a fun loving 11.4kg otter slides up a hill and then back down to the same place. If she starts up at 5.75 m/s and returns at 3.75 m/s, how much mechanical energy did she lose on the hill and what happened to that energy
so i did Ki= 1/2mv^2 = 1/2(11.4kg)(5.75 m/s)2 = 188.45 J
Kf= 1/2mv^2
1/2(11.4kg)(3.75m/s)2= 80.15 J
so I took 188.45 - 80.15 and got 108 J is this correct
yes
Thank you!
Figure the KE at start, subtract the KE at the finish, that is the friction loss.
Well, it looks like we have a sliding otter on a hill here! Let's do some calculations and put a smile on those serious physics faces!
To find out how much mechanical energy our otter friend lost on the hill, we need to calculate the difference between her initial and final mechanical energies.
The formula for mechanical energy is given by:
Mechanical Energy (ME) = Potential Energy (PE) + Kinetic Energy (KE)
Since the otter starts at the same place, the potential energy at the beginning and end will be the same, meaning potential energy doesn't change. So, we can just focus on the kinetic energy.
Kinetic Energy (KE) = 1/2 * mass * velocity^2
Let's plug in the numbers for our playful otter:
Initial kinetic energy (KE1) = 1/2 * 11.4 kg * (5.75 m/s)^2
Final kinetic energy (KE2) = 1/2 * 11.4 kg * (3.75 m/s)^2
Now let's calculate them:
KE1 = 1/2 * 11.4 kg * 33.0625 m^2/s^2 ≈ 198.06375 Joules
KE2 = 1/2 * 11.4 kg * 14.0625 m^2/s^2 ≈ 89.95425 Joules
To find out how much mechanical energy our otter lost, we subtract the final kinetic energy from the initial kinetic energy:
E_lost = KE1 - KE2
E_lost ≈ 198.06375 J - 89.95425 J ≈ 108.1095 J
So, our fun-loving otter lost approximately 108.1095 Joules of mechanical energy on the hill. But don't worry, the energy doesn't just disappear! It gets converted into other forms. In this case, some of the energy is likely converted into heat due to friction between the otter and the hill. So, our otter friend made a hot slide down that hill!
To calculate the mechanical energy lost by the otter on the hill, we need to use the conservation of energy principle. Mechanical energy refers to the sum of kinetic energy and potential energy of an object.
First, let's calculate the initial mechanical energy of the otter when it starts up the hill. The formula for kinetic energy is:
Kinetic Energy = (1/2) * mass * velocity^2
Given that the mass of the otter is 11.4 kg and the initial velocity is 5.75 m/s, we can calculate the initial kinetic energy:
Initial Kinetic Energy = (1/2) * 11.4 kg * (5.75 m/s)^2
Next, let's calculate the final mechanical energy of the otter when it returns at 3.75 m/s. Using the same formula, we find:
Final Kinetic Energy = (1/2) * 11.4 kg * (3.75 m/s)^2
To find the mechanical energy lost on the hill, we subtract the final kinetic energy from the initial kinetic energy:
Mechanical Energy Lost = Initial Kinetic Energy - Final Kinetic Energy
Now, let's calculate it step by step:
Initial Kinetic Energy = (1/2) * 11.4 kg * (5.75 m/s)^2
Final Kinetic Energy = (1/2) * 11.4 kg * (3.75 m/s)^2
Mechanical Energy Lost = Initial Kinetic Energy - Final Kinetic Energy
After obtaining the numerical values, the mechanical energy lost can be calculated, revealing how much energy was lost by the otter on the hill.
As for what happened to that energy, it was most likely converted into other forms of energy, such as heat or sound, due to friction and air resistance during the otter's slide up and down the hill. Some of the energy might have also been dissipated as potential energy when the otter reached the highest point on the hill before sliding back down.