A thrill-seeking cat with mass 4.00 kg is attached by a harness to an ideal spring of negligible mass and oscillates vertically in SHM. The amplitude is 0.050 m, and at the highest point of the motion the spring has its natural unstretched length. Calculate the elastic potential energy of the spring (take it to be zero for the unstretched spring), the kinetic energy of the cat, the gravitational potential energy of the system relative to the lowest point of the motion, and the sum of these three energies when the cat is (a) at its highest point.

Video transcript

Hey everyone in this problem, we have a baby of mass 12 kg sitting in a baby bouncer, the baby bouncer is suspended in a room with the help of a light elastic cord. The unstrapped length of the elastic cord is two m. When the baby bounces, she executes a simple vertical motion with an amplitude of eight cm. The cord has its natural unstrap etched length at the highest point of motion. The elastic potential energy of the unscratched cord is assumed to be zero, and the lowest point reached by the baby is going to be a reference level. Okay, so we're asked to calculate the kinetic energy, the elastic potential energy and the gravitational potential energy at the baby's highest point. Okay, alright so let's start with just a little diagram. Okay so we have this baby this chord, Okay and without the baby just this unstructured cord, Okay, has a length of two m. Alright and then once we add the baby there, okay we're gonna pretend that this is our baby and our bouncer, this little ball here. Now we're told that the baby's highest point of motion, Okay, is that the unstrap hte position? Okay, so when the baby bounces up high, Okay, it's highest positions are gonna be here, we're told that it has an amplitude of 8cm. So the distance between here and here is going to be 8cm and it's also going to reach a low point down here And that distance is also going to be eight cm, okay that's going to be negatively inflow tooth. Now we're told that this is a reference point. So Alright, so this is what it looks like. Now let's go ahead and calculate some of these energies. Alright. Starting with part one. The kinetic energy. Okay, well the kinetic energy at the highest point it's going to be what what the highest point. The baby is going to be stopped momentarily as they change direction from going upwards to going downwards. So the speed is going to be zero. Okay, so our kinetic energy K is also going to be zero since we Okay, so the kinetic energy at that point is just zero. Okay, so if we look at our answer choices, we've already eliminated answer B. Okay, let's move on to part two. Part two is asking for the elastic potential energy. Alright, well, what do we know about the elastic potential energy? Okay, now the elastic potential energy, we're looking for this at the highest point of the baby. Now we know that the highest point is right here. Okay, Where we have this unstrap length. Okay, well we're also told that the elastic potential energy of the unsearched court is assumed to be zero. Okay, so at this point the cord is going to be unstrap etched and stretched. And so the elastic potential energy you it's just going to be equal to zero. Alright, so we have the kinetic energy at this point is zero. The elastic potential energy at this point is zero. Okay, so we're looking at options A or D And we have one more calculation to do. Okay. And that is for the gravitational potential energy. So part three. We want to find the gravitational potential energy. We're gonna call it Yugi. Okay. And recalling the gravitational potential energy is equal to m G H. Okay, well in our problem, the mass of the baby is 12 kg gravitational acceleration 9.8 m per second squared. Ok. And what is H H is gonna be the height according to our reference point. Okay, let's look at our diagram. Okay, We're considering this reference point to be the lowest point of the baby. Okay. And we're calculating the gravitational potential energy at the highest point of the baby. The difference here is going to be two times the amplitude, Which we know is 16 cm. So the height of the baby is going to be considered to be 16cm. Okay? And if we convert this to meters one m per 100 centimeters. Okay, So we divide by 100 unit of centimeter cancels. We're left with 0.16 m. So putting that into our equation for the gravitational potential energy, we have 12 kg to 9.8 m per second squared times 0.16 m. Okay, This is gonna give us kilogram meters squared per second square which is equivalent to a newton times meter, which is a jewel. Okay, so we get the unit. We want for energy and we have approximately 18.816 jules. Okay. All right, so our kinetic energy we found was zero. Are elastic potential energy. We found was zero In our gravitational potential energy we found was 18.816 jewels. If we go back to our answer choices, okay? We see that we're gonna have answer choice. D. Okay? And again, at the highest point the Kinetic energy is zero. The elastic potential energy is zero and the gravitational potential energy is approximately 18.8 jules. Thanks everyone for watching. I hope this video helped see you in the next one.