# What is Mechanical energy: Definition and 358 Discussions

In physical sciences, mechanical energy is the sum of potential energy and kinetic energy. It is the macroscopic energy associated with a system. The principle of conservation of mechanical energy states that if an isolated system is subject only to conservative forces, then the mechanical energy is constant. If an object moves in the opposite direction of a conservative net force, the potential energy will increase; and if the speed (not the velocity) of the object changes, the kinetic energy of the object also changes. In all real systems, however, nonconservative forces, such as frictional forces, will be present, but if they are of negligible magnitude, the mechanical energy changes little and its conservation is a useful approximation. In elastic collisions, the kinetic energy is conserved, but in inelastic collisions some mechanical energy may be converted into thermal energy. The equivalence between lost mechanical energy (dissipation) and an increase in temperature was discovered by James Prescott Joule.
Many devices are used to convert mechanical energy to or from other forms of energy, e.g. an electric motor converts electrical energy to mechanical energy, an electric generator converts mechanical energy into electrical energy and a heat engine converts heat energy to mechanical energy.

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2. ### Why is mechanical energy not conserved in this setup? (frictionless spinning cylinder's motion is changed)

We all know we need to apply conservation of angular momentum here. This necessarily leads to a difference in mechanical energy. Since initial rotational inertial is less than final rotational inertia, there is a loss of mechanical energy. However, I have not been able to convince myself what's...
3. ### Speed of ball on pendulum with Mechanical Energy

Started by analyzing the change in energy from the initial position to the final position which gives us mgh=1/2mv^2 Since we are trying to find speed, we rearrange the equation to solve for v, which gives us √2gL. My question is, do we need to take a component of L for √2gL because it is at...
4. ### Mechanical energy in an orbit

Obviously the mechanical energy of the total system remains the same. But I'm having a hard time determining of the ME of the planet is constant or if it is changing.
5. ### Graphing Elastic Potential Energy

Good afternoon, I have a question on graphing this problem. There seems to be something weird going on. In Excel, I set up the potential energy function (kx²/2) and plotted it from x = -0.300m to 0.300m, which looks like the following: The overall shape of the graph looks like what's...

For this, They say internal energy is the sum of the all the mechanical energies of each particle in within the thermodynamic system, however, they then define internal energy differently using the average mechanical energy for all particles within the system (Pink equation). Does someone...
7. ### Differentiating the equation for the mechanical energy of a spring

Why when we differentiate ## E = \frac {1}{2}mv^2 + \frac {1}{2}kx^2 ## with respect to time the answer is ## \frac {dE}{dt} = mva + kxv ##? I though it would be ##\frac {dE}{dt} = ma + kv ##. Many thanks!
8. ### Conservation of momentum and mechanical energy on an inclined plane

So i am tried to conserve momentum and use conservation of mechanical energy but won't there be psuedo force acting on the block if i am solving from non inertial frame ?. If i ignore the pseudo force and simply use C.O.M.E and include the K.E of the wedge and solve normally i do get the...
9. ### Question about the conservation of mechanical energy

For the first part, the mass sits at rest on the spring, so it is at the equilibrium position and thus mg = kd So, d = mg/k For the second part, I assume the uncompressed spring position is 0. When the mass at rest at the top. Its KE and PE is 0. When the mass at distance D, the question said...
10. ### I Exploring the Mechanics of Energy Conservation: Understanding the Paradox

Hello everyone! I've been studying work and energy, and one problem I have is understanding conservation of mechanical energy. If on a rollercoaster you have two points A and B you expect the mechanical energy at A to be equal to the mechanical energy at point B, makes sense to me; but I started...

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12. ### Exponential potential energy state diagram

It is my second "energy state diagram problem" and I would want to know if I am thinking correctly. First I have done some function analysis to get a glimpse of the plot: - no roots but ##\lim\limits_{x\to-\infty}U(x)=\lim\limits_{x\to+\infty}U(x)=0## - y interception: ##U(0)=-U_0## - even...
13. ### Mechanical energy- how to solve for v

Hi there, I am doing a mechanical energy question. I think the solution is simple but I'm stuck on an algebra step. This is the solution but I am really not sure how they have simplified down to Va. For example I tried to factor out the m resulting in 1/2mv^2=m(1/2va^2+gh) Then I cancel...
14. ### Conservation of Mechanical Energy

Okay For a this is what I did. a. I'm confused about B. I understand that it has something to do with the Conservation of Mechanical Energy, but I don't exactly know what to do.

16. ### Proving that the total mechanical energy is conserved with time

To prove: total mechanical energy is constant with time where ##E(t)## is the total mechanical energy and ##V(x(t))## is the potential energy of the object-system. $$E(t) = 1/2 mv^2 + V(x(t))$$ taking the the derivative of ##E(t)## with respect time should give 0. in the third step in the...
17. ### Mechanical Energy of two Cannonballs fired at two different angles

I solved for both heights: h1 = (1.85x10^4)m, h2 = (5.10 x 10^4)m Question is knowing ME = PE + KE for ball at h1 (angled 37 degrees), is it safe to assume there would be no KE as velocity would equal zero at the highest point? So the mechanical energy = mgh ? Would it be the same for ball at h2?

