T ─ (1500 kg) (9.8 m/s²) = (1500 kg) (1.0 m/s²) P = T (2.0 m/s) (a) Write a realistic problem for which this is the correct equation(s).

Question

Accepted Answer

Hey everyone. So this problem is dealing with tension and power. So let's see what it's asking us for T minus 2000 kg, multiplied by 9.8 m per second squared equals 2000 kg multiplied by three m per second squared and P equals T multiplied by six m per second. Select a choice that describes a situation that matches the given equations. So this is an interesting problem because it is almost the backwards of a lot of problems that we're used to in physics. So instead of coming instead of reading about a situation or a scenario and coming up with equations, they're giving us an equation and asking us to figure out what this scenario is. So we have multiple choice answers A through D here. So let's talk through how to figure out what situation matches these equations. When we look at these equations, there are a few things that pop out. So one of our, you know, tenants of physics equations, we can recall Newton's second law is that the sum of the forces is equal to mass multiplied by acceleration. In a lot of cases, acceleration is gravity when we're working in the vertical direction. So that 9.8 m per second squared given is a big hint. Hey, that's gravity. So that's probably a force, right? We have mass 2000 kg multiplied by acceleration or graphing. So that's one hint. The other hint here is for power. So power is given by force multiplied by velocity. So we've established from our first re recollection of Newton's second law that we have a force here with T. And then we have this other force given by the second equation or second part of that equation. And so T is a force and then six m per second, that's those units, that's velocity. So we can kind of confirm here that tea is a force and the speed at which this um situation is happening is six m per second. So let's then take a look just with that information, let's take a look at our potential answers. So we have here cable dropping the car downward or upward. And then in answer choices C MD, we have the cable towing the car to the right or to the left because we are working with gravity here. We can't, we've already established that we're working in the vertical direction. There's nothing here that indicates we're working in a horizontal direction with left and right. So we can eliminate answer choices C and D and then from there, we can start to draw our free body diagram of what is going on in this problem. So we have positive team, we have so O T minus 2000 kg multiplied by gravity, which looks a whole lot like weight, right weight is given by mass multiplied by gravity. And then all of that is equal to this third force, 2000 kg multiplied by three m per second. And that is going, that force is working in the same direction as that T force. And so that tells you that it is positive and so that force that acceleration is lifting up. And so that helps us eliminate the last potential choice A because the cable is not dropping the card downward, we are moving the cable upward with a positive acceleration of three m per second. So if we look at everything that's happening in this problem, we have a cable attached to the machine lifting a car that weighs 200 kg or sorry, 2000 kg. The cable lifts the car upward with an acceleration of three m per second. And power is determined by that force multiplied by a velocity of six m per second. And so that is how we can determine that the correct answer for this problem is answer choice B so that's all we have for this one. We'll see you in the next video.

T ─ (1500 kg) (9.8 m/s²) = (1500 kg) (1.0 m/s²) P = T (2.0 m/s) (a) Write a realistic problem for which this is the correct equation(s).

Verified video answer for a similar problem:

Key Concepts

Newton's Second Law of Motion

Tension in a Rope

Free Body Diagram