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Is −(4x − y)ˆx + (2y + x)ˆy − 3ˆz a conservative force?
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- The potential energy of a pair of hydrogen atoms separated by a large distance xx is given by U(x)=−C6/x6U(x)=−C6/x6, where C6C6 is a positive constant. What is the force that one atom exerts on the other? Express your answer in terms of C6C6C_6 and xxx. Is this force attractive or repulsive?Show that the total energy for a conservative system is constant.The figure shows a system of masses. The mass of 2m is connected to an immobile wall with a spring of constant 2k, while the mass of m is connected to an immobile wall with a spring of constant k. The masses are then coupled to each other with an elastic band of length L, under tension T =2kL. The masses are constrained to move in the x direction only. At equilibrium. the masses have the same x position and the springs are uncompressed. There is no friction or gravity. The displacements from equilibrium are small enough (x1, x2 << L), so that the tension in the band stays constant. 1-Write down the coupled differential equations describing the displacement of the masses from equilibrium {x1, x2}.
- A mass of 700 kg moving at a speed of 36 km/h collides with a horizontally mounted spring of spring constant 6.26*10^3 N/m, what is the maximum compression (meters) of the spring?A particle with mass m=1 starts moving subject to a conservative force, with initial total energy E=4 Joules (=kgm^2s^−2). Find the potential energy of the particle at time t1, when it has velocity v(t1)=3(ms−1). U(t1)=Rank the following quantities of energy from largest to the smallest. State if any are equal. (a) the absolute value of the average potential energy of the SunEarth system (b) the average kinetic energy of the Earth in its orbital motion relative to the Sun (c) the absolute value of the total energy of the SunEarth system
- Show that the Force of Gravity is conservative.Compute for the kinetic energy in ergs and in joules of a 2.0 gram riffle bullet traveling at 500 m/sec?Ans. 2.5 X 109 ergs ; 250 joules Please give me the solution.Suppose that a spacecraft of mass 6.9 x 104 kg at rest in space fires its rockets to achieve a speed of 5.2 x 103 m/s. How much work has the fuel done on the spacecraft?
- Calculate the valu of the time of flight of K-39 (K39) ion that has a kinetic energy of 12.2 x 10-18 J when the distance of the flight tube is 80 cm longWhen 20 N of force is applied to a spring of natural length 2 m, the resulting compression is 0.5 m. The work (in joules) done in compressing the spring from 1.5m to 1.0 m is given by the integralA spring with a fixed spring of K=200 (N/m) was attached to an object of M=8 (kg), which is stagnant on a horizontal ground without friction. An object of m=2 (kg) with the Mcismi shown in the figure is held with the spring x=0.8 (m). How much(m/s) is the speed of mass M when the system is released?