20. ### Can we say that work done can be used only for mechanical energy?

When we say that we apply force to a wall then we didn't transferred energy because of no displacement, but I think we somehow increase many types of energy of the wall. For e.g:- potential energy of particles in wall e.t.c. So according to me it means that we defined work only for mechanical...
21. ### Climbing with Tension: Exploring Muscle vs. Mechanical Energy

Here the upward force on the camp is Tsinx <=360 Therefore T(max)=720N Here they have taken the equation that T-mg=ma This shows that the man is climbing due to tension. But I can't visualise how tension helps in climbing. Isn't it our own energy that helps us to climb. The muscle energy gets...
22. ### How exactly does a turbine convert mechanical energy into electrical?

I understand that the turbine drives rotational motion of a low and high speed shaft which rotates within the generator, but how exactly, and with what components/materials does this create electrical energy? Is there a minimum required rotational speed or torque required to generate...
23. ### Is Bernoulli's Equation related to the Conservation of Mechanical Energy?

So the Bernoulli's Equation.. My question : Are the terms on the left hand side equal to the total mechanical energy? So can I rewrite this equation as ?
24. ### How does the energy from ATP get to converted to mechanical energy?

OK, so ATP releases energy. At what point are things moving? How does this "energy" lead to a muscle fiber contracting?
25. ### Problem involving energy/motion

Homework Statement A ball of mass m=0.300 kg is connected by a strong massless rod of length L = 0.800 m to a pivot and held in place with the rod vertical. A wind exerts constant force F to the right on the ball as shown below. The ball is released from rest. The wind makes it swing up to...
26. ### Calculate the change in mechanical energy during collision

Homework Statement A 15 kg block is attached to a very light horizontal spring of force constant 5000.0 N/m and is resting on a frictionless table. It is struck by a 3.00 kg stone at 8.00 m/s to the right, then rebounds at 2.00 m/s to the left. Homework Equations ΔE = ΔK + ΔU The Attempt at...
27. ### Calculating Mechanical Energy of a Launched Ball

Hi Everyone, I can't seem to figure this problem out. Please help! 1. Homework Statement A ball was launched upwards and vertically at a speed 3 m/second up to a height 4m. Calculate the mechanical energy of the ball if its weight is 5 Newtons and has a mass 0.5kg . Homework Equations...
28. ### Percentage energy loss (mechanical energy) problem

Homework Statement Problem: An object with mass 2.0 kg slides down a low-friction incline and its speed measured at the bottom is 2.7 m/s. The object starts sliding at a height of 0.50 m over the tabletop and its speed is measured 0.10 m over the tabletop. How big is the percentage energy loss...
29. ### Mechanical energy for planet in elliptical orbit around star

Homework Statement A planet is in an elliptical orbit around a star. Which of the following best represents the mechanical energy E_planet of just the planet and the mechanical energy Es_tar-planet of the star-planet system as functions of time for one complete orbit? Homework Equations...
30. ### Mechanical energy lost when child jumps onto merry-go-round

Homework Statement I have a basic problem where a child jumps tangentially onto the outer edge of a stationary merry-go-round, and you have to use conservation of momentum to find the final angular speed of the merry-go-round. But the next part of the question asks "how much mechanical energy...
31. ### B Constant Force: Energy Conservation & Path Independence

I had an argument with my friend regarding constant forces.He said that work done by constant forces are conservative as we can take the force out of the integral and it doesn't depend on the path .But the fact that this information is not given in my textbook as well as by teachers makes me...
32. ### Small scale mechanical energy battery

Hi there. I am a novice but I was wondering what you all think is the most applicable mechanical energy storage device for small scale off grid applications is. I just read the thread on pump storage and it seems like a good idea but I thought I would keep it broad. Thanks!
33. ### How to Find the Potential Energy of a Particle # 9 - YouTube

How can one find the potential energy of a particle. The derivation of PE can be done by the fact that change in PE of a particle is equal to negative of work done by a force on the particle. This combined with Kinetic energy work theorem gives us an equation on conservation of mechanical energy.
34. K

### Side kick on a falling object, mechanical energy and work

If an object with 1kg mass falls free (no air drag), from 100 meters high, and the gravitational acceleration is 9.81, then the mechanical energy will be: 1*9.81*100 = 981 joules. The work the gravitational force does on the object will be: 9.81N*100m = 981 joules. Another object with same...
35. ### Conservation of mechanical energy

