A 10 kg crate is placed on a horizontal conveyor belt. The materials are such that mu(s) = 0.5 and mu(k) = 0.3. (b) Draw a free-body diagram showing all the forces on the crate if the conveyer belt is speeding up.

Video transcript

Hey, everyone in this problem, a goods truck is carrying a 25 kg box and want us to draw a free body diagram showing all the forces on the box. If the truck is speeding up in the eastward direction, and we're told to consider the coefficient of static friction to be 0.45 and the coefficient of kinetic friction to be 0.25. Now we're given four answer traces. I'm gonna scroll down so we can see them all at the same time. A and all of them are free body diagrams options A through D that show these different forces in the X and Y direction. Now the first two, we're gonna start with, with the normal force. OK. This box is resting on the back of the truck. So we know there's gonna be a normal force pointing upwards in the Y direction. We know that we're gonna have the force of gravity pointing downwards in the negative Y direction. OK? So we have those two forces and those are in all four of these answer choices. OK? So that's not gonna take the correct answer here. Now, the direction of Moulton, we're told is to the east, we're gonna have the east pointing to the right. And so all of these show the direction of motion pointing to the right. So that's not gonna decide what's going on here either. I want to think about some friction. Right now. The box is not moving. It's sitting in that truck as that truck is speeding up. That means that we're gonna have a force of static friction acting on this box, not a force of kinetic friction. If the box is stationary, then we're talking about static friction. Once it starts to move, we switch to Connecticut. So we can eliminate answer choices. B indeed, we're gonna eliminate the two on the right because they have kinetic friction and not. OK. So now we're down to option A or C we know we have static friction. Now we need to figure out what direction that static friction acts. Now, if we think about a box in the back of a truck and the car or the truck is accelerating to the right, it's speeding up to the right. That means that the box is gonna wanna move to the left. Now, you can imagine if you have something in the back of your car and you accelerate really quickly, it's gonna fly back. OK. So that bar is gonna wanna move to the left, the force of static friction is gonna oppose that motion. And so it's gonna point to the right. And so the correct answer here is option C OK. We have the normal force pointing to the right or pointing straight up. Sorry, we have the force of gravity pointing straight down and we have the static friction force pointing to the right with the direction of motion to the right as well. That's it for this one. Thanks everyone for watching. See you in the next video.