A single conservative force Fx = (6x-12) N (x is in meter) acts on a particle moving along the x axis. The potential energy associated with this force is assigned a value of +20 J at x = 0. What is the potential energy at x = 3.0 m?

Q: A force on an object is given by F (x) = (-4.00N / m) x + (2.00N / m ^ 3) x ^ 3. What is the change…

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Q: The students is given 130 cm long ideal spring whose unstretched position is at x=0.00 cm. A student…

A: Spring constant, k=41.1 N/m xi=22.2 cm = 0.222 m xf=30.5 cm =0.305 m

Q: A 1100 kg car drives up a hill that is 15.2 mm high. During the drive, two nonconservative forces do…

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Q: A potential energy function for a system in which a two-dimensional force acts is of the form U =…

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Q: The force required to compress a non-standard spring as a function of displacement is given by the…

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Q: The normal force from the pogo stick on your feet has magnitude Npy(y) = F1(1 −y/h) where F1 =…

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Q: A 63kg skier coasts down a 30◦ slope. At the top of the slope her speed is 3.6m/s. She accelerates…

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Q: The potential energy function associated with a force acting on a system is U = 3x6y − 8x. What is…

A: Potential energy function is given by : U(x,y) = 3x6y - 8x To find : Force at the point (x,y)

Q: A potential energy function for a two- dimensional force is of the form U = ax3y + bx , where a=…

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Q: It takes you 1.5 s to push a 28 kg box by 4.4 m across a horizontal floor with a constant force of…

A: Given that,The time : t = 1.5 (sec)The mass of block : m = 28 (kg)The displacement of the block…

Q: A particle moves in a region where the potential energy is given by PE=2x^2 + x^4 ; PE is in Joules…

A: Solution:   Given the Potential Energy of the system (PE) =2x2+x4   Where,   PE is in Joules and x…

Q: A 69.0-kg athlete leaps straight up into the air from a trampoline with an initial speed of 8.9 m/s.…

A: The objective of the question is to find the maximum height the athlete attains, her speed at half…

Q: A hockey puck of mass 0.25 kg is sliding along a slippery lake with an initial speed of 60 m/s. the…

A: Given that Mass m = 0.25 kg Initial speed u = 60 m/s Coefficient of friction μ = 0.030 Final speed V…

Q: A time dependent force F = 6t acts on a particle of mass 1 kg. If the particle starts from rest,…

A: We are aware that a particle with mass 1 kg is subject to the time-dependent force F=6t. We need to…

Q: A bag of wheat weight 320 kg .To what height should it be raised so that potential energy is 8460 J?…

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Q: A 520-kg dragster accelerates from rest to a final speed of 105 m/s in 390 m, during which it…

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Q: A 5.5 g marble is fired vertically upward using a spring gun. The spring must be compressed 8.0 cm…

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Q: speed at x = -4.5 m is v = 22.C

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Q: A particle of mass 2.9 kg moves along the horizontal x-axis. In the x direction the only force…

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Q: As a 1.5×104 kg k g jet plane lands on an aircraft carrier, its tail hook snags a cable to slow it…

A: Given: Mass of the plane (m) =1.5×104 kg spring constant (k) = 5.8×104 N/m e = 28 m

Q: Hk(X)=0.04x+0.1, where x is in meter. What is the work done by the friction force while the block…

A: Given: Mass (m) = 6.2 kg Angle of inclination (ϴ) = 300   The free-body diagram is shown as,…

Q: A single force acts on a I kg panticle-like object in such a way that the position of the object as…

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Q: Consider a mass and spring system. If the mass is pulled by distance x, stretching the spring by x,…

A: We have given a mass-spring system. The mass is pulled by distance x.

Q: The potential energy function associated with a force acting on a system is U = 3x4y − 2x.What is…

A: The vector force acting on system kept in a potential field U is given by- F→=-∂U∂xi^-∂U∂yj^

Q: A 5kg mass is attached to a spring and dropped. If the spring has a total elastic potential energy…

A: Write a given values of this question. PEe=34Jx=0.8mPEg=9800J  Attached mass with a spring. m1=5kg…

Q: F = −ax^2 , where a = 3 N/m2 what are the potential energies of the particle at x = 1 m and x = 2 m…

A: The force can be written as the negative gradient of potential and it is F=-∇UU=-∫F·dx…

Q: A 3.00 [kg] brick slides head-on to a spring with spring constant k = 320 [N/m]. When the 1 stops,…

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Q: A particle has a potential energy given by the function PE = - 6x3 + 43x, where x is meters.  Find…

A: Force F=-dUdx=-ddx-6x3+43x=18x2-43

Q: lock of mass m = 2.9 kg is placed on a rough incline surface making an angle θ = 13.8°  with…

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Q: A roller coaster cart of mass m = 241 kg starts stationary at point A, where h1 = 39.4 m and a while…

A: The potential energy of the car at A relative to the ground is given by, UA=mgh1

Q: fter it has traveled a certain distance and reached a point x = 45.0 m, y=90.0 m, the helicopter's…

A: Page 1

Q: The force F = (5.69 N)i + (7.69 N)j acts on a particle as it moves first along the x axis from x =…

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Q: A typical muscle fiber is 2cm long and has a cross-section area of 3.1x10^-9m^2. When the muscle…

A: Work don by muscle is  W = Force × Change in length      = F × dr.

Q: A physicist has been studying the effects of an unknown force. The work required to move an object…

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Q: You throw a ball of mass 15.0 kg straight upward into free fall with an initial kinetic energy of…

A: Given: Mass of ball = 15.0 kg. Initial kinetic energy = 7.0 J

Q: A box m = 85 kg is being pulled by a constant force F = 150 N at an angle of θ= 25 degrees. The…

A: Given data *The mass of the box is m = 85 kg *The angle is θ= 25 degrees *The block moves a distance…

Simple harmonic motion

Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.

Simple Pendulum

A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.

Oscillation

In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.