droplets of water, each of radius 0.2 mm, coalesce into a single drop. Find the change in total surface energy. (surface tension 0.072 N / m)
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- 1. A particle moves in one dimension and is subject to a conservative force, whose potential energy function is given by U(x), where a and b are positive constants. U ( x ) = a x 3 − b x a) Find the two equilibrium positions of the particle. b) For each of the two equilibrium positions, determine whether the equilibrium is stable or unstable.SMH7(a) Take U = 5 for a system with a particle at position x = 0 and calculate the potential energy of the system as a function of the particle position x. The force on the particle is given by (8e-2x) î . (b) Explain whether the force is conservative or nonconservative and how you can tell.
- In Lagrangian mechanics, the Lagrangian technique tells us that when dealing with particles or rigid bodies that can be treated as particles, the Lagrangian can be defined as: L = T-V where T is the kinetic energy of the particle, and V the potential energy of the particle. It is also advised to start with Cartesian coordinates when expressing the kinetic energy and potential energy components of the Lagrangian e.g. T = m (x² + y² + 2²). To express the kinetic energy and potential energy in some other coordinate system requires a set of transformation equations. 3.1 Taking into consideration the information given above, show that the Lagrangian for a pendulum of length 1, mass m, free to with angular displacement - i.e. angle between the string and the perpendicular is given by: 3.2 4.1 4.1.1 4.1.2 4.1.3 4.1.4 4.2 L = T-V = ²² +mg | Cos Write down the Lagrange equation for a single generalised coordinate q. State name the number of generalised coordinates in problem 3.1. Hence write…m, A particle of mass 2.00 × 10-10 kg is confined in a hollow cubical three-dimensional box, each edge of which has a length, 2.00 × 10-10 and for which the potential energy function is zero inside, and infinite outside, the box. The total energy of the particle is 2.47 × 10-37 J. FindYou have been asked to design a "ballistic spring system" to measure the speed of bullets. A bullet of mass m is fired into a block of mass M. The block, with the embedded bullet, then slides across a frictionless table and collides with a horizontal spring whose spring constant is k. The opposite end of the spring is anchored to a wall. The spring's maximum compression d is measured. What percentage of the bullet's energy is "lost"?
- A bullet having mass of 0.002kg hits a stationary block of wood having a mass of 14kg. The coefficient of kinetic friction between the block and floor is 0.12, and the block slides 3mm on the floor as a result of impact. Compute the energy lost during the impact. Provide FBD. Thank yooou.A 6.23 kg bundle starts up a 32.9° incline with 146 J of kinetic energy. How far will it slide up the incline if the coefficient of kinetic friction between bundle and incline is 0.175? I tried to solve this and used the equation ((146-sin(32.9)*0.175*6.23*9.8)/(9.8*6.23)) and came up with the awnser of 2.2962701829236 which is incorrect. can you tell me where I made my mistake?Use the sine and cosine law to add the vectors a→=12 N [E 12° S] and b→=80.0 N [S 20° E].
- What is the power in kW produced by the La Rance tidal power station in France if the usable tidal range is 10 m? The barrage is 140m long and the area of the basin behind the barrage is 22 km2. Tidal period is 12h 25minutes. Density of salt water is 1020 kg/m3. Use proper units and 3 significant figures.Edrops Epuddle If a puddle of liquid on a table is converted into a collection of 28 drops, by what factor c = does the surface energy change? Round your answer to two decimals. Assume that the original pool was flat with a depth of 1.2 mm and that the drops are spherical caps (you can Google this), each with a height of 4.0 mm and a radius of 10.5 mm. The side area of the puddle can be neglected. c =An astronaut lands on a newly-discovered planet (without an atmosphere). As an experiment, she throws vertically upwards a pure vanadium sphere of radius 2.0 cm and density 5.5 × 103 kg m3 with an initial speed of 3.0 ms 1. The point of release is 1.2 m above the ground. She observes the sphere to travel 4.8 m before it starts falling to the ground. Calculate the kinetic energy of the projectile just as it hits the ground.