A ball of mass m, initially at rest, falls from a height h through a curved path to ground level (see figure). Then it is damped by a spring with a constant of elasticity k, until it stops. Using the law of conservation of mechanical energy, find the velocity of the ball just before it touches the spring and the distance the spring is compressed from its equilibrium length to when the ball stops.

Q: A block of massm = 8.2 kg slides on a rough surface and moves toward a spring with a spring constant…

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Q: height ℎ, with negligible friction. At the bottom, where it is moving horizontally, it collides with…

A: a) First, we need to calculate the speed v1 of the crate of mass m1 at the bottom of the hill using…

Q: A 2.5-kg block moving at 2.0 m/s collides with a spring whose spring constant is 3900 N/m, as shown…

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Q: A box is attached to a spring and at rest at the equilibrium position of the spring when a bullet…

A: When the body is placed at the surface with coefficient of friction μ, the friction force is given…

Q: A block of mass m = 1.5 kg initially moving to the right with a speed of 3 m/s on a frictionless,…

A: Given data:  Mass (m) = 1.5 kg Initial speed (v) = 3 m/s Spring constant (k) = 400 N/m Final speed…

Q: A child is on a swing. At the bottom of the swing’s oscillation, the speed and height above the…

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Q: A roller coaster begins with the 500 [kg] car (including riders) on the lowest horizontal section of…

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Q: Consider a 10.0 g bullet shot into a 4.0 kg block that rest on a frictionalhorizontal surface, where…

A: The objective of this question is to find the initial velocity of the bullet and the force that the…

Q: A wooden block with mass 1.85 kg is placed against a compressed spring at the bottom of a slope…

A: Part A. The distance between point A and B is d=7.55 m. So, according to the given conditions, the…

Q: A 2-kg block is initially at rest and pressed against a spring (k = 500 N/m) at A compressing the…

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Q: 0.25 kg mass is held against a compressed spring with a spring constant of 2,658 N/m. The mass is…

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Q: A 5.0-kg block, initially at rest, travelled from point A to point D where it compressed a spring by…

A: Let us analyse the question in step 2.

Q: A 2-kg block on a rough horizontal surface is attached to spring (k = 800 N/m); the other end of the…

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Q: given by u = 0.400. How far has the spring compressed by the time the block first momentarily comes…

A: Here some of the initial kinetic energy changes into potential energy of spring and some will…

Q: crate of mass m1 slides down a well-lubricated hill of height h, with negligible friction. At the…

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Q: A 2.5-kg block moving at 2. 0 m/s collides with a spring whose spring constant is 390 N/m, as shown…

A: a. according to the conservation of energy, for the given case, 12mvi2+mgh=12kΔx2

Q: The figure shows a track made up of two sections and located in a vertical plane. Section ab is…

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Q: A block of mass m=7.3kg slides on a rough surface and moves toward a spring with a spring constant…

A: We have givenMass of block (m)=7.3 kgSpring constant (k) = 1659 N/mWhen Block is d=22.6 m away from…

Q: A 0.87 kg block on a connected to a spring (whose spring constant is 3.80 N/m). The horizontal…

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Q: A 45 kg gymnast is bouncing on a trampoline. Model the gymnast as a particle and the trampoline as a…

A: given that,k=15000 NmA=30cm=0.3 mm=45 kgg=9.8ms2

Q: A 500-g block is released from rest and slides down a frictionless track that begins 1.90 m above…

A: Given data: Mass of the block is, m = 500 g = 0.5 kg Height of the block from horizontal is, h =…

Q: A 1.10-kg object slides to the right on a surface having a coefficient of kinetic friction 0.250…

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Q: A 1.30-kg object slides to the right on a surface having a coefficient of kinetic friction 0.250…

A: (a) Applying law of conservation of mechanical energy between (b) and (c) in figure…

Q: A 1.10-kg object slides to the right on a surface having a coefficient of kinetic friction 0.250…

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Q: spring-loaded toy gun is aimed vertically and fired after a spherical projectile of mass m = 28.0 g…

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Q: A 10-kilogram block is dropped from point A as shown. The rail is frictionless except for the 6 m…

A: The expression for the work done by the friction force,   The expression for the initial kinetic…

Q: We are looking at an elastic pendulum which is constructed by suspending a weight of mass m = 0.100…

A: There are many different types of motion that can occur in an elastic pendulum, which is a simple…

Q: spring constant is 400 N/m, the height of the incline is 2.0o m, and the horizontal surface is…

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Q: A spring is attached to an inclined plane as shown in the figure. A block of mass m is placed on the…

A: Mass = m Distance = d Initial speed = v Incline angle = θ The surface is friction-less.  Let the…

Q: A block of mass m = 4.30 kg initially slides along a frictionless horizontal surface with velocity…

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Q: A crate of mass m1 slides down a well-lubricated hill of height h, with negligible friction. At the…

A: We are given spring constant and mass of crate attached to spring. We are also given compression in…

Q: A block of mass m=0.25 kg starts at rest at the top of an inclined plane of height h=0.8 m as shown…

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Q: A 0.28 kg mass is held against a compressed spring with a spring constant of 2,446 N/m. The mass is…

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Q: A horizontal spring on a frictionless surface with a spring constant of 50 N/m is compressed 0.4 m…

A: We will use conservation of energy,

Q: A 17.0 g marble is fired vertically upward using a spring gun. The spring must be compressed 16.0…

A: Given data:  Mass of marble (m) = 17.0 g = 0.017 kg Compression in spring (x) = 16.0 cm = 0.16 m…

Q: A block of mass 2.9 kg is sitting on a frictionless ramp with a spring at the bottom that has a…

A: Given data: Mass of the block m=2.9kg Spring constant k=470 N/m The angle of the ramp θ=13° Distance…

Q: An object with a weight of 5 N is left on the arc with a coefficient k = 2 N / cm from the height h.…

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Spring Potential Energy

The potential energy is the energy possessed by a body by virtue of its position or the energy held by the object due to its position relative to other objects, its force like stresses, charge, and other factors affecting the particles of the body. The potential energy is the measure of the net work done by or on the body. The spring potential energy is the potential energy stored due to the deformation of an elastic spring and this elasticity is due to the stretched spring. The elasticity is the ability of a solid-state matter to come back to its equilibrium position or original position after any kind of external force is acted on it. It is also known as Elastic potential energy. The potential energy here is caused due to the displacement of the spring from its equilibrium position to another position and this potential energy is equal to the net work done due to the stretching of the spring. It also resembles the same mechanics of the oscillation of a simple pendulum, where due to the external force, the object moves from its equilibrium position to its maximum ends and the periodic motion continues till it comes back to the equilibrium position to rest.