Q₁ = -2.0 C and Q2 = 4.0 C. If Q₁ is at the origin (x = 0.0 m) and Q₂ is at x = 1.0 m, then is the force attractive or repulsive? Does the force on Q₁ due to Q₂ point in the - x or + x direction?
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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?(a) Newton’s Law of Gravitation states that two bodies withmasses m1 and m2 and attract each other with a force F= G m1m2/rsq. where r is the distance between the bodies and G is thegravitational constant. If one of the bodies is fixed, findthe work needed to move the other from r=a to r=bCalculate the work done by the force F(x, y) = y2 i + xy j in moving a particle along the line whichconnects (−1, 1) to (0, 0) and then along the parabola y = x2 from (0, 0) to (1, 1)
- A 1000 kg spacecraft is approaching Jupiter (which is at the origin). The position of the spacecraft is given by the vector RSC = (0.0,-2.533) x 106km. The velocity is given by VSC= (+6.00, +8.00) km/sec. The mass of Jupiter, (MJ=318 MEarth) and MEarth = 5.97 x 1024 kg. A) What is the potential and kinetic energy of the spacecraft (write each to 3 sig figs.) What is the total energy of the spacecraft? Call the total energy Ei. B) Can it escape Jupiter? Justify your answer. C) What is the angular momentum of the spacecraft around Jupiter? Call this Li.Find the work done by the force F= <(y+z), -(x+z), (x+y)> along each of the following closed paths: a. The circle x^2+y^2=1 in the z=0 plane, taken counterclockwise b. The circle x^2+z^2=1 in the y=0 plane, taken counterclockwiseFind the work done in moving a particle in a force field given by F = (3xy)i - (5z)j + (10x)k. Along the curve x = t^2 + 1, y = 2t^2, z = t^3 from t=1 to t=2.
- If a green particle (8 gm) is equally separated by a distance (d = 5 m) from two particle (A = 4 kg and B = 5 kg), Calculate the net gravitational force and the direction working on the green particle?(consider the following figure)Suppose a force field is given by F=(2x-y+z)i+(x+y z^{2}) } +(3x-2y+4z)k Find the work done in moving a particle once around a circle C in the xy-plane with its center at the origin and a radius of 3The three spheres in the figure, with masses mA = 83 g, mB = 8 g, and mC = 17 g, have their centers on a common line, with L = 23 cm and d = 5 cm. You move sphere B along the line until its center-to-center separation from C is d = 5 cm. How much work is done on sphere B(a) by you and (b) by the net gravitational force on B due to spheres A and C?
- Calculate the work done by the force field F(x,y,z)=(2xy,x2,3z) to move a particle from the point (0,0,0) to point (2,2,8) along the curve given by the intersection of the surfaces z=x2+y2 and x=y.Find the work done in moving a particle in a force field F = 3xyi - 5xyzj + 10xk along: straight line (0,0,0) to (2,3,4) space curve x = 2t3, y = 2t2 , z = 3t3-t2 from t = 0 to t = 3 The curve defined by x2 = 4y, 3x3 = 8z from x = 1 to x=3Consider an object of mass m = 4 kg on a frictionless table. The object experiences a repulsive force F = a/x2 + b/x, where F is in newtons and x is the position of the object relative to the origin. If the object starts at rest at a position x3 = 1.3 m and is released, at what speed v, in meters per second, will the object be moving when it is at position x4 = 12.5 m?