plug in we get four sub static friction is less than equal to 0.4 and our normal force which is 16.5 Millions. So this comes out to force of friction is equal to Yeah. All right. Not equal to his less than equal to 6.6. Newton's Okay. So since static friction can be bigger then are pulling force of F. That means that the force of static friction is only going to balance it out. So our static friction in part A. Is six newtons. We don't have to worry about carrie correction. So part of our friction is going to be six. Newtons just exactly balancing out are pulling force of F. So part B. Same thing. We're gonna start with static friction less than equal to 0.4 times 14.5 Newtons. And this comes out to remember Yeah, Which only comes out to 5.8. So, since our number is less than six, we have to switch over to kinetic friction. So when we plug in for kinetic friction, That's .25 times are 145. Newton number force. So our force of friction kinetic In this scenario is going to be 3625, which will earn a 36 newtons. Mhm. And part C. Mm. Well, since our force of friction was less than six in part B, it's going to be even less than that. So, we can skip the force of static friction in this part and go right to kinetic. So .25, 10- 12.5 Newtons. And this comes out to are force of friction. It is 3.1 newtons. So in part A it's static friction exactly equal to six. The block is not moving at all, and then part B and C. It's kinetic friction, and we have our two values here.