# mechanical energy Definition and Topics - 23 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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1. ### 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...
2. ### B Constant force?

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...
3. ### 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.
4. 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...
5. ### 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)...
6. ### 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...
7. ### Arrow Loses 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 =...
8. ### 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 physic intrested 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 12.5m...
9. ### 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.
10. ### Energy for Linear 1D Systems - 1D potential

Homework Statement A particle of mass m moves along the x–axis under the influence of force ##F_x=-ax+bx^3## , where a and b are known positive constants. (a) Find, and sketch, the particle's potential energy, taking U(0) = 0 (b) Identify and classify all equilibrium points (c) Find the...
11. ### Mechanical energy in an harmonic wave and in normal modes

I think I miss something about energy of a mechanical wave. In absence of dissipation the mechanical energy transported by an harmonic wave is constant. $$E=\frac{1}{2} A^2 \omega^2 m$$ But, while studying normal modes on a rope, I find that the mechanical energy of a normal mode (still...
12. ### Mechanical energy of element of a rope with sinousoidal wave

I'm confused about energy driven by a wave. Consider a sinousoidal wave moving in a rope. Each element ##dm## of the rope follows a simple harmonic motion in time. That means that the mechanical energy ##dE=dK+dU## of the element ##dm## is constant. Nevertheless on Halliday-Resnik-Krane I...
13. ### Question on energy conservation with centripetal acceleratio

Homework Statement The right answer is E, and I have no idea how to solve this problem. Please advise on how to proceed. Thanks in advance. Homework Equations conservation of mechanical energy?? The Attempt at a Solution Many attempts were done, but I am lacking on theory with this. How...
14. ### Smooth rolling motion - conservation of energy?

This isn't about a specific physics problem, but rather a question: Given I have a ball or cylinder rolling smoothly along some path, is it generally true that mechanical energy is conserved? I.e. if ##E_mech = K+U = K_{trans} + K_{rot} + U##, then ##\Delta E_mech = 0##? I have been able to...
15. ### Impulse of force correct here?

Im sure Imma mess this up, probably because Im really tired....but I have a bullet that weights .015kg's and is moving at 285m/s, so 609.18J's as with KE. I hit a 70kg block, penetrates .3048 meters thus exerting 1998.62N's of force, which is a lot of force. .3048/285m/s so 0.00106 seconds...

Homework Statement At a certain location, wind is blowing steadily at 10m/s . Determine the mechanical energy of air per unit mass and the power generation potential of a wind turbine with 60m diameter blades at the location. Density of air is 1.25kgm-3. ( ans : 0.05kJ/kg, 1770kW ) Homework...
17. ### Change in mechanical energy (gravitation)

I got a little bit confused while studying gravitational potential energy, particularly the expression for long distances: (-GMm/r). An exercise asks me for the velocity, period and radial acceleration for a 1000kg satellite that I wish to put into orbit. That's okay. But after that, I'm...
18. ### Conservation of Mechanical Energy

Homework Statement This is my first time posting here guys so correct me if I am wrong. This question was on my test and I wanted to know if I did it right. There is a block of mass m and it is moving at a certain velocity before pressing against a spring which compresses distance x. Find...
19. ### "Attraction Force x Energy Accumulation" clarification

First of all, I did not major in Physics, but I did pass GCE with A. (This is to make a point, not to boast.) But there's a matter that doesn't make any sense to me, and none of my acquaintances could give me the clarification so I came to this forum, hoping someone can make me understand this...
20. ### Energy dissipation of steel washers

Is there an optimum number of washers to be used on a threaded bolt in respect to dissipation of energy towards the nut? And how would one calculate the dissipation rate of each washer?
21. ### Mechanical energy of frictionless pulley

Homework Statement In the system shown, the block M (mass of 15.65 kg) is initially moving to the left with a speed of 3.4 m/s The mass of m is 8.26 kg and the coefficients of friction are μs=0.411 and μk=0.304. The string is massless and the pulley is massless and frictionless. How fast will M...
22. ### Kinetic and potential energy in firing a cannon

Homework Statement A 20.0 kg cannonball is fired from a cannon with a muzzle speed of 1000 m/s at an angle of 37.0° with the horizontal. A second ball is fired at an angle of 90.0°. (a) Use the isolated system model to find the maximum height reached by each ball. (b) What is the total...
23. ### Block Sliding Down a Ramp that is Free to Slide

Homework Statement A block with mass m rests on a smooth, frictionless ramp with mass M and height h. The ramp itself sits on a frictionless horizontal surface in which it is free to slide. The block slides smoothly down the ramp from rest. We want to find the speed of the block after it has...