The cable of a crane is lifting a 750 kg girder. The girder increases its speed from 0.25 m/s to 0.75 m/s in a distance of 3.5 m.
(a) How much work is done by gravity?

Question

The cable of a crane is lifting a 750 kg girder. The girder increases its speed from 0.25 m/s to 0.75 m/s in a distance of 3.5 m. 
(a) How much work is done by gravity?

Accepted Answer

Hi, everyone in this practice problem. We're being asked to calculate the total work done by gravity on a roller coaster car. We will have a roller coaster car with a mass of 500 kg released from the top of a hill with a height of 50 m as the car descends on the hill. Uh it actually increases its speed from 0 to 30 m per second. And if the total distance traveled by the roller coaster is 100 m, we're being asked to calculate the total work done by the gravity on the roller coaster car. The options given are a negative Joles B 245 Joles C negative 245 kg joules and D kilojoules. So we will use the particle model for the roller coaster car and at which we're considering the roller coaster car as a particle. The downward displacement of the roller coaster car is going to be pretty much the height of the hill. So delta Y will then actually equals to zero m minus 50 m or the final which is going to be Y F minus Y not which is going to be negative 50 m, the total vertical displacement. So we wanna recall that total work done is going to be equals to force multiplied by the displacement which is delta Y. And in this case, we're being asked to calculate the work done by gravity. So the force here is going to be the force by the gravity or gravitational force which is just the weight of the roller coaster car itself. So force in this case will equals to F G and F G will equals to M multiplied by G. We want to recall that in this case, the G is going to be actually pointing downwards. So we wanna add the negative sign in front of M and G. So force equals to negative M G. So we want to substitute that into our equation here so that we get work equals to negative M multiplied by G multiplied that by the displacement which is delta Y, we want to substitute everything that we know into this equation right here. We know that the mass is 500 kg. So negative M is negative 500 kg multiply that by G which is going to be 9.81 m per second squared. You're gonna multiply that by the displacement which is negative 50 m and that will actually give us a work value equals to 245,000 tools which will equals to 245 kg Jules. So the correct answer or the total work done by the gravity on the roller coaster car is going to equals to 245 kg joules, which is going to correspond to option D in our answer choices. So answer D or option D is going to be the answer to this practice problem. And that'll be it for this video. If you guys still have any sort of confusion, please make sure to check out our other lesson videos on similar topics and that'll be it for this one. Thank you.

The cable of a crane is lifting a 750 kg girder. The girder increases its speed from 0.25 m/s to 0.75 m/s in a distance of 3.5 m. (a) How much work is done by gravity?

Verified Solution

Key Concepts

Work Done by Gravity

Kinetic Energy

Conservation of Energy