Derive equation v= √((2gh)/(1+.5(m/M)(r/R)^2)) by applying conservation of mechanical energy. A string is attached to a hanging mass and wrapped around a small cylinder. The hanging mass is released from rest from an initial height (h) and accelerates to the floor. The theoretical velocity (v)...
36. T

### What exactly is mechanical energy?

Regards my question is the following. I know that mechanical energy is considered as a sum of potential and kinetic energy. But I still do not understand exactly what is the mechanical energy.Whether kinetic energy and potential energy are forms of mechanical energy or that the kinetic and...
37. T

### How does an electric motor convert electrical energy to mechanical energy?

how does electric motor convert electrical energy to mechanical energy. Hello I do not understand the following electric power is P = V * I electric motors operate on the principle of repulsion and attraction of magnetism. What confuses me where that power ends because as far as I know, the...
38. ### Mechanical energy of a block sliding on a circular path

Homework Statement ( The following problem is taken from kleppner's " Introduction to mechanics" ) ( The question in the book talks about the velocity but my confusion is related to the Energy ) Homework Equations Conservation of Mechanical energy : Ef - Ei = 0 Consevation of Momentum : Pf -...
39. ### Mechanical energy to kinetic energy storage....?

Can there be a system that utilizes mechanical energy to produce kinetic energy, but "storing" the mechanical energy to be used at a different time for kinetic energy? Like a bike where you pedal but don't move; that mechanical energy is waiting to be "released" by some mechanism *** exclude...
40. ### How Fast Does a Rock Fall from 20 Meters?

Homework Statement A rock with a mass of 0.2 kg is dropped from a height of 20 m. At what velocity does the rock strike the ground?Homework Equations KE= 1/2mv^2 PE=mgh The Attempt at a Solution 0.2x9.81x20=1/2mv^2. 39.24=.1(v^2) 392.4=v^2 v=19.8 m/s First time doing one of these problems...
41. ### Conservation of Mechanical Energy: Equations not equivalent?

1. The problem A very simple question on a quiz given to me states that, "A 63 kg diver is standing on a diving board waiting to commence her dive. The diving board has compressed 0.08 m. Determine the elastic potential energy of the diver." 2. The attempt at a solution I thought this question...
42. ### Electrical and Mechanical Energy as it relates to Capacitors

Homework Statement In my lab, we are studying the efficiency of a simple DC motor. In order to do this, we related the initial potential energy of the capacitor to the final potential energy of a mass (which remained constant for all three capacitors) that the motor lifted. I was instructed...
43. ### Mechanical Energy Problem/non-conservative forces

Homework Statement A body of mass "m" is let go from on top of a surface A, where it slides down to B(without friction). From that point on, it displaces itself on an horizontal surface 5 meters away from B, where it stops at C. Being "m" a mass in kg "h" in meters and g = 10 m/s^2 The value...
44. ### Finding the total mechanical energy

Homework Statement A bead is sliding on a surface. At point A it is 80 cm above the ground, at point B it has just hit the ground and at point C it is 50 cm above the ground. At point A it has a speed of 200 m/s, so what will its speed be at point B and C? Homework Equations W=F.d Kinetic...
45. ### Find the potential, kinetic, and mechanical energy

Homework Statement A 1.40 kg block slides with a speed of 0.885 m/s on a frictionless horizontal surface until it encounters a spring with a force constant of 637 N/m . The block comes to rest after compressing the spring 4.15 cm. Part A Find the spring potential energy, U, the kinetic energy...
46. ### Find final speed using mechanical energy formula

Homework Statement A skateboarder at a skate park rides along the path shown in (Figure 1) .If the speed of the skateboarder at point A is v=1.3m/s, what is her speed at point B? Assume that friction is negligible. Homework Equations ui+ki=uf+kf u=mgh k=1/2mv2 The Attempt at a Solution...
47. ### Calculating Maximum Height of an Arrow with Loss of Mechanical Energy

Homework Statement A 125 - G arrow is shot vertically upwards with a Vi of 28/ms. Assuming a 20% loss in Mechanical Energy while ascending, what maximum height above the position it was shot does it reach? Homework Equations Vi= 28m/s Vf= O m/s D= ? a= -9.8 m/s Vf^2= Vi^2 + 2aD Eg = mgh Ek =...
48. ### Need help with Mechanic Energy math problem.

Homework Statement "A little girl is sliding down a snowy hill on her sledge and out on a horizontall flat area. The girl has a physics interested mom which wants to know what the maxium speed the sledge can reach. She measures that the hill is 3,0m high and 6,0m long. The sledge slides for...
49. ### Conservative forces and conservation of mechanical energy

Why do conservative forces conserve mechanical energy while non conservative forces do not? According to me, What makes the conservative forces path independent is that for a particular case they always act in a fixed direction irrespective of the direction of motion of the object on which they...
50. ### Frames of Reference: A Skateboarder's View - Comments

kuruman submitted a new PF Insights post Frames of Reference: A Skateboarder's View Continue reading the Original PF Insights Post.