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- