A cable with 20.0 N of tension pulls straight up on a 1.50 kg block that is initially at rest. What is the block's speed after being lifted 2.00 m? Solve this problem using work and energy.

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Hey, everyone in this problem, a rope tensioned at 165 Newtons is used to lift an initially stationary nine kg bucket vertically upward from a well, We're asked to determine the speed of the bucket when it has covered a height of 6.5 m using work and energy principles. The answer choices were given are a 4.06 m/s. B 10.5 m/s. C 31.6 m per second and D 5.27 m per second. Now we can draw this initial situation, ok. So we have a rope that is attached to a bucket. The bucket has an initial speed of zero m/s. It is nine kg And this rope is tensioned at 165 Newtons. You can draw the situation afterwards, ok? When the rope has pulled that bucket upwards. OK. So we have our same bucket of mass nine kg. And now Our bucket has risen 6. m and we want to find the speed at this point of our bucket. We're gonna take up to be our positive wider action and we're told to use work energy principles. OK. So we're told to use work energy principles. Let's recall that the work W is equal to the change in kinetic energy. Delta K. What does our work consist of? In this case, we have the work due to tension. OK? Because we have tension in the rope and we also have the work done by gravity because we have the force of gravity acting on our buck. OK? And the sum of these two is gonna be equal to the change in kinetic energy. The work done by the tension is gonna be the force which is t multiplied by the distance that that force acts over just gonna be the height H the gravitational. The work due to gravity is gonna be the mass multiplied by G, the gravitational acceleration multiplied by the height H and this is going to equal the change in kinetic energy one half multiplied by M multiplied by V F squared minus one half M multiplied by V not squared. All right, attention T Is 165 newtons. So we have 165 newtons multiplied by the height that the bucket is pulled 6.5 m. Now, the war due to gravity is actually going to be negative. OK. Why is that? Well, when you're pulling a bucket upwards, OK, you're working against gravity. Gravity wants to pull the bucket down, you're doing the opposite. And so we have negative The mass of nine kg gravitational acceleration 9.8 m/s squared times that height 6.5 m. Now our initial speed of our bucket was zero. So the second term on the right hand side goes to zero and we're left with just the first term we have one half multiplied by nine kg multiplied by V F squared. And remember that, that final speed V F is what we're looking to find. OK, we filled in all the other values. So now we just need to solve for va If we simplify on the left hand side, we get 1,072. Newton m minus 573. kg meter squared per second squared. That's going to equal on the right hand side, 4.5 kg multiplied by V F squared. Now we have Newton times meter and we have kilogram meter squared per second squared. We call it, those are the same thing, OK. A Newton times a meter is a jewel and a jewel is equivalent to kilogram meter squared per second squared. So we can divide both sides by 4.5 kg. Simplify on the left hand side. And we get that V F squared is equal to 110.933. We had kilogram meter squared per second squared, we divide it by kilograms. And so we have the unit meter squared per second squared When we take the square root, we get that the speed via of the bucket is positive or negative 10.53 m/s. We have to get, we have to remember that positive and negative route. When we take the square root, In this case, we're just asked to find speed, OK? We just want the magnitude, we don't care about the direction and so we can take the positive route. We have VF is equal to 10. m/s. Moving back up to our answer choices and we have three significant digits in our answer choices. We found that the speed of the bucket when it has covered that height of 6.5 m is approximately 10.5 m per second, which corresponds with answer choice B thanks everyone for watching. See you in the next video.

A cable with 20.0 N of tension pulls straight up on a 1.50 kg block that is initially at rest. What is the block's speed after being lifted 2.00 m? Solve this problem using work and energy.

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Key Concepts

Work

Kinetic Energy

Conservation of Energy