A man pushes on a piano with mass 180 kg; it slides at constant velocity down a ramp that is inclined at 19.0° above the horizontal floor. Neglect any friction acting on the piano. Calculate the magnitude of the force applied by the man if he pushes (a) parallel to the incline

Video transcript

Everyone in this problem. We have a 130 kg box placed on a frictionless incline with an angle of 24° above the horizontal. The box slides at constant velocity down the incline as you push it and were asked to determine the magnitude of the force you apply. The force is parallel to the inclined surface. Alright, so let's draw a little diagram here, get an idea of what's happening. You have this incline, is that 24°? Okay. We have a block 130 kg. Hey, this is frictionless. The box is gonna be sliding down with some constant velocity um And we're gonna push it. Okay? All right, so we have our block here. We're gonna draw a free body day. Right, Okay, So our block is this central point here, we know we always have a normal force which points perpendicular to the surface is gonna point up into the right in this direction. Okay, That's our normal force and we have our weight equal to MG, which always points straight down. We have no friction, so we don't have to worry about friction. Okay? And then we have the force that we're applying and we're going to assume that the force we're applying is in this direction to the left, we're pushing it kind of up. Well, it's coming down towards us and if that assumption is wrong, we'll just see it in the sign of the force that we find. Okay, so we're gonna assume it's pointing this way in our diagram. But the calculation we do, we'll get a particular sign that's gonna tell us in which direction this force points. Okay. All right. So let's take our coordinate system to be tilted. It's going to be tilted so that the normal force N in this force we applied F are perfectly in that coordinate system. Okay. And we'll have to decompose W. Okay, into the X and Y components according to our new coordinate system. This is common when you have an incline like this to tilt the coordinate system so that it's kind of parallel to that parallel and perpendicular to your incline. So this is going to be W Y. The weight, the Y component of the weight. And then we have W X. The X component of the weight. Okay, Alright. So this is our free body diagram and we're going to work off this now, what are we trying to find? We're trying to find the force F. And in our problem, the force F works in the X direction. Okay. According to our coordinate system. So let's start with the X direction. We know from Newton's law to the sum of the forces in the X direction, it's going to be equal to M A X acceleration. K. Newton's second law. Now we have constant velocity. We're told when we have constant velocity that means the acceleration is zero. And so this summer forces is going to be equal to zero. All right, So let's do the sum of our forces in the extraction. What forces do we have? Well, in the positive extraction, we have W. X. And going the opposite direction. We have our force that we're applying F. Okay? We know that this is equal to zero. And so this tells us that our force F is going to be equal to W. X. K. The X. Component of the weight. What is the X. Component of the weight? Well, it's going to be M. G. Sine of theta. And we know all these values. So plugging in the values K. The mass is 130 kg. The acceleration due to gravity 9.8 m/s squared Sine of the angle the angle of incline is 24°, so sign of 24°. And if we work all of this out, we get a force approximately 518. newtons. So the force applied. The magnitude of the force we apply is 518.2 newtons. Okay, this is positive. Which tells us that the force was pointing in the proper direction. Okay. All right. And if we look at our answer choices, we're gonna approximate to the nearest Newton and we get D Newtons. That's it for this one. Thanks everyone for watching. See you in the next video