What is the acceleration of a particle at x=10 m if the mass of the particle is 0.2 kg ? the particle is moving along x axis with the potential energy U(x)= 8x^2-2x^4
- print Print
- list Cite
Expert Answers
calendarEducator since 2010
write12,551 answers
starTop subjects are Math, Science, and Business
Work is given by the product of the force and distance. The work done contributes to an increase in potential energy.
Work = -delta U.
Force* distance = -delta U
Here we have the function of the potential energy given as U(x) = 8*x^2 - 2*x^4.
For an infinitesimally small change in distance
d/dx (Force* distance) = -U'(x)
Force = -U'(x)
U'(x) = 16x - 8x^3
At x = 10,
U'(x) = 16*10 - 8*1000
=> 160 - 8000
=> -7840
=> Force = - (-7840)
=> Force = 7840
So the force at this point is 7840.
Force is the product of the mass and acceleration. We know that the mass is 0.2 kg.
Therefore the acceleration is 7840 / 0.2 = 39200 m/s^2
Related Questions
- Can an object have kinetic energy and potential energy at the same time?
- 1 Educator Answer
- A 3 kg stone is dropped from a height of 100 m . Find its kinetic and potential energies when it...
- 1 Educator Answer
- A particle of mass m moves along the x axis. Its position varies with time according to...
- 1 Educator Answer
- In the context of conservation of energy what effect does friction have on kinetic energy and...
- 1 Educator Answer
- The mass of the Earth to be 5.98 X 10^24 kg. If the Earth's gravitational force causes a falling...
- 1 Educator Answer
The acceleration is the ratio of the force and the unit mass.
Since we know the potential energy, we'll determine the intensity that is the same as acceleration.
dU/dx = d(8x^2-2x^4)/dx
dU/dx = 16x - 8x^3
Now, we'll substitute x by 10 m:
T = dU/dx
T = 16*10 - 8*10^3
T = 160 - 8000
T = a = -7840 m/s^2
Student Answers