a block with 3 kg attached on spring , the spring elongate by 1.5 cm , the the block removed and another block 1kg attahced. calculate : a- the elongation in this state b- the work done to the spring to make an eleongation 4 cm from its equilibruim position

a block with 3 kg attached on spring , the spring elongate by 1.5 cm , the the block removed and another block 1kg attahced. calculate : a- the elongation in this state b- the work done to the spring to make an eleongation 4 cm from its equilibruim position

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter7: Hamilton's Principle-lagrangian And Hamiltonian Dynamics

Section: Chapter Questions

Problem 7.18P

See similar textbooks

Related questions

Q: Suppose the potential energy function for a particle moving in 1D is given by U(x) below. Find all…

A: To find the equilibrium points

Q: An ideal spring is holding up a massless pulley as shown above. The end of the rope running over the…

Q: A 2.00-kg pendulum ball is attached to a light-uniform cable of length 1.20 m that is hanging from…

A: Given Information:- Mass of the pendulum ball is mP=2.00 kg. Length of the cable is l=1.20 m. The…

Q: A body of mass m is suspended by a rod of length L that pivots without friction (as shown). The mass…

A: a. Draw the free-body diagram of the mass m.

Q: A pendulum consists of a 2.0-kg block hanging on a 1.5-m length string. A 10-g bullet moving with a…

A: Given, mass of block mblock = 2 Kg Length of sting L = 1.5 m Mass od bullet mbullet = 10 g = 0.01 m…

Q: A ball is held at rest at some height above a horizontal surface. Once the ball is released at time…

A: In this question we are given that a ball is held at rest at some height above a horizontal surface.…

Q: The spring of a spring gun has force constant k = 406 N/m and negligible mass. The spring is…

Q: A weight of 40N is placed on a horizontal plane touching one end of a horizontal spring whose other…

A: Given spring constant k= 5N/mm=5000N/m Weight of block =40N this gives mass m of block =4.08kg ~4 kg…

Q: A 5.00-kg block is moving at 5.00 m/s along a horizontal frictionless surface toward an ideal…

A: Given data: Mass of the block, m=5.00 kg Speed of the block, u=5.00 m/s Compression in the spring,…

Q: A 2.00-kg pendulum ball is attached to a light-uniform cable of length 1.20 m that is hanging from…

A: When pendulum moves its total energy is conserved, hence Potential energy at A = Kinetic energy at B…

Q: A ball of mass m, is released from the rest at point A and it collides with the second ball of mass…

Q: Consider a system of two objects and Earth. Object X and object Y are held together by a light…

A: Mass of object X = MxMass of object Y = MyInitial height of both objects = H My is greater than Mx

Q: he block shown lies on a horizontal frictionless surface, and the spring constant is 70 N/m.…

A: To determine,The position(x) of the block in meters.given,spring constant(k) =70 N/mmagnitude of…

Q: A ball of unknown mass mm is tossed straight up with initial speed vv. At the moment it is released,…

A: Energy conservation law,

Q: A 6.50 ✕ 105 kg subway train is brought to a stop from a speed of 0.600 m/s in 0.800 m by a large…

A: According to question---- Given data--- Mass m = 6.5 × 105 kg. Speed = 0.6 m / sec. X = 0.8 m. We…

Q: A cube with the dimensions bxbxb and a mass, m, lies on a horizontal surface. The cube is subjected…

A: To determine: The distance travelled by the cube on the horizontal surface.The mass of the cube is…

Q: Consider a linear spring, as in Figure 7.7(a), with mass M uniformly distributed along its length.…

Q: Consider a concrete block weighing 1 kg. How far do we have to drop to change the positional energy…

A: Given data: Mass of the block (m) = 1 kg Change in positional energy (ΔPE) = 1 kJ = 1000 J Required:…

Q: A box of mass m is pressed against (but is not attached to) an ideal spring of force constant k and…

A: Answer:- the box will go up the incline twice as high as before according to below one solution of…

Q: A ball of unknown mass m is tossed straight up with initial speed v. At the moment it is released,…

