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A: Option A is correct. 8Explanation:
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- The force on a particle is described by 6x° + 1 at a point x along the x-axis. Find the work done in - 2. moving the particle from the origin to x =I can't find the tangential component of the accelerationThe force on a particle is described by 5x° – 5 at a point x along the x-axis. Find the work done in moving the particle from the origin to x = 4. -
- 65. If a bucket of water spins about a vertical axis with constant angular velocity o (in radians per second), the water climbs up the side of the bucket until it reaches an equilibrium position (Figure 11). Two forces act on a particle located at a distance x from the vertical axis: the gravitational force -mg acting downward and the force of the bucket on the particle (transmitted indirectly through the liquid) in the direction perpendicular to the surface of the water. These two forces must combine to supply a centripetal force mo?x, and this occurs if the diagonal of the rectangle in Figure 11 is normal to the water's surface (i.e., perpendicular to the tangent line). Prove that if y = f(x) is the equation of the curve obtained by taking a vertical cross section through the axis, then -1/y' = -8/(@²x). Show that y = f(x) is a parabola. y =fr) mw?x mg FIGURE 11The motion of a point on the circumference of a rolling wheel of radius 2 feet is described by the vector function r(t) = 2(23t sin (23t))i + 2(1 - cos(23t))j - Find the velocity vector of the point. v(t) = Find the acceleration vector of the point. a(t) = Find the speed of the point. s(t) =The motion of a point on the circumference of a rolling wheel of radius 3 feet is described by the vector function 7(t) = 3(10t – sin(10t))ỉ + 3(1 – cos(104))} Find the velocity vector of the point. v(t) = Find the acceleration vector of the point. a(t) Find the speed of the point. s(t) =
- Show the complete solution for this force vibration without damping equationWhen a particle is located at a distance x feet from the origin, a force of x + 2x pounds acts on it. How much work is done in moving it from x=1 to x= 2?Find the work done by the force F = -2yi + 4xj along one loop of the curve r = sin 80 (in the positive direction).