A: according to the conservation of energy, KEinitial+PEinitial=PEfinal

Q: An object undergoes simple harmonic motion. When it momentarily passes through the equilibrium…

Q: Submit Answer Tries 0/8 Iter m, leaves the spring, it slides across the table and makes an inelastic…

A: We know that spring force is given as F = kx where k is the spring constant x is the displacement…

Q: A projectile of mass m is fired with a velocity of 50 m/s at an angle of 60° with the horizontal. At…

Q: When a 4 kg mass is hung vertically on a certain light spring that obeys Hooke's law, the spring…

Q: A 2.00-kg pendulum ball is attached to a light-uniform cable of length 1.20 m that is hanging from…

A: Mass of pendulum, m1=2.00 kgAngle with the vertical, θ=50.0°Length of cable, L=1.20 mMass of block,…

Q: A 6.50 ✕ 105 kg subway train is brought to a stop from a speed of 0.500 m/s in 0.600 m by a large…

A: Given that - mass of the Subway train Speed of the train Distance from the spring bumper To Find -…

Q: Two steel balls are suspended by vertical strings (not necessarily of the same length), so that at…

A: This problem is based on the energy conservation. If one of steel ball touches the other when it…

Q: o persons were practicing social distancing to alleviate the spread of COVID-19. Social distancing…

A: Given Mass m1 = 60 kg Mass m2 = 68 kg Initial distance r1 = 3 ft = 90 cm = 0.9 m Final distance r2 =…

Q: A ball of unknown mass m is tossed straight up with initial speed v. At the moment it is released,…

A: Solution:- Step-1

Q: 7.14 •• An ideal spring of negligible mass is 12.00 cm long when nothing is attached to it. When you…

Q: A ball of unknown mass m is tossed straight up with initial speed v. At the moment it is released,…

A: Consider the motion of the ball when mass is going down at the same location where it is in…

Q: Two rigid bodies, A and B, both 1 kg in mass, are connected by a linear spring with a spring…

Q: consider a popgun with a spring constant 843 N/m. A projectile of mass 0.06 kg is inserted into the…

A: Apply the conservation of energy between final position (max height) and initial position.

Q: Find the work done in joules by gravity as an object of the mass m=10 kg is raised up at constant…

Q: A force F, where F (61- 36rj + 541 k) N, acts at time seconds on a particule P of mass 3 kg.…

Q: An ideal spring of negligible mass is 12.00 cm long when nothing is attached to it. When you hang a…

A: Length, L = 12cm mass, m = 3.15 kg length, L' = 13.40 cm U = 10 J

Q: The Brachistochrone Problem: Show that if the particle is projected with an initial kinetic energy…

A: Using energy conservation we get, mgh = mgy - ½mv02 Where h is the initial height , y is the height…

Q: please answer all with steps

Q: A block of mass m is moving with speed v along a horizontal frictionless surface toward an ideal…

Q: "A particle with a mass of .7 kg is attached to a horizonal spring with a force constant of 40 N/m.…

Q: Consider the Time Independent Schrödinger equation for a free particle, i.e. V (x)= 0: h? d'y(x) _…

A: A particle of mas m is in a region where its total energy EE is less than its potential energy U.U.…

Concept explainers

Center of Gravity of a system

The centre of gravity is a property that is based on the geometry of a rigid body or any particle. It is described as an equilibrium point or a hypothetical location where the total weight of the body is concentrated.

Question

classical mechanics :

a block with 3 kg attached on spring , the spring elongate by 1.5 cm , the the block removed and another block 1kg attahced.

calculate :

a- the elongation in this state

b- the work done to the spring to make an eleongation 4 cm from its equilibruim position

Branch of physics that focuses on the motion of an object when subjected to external forces. The object will be in equilibrium when the external forces are balanced.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

A 0.4 Gram mass is required to stretch a soap film confined in arectangular frame by 2mm downward before the film breaks. If the length of the movable bar is 2.5 cm, what will be the surface tension and change in surface free energy of the soap film?
Two steel balls are suspended by vertical strings (not necessarily of the same length), so thatat rest they are just in contact, with their centres at the same height. One is pulled aside in the vertical plane defined by the strings and released when it is at a height H above its original position. Determine the maximum possible height to which the other can rise, and the condition (the mass ratio) for this to happen.
Consider the van der Waals potential U(r)=U0[( R 0 r)122( R 0 r)6] , used to model the potential energy function of two molecules, where the minimum potential is at r=R0 . Find the force as a function of r. Consider a small displacement R=R0+r and use the binomial theorem: (1+x)n=1+nx+n( n1)2!x2+n( n1)( n2)3!x3+ , to show that the force does approximate a Hooke’s law force.
Consider a particle moving in the region x > 0 under the influence of the potential where U0 = 1 J and α = 2 m. Plot the potential, find the equilibrium points, and determine whether they are maxima or minima.
Show that the one-dimensional p(x) = Ae−ikx and three-dimensional expression p(x, y, z) = Ae−ikr is asolution to the Cartesian form of the Helmholtz equation, ∇2p + k2p = 0
A body of mass m is suspended by a rod of length L that pivots without friction (as shown). The mass is slowly lifted along a circular arc to a height h. a. Assuming the only force acting on the mass is the gravitational force, show that the component of this force acting along the arc of motion is F = mg sin u. b. Noting that an element of length along the path of the pendulum is ds = L du, evaluate an integral in u to show that the work done in lifting the mass to a height h is mgh.
An object of mass m is dropped from the top of an inclined plane of height h and large Θ and collides with a horizontal spring of elastic constant k that is at a distance d from the inclined plane. Determine a) The velocity of the object upon reaching the spring and its deformation; b) The speed of the ball considering friction μ only at the distance d from the horizontal surface and the deformation of the spring and then consider the friction in the inclined plane.
A ladder of length L and mass M is leaning against a wall. Assuming thewall and the floor are friction-less, the ladder will slide down the wall andalong the floor until the left end loses contact with the wall. Before the ladder loses contact with the wall there is one degree of freedom (θ). Using the formula for Euler-Lagrange EOM to find the Lagrangian and then the EOM for the ladder. Assume that gravity is present.
Physics students design an experiment to measure assorted coefficients of friction using a set-up similar to the one shown (not drawn to scale). A small balloon containing sand with a combined mass of 98.2gg is suspended with an ideal string of length 86.6cmcm, forming a simple pendulum. The pendulum is released from an angle of 41.4∘∘ with the vertical, and it collides with a block of mass 333gg located where the pendulum string becomes vertical. Because the balloon weighted with sand is soft and deformable, the collision is totally inelastic. The block slides for a distance of 30.8mmmm before coming to rest. a) Calculate the speed, in meters per second, of the sand-filled balloon at the instant prior to the collision. b) Calculate the speed, in meters per second, of the block at the instant following the collision. c)
A uniform density sheet of metal is cut into the shape of an isosceles triangle, which is oriented with the base at the bottom and a corner at the top. It has a base B = 13 cm, height H = 19 cm, and area mass density σ. e) Set up an integral to calculate the vertical center of mass of the triangle, assuming it will have the form C ∫ f(y) where C has all the constants in it and f(y) is a function of y. What is f(y)? f)Integrate to find an equation for the location of the center of mass in the vertical direction. Use the coordinate system specified in the previous parts, with the origin at the top and positive downward. g) Find the numeric value for the distance between the top of the triangle and the center of mass in cm.
A massless spring with equilibrium length d and spring constant k connects two particles. The system is flat and horizontal, yet it may spin and vibrate (ccompress\stretch).1- Determine the system's Lagrangian.2- Determine the system's Hamiltonian.3- Calculate Hamilton's equations of motion. It should be noted that the generalized momenta can be omitted. -It is worth noting that as the mass spins, it begins to expand. Hint: make your coordinate system's origin the center of the unstretched spring. also In generalized coordinates of (r_i) and (theta_i) , express your equations.
Calculate the moments Mx and My and the center of mass (x¯,y¯)(x¯,y¯) of a lamina with the given density and shape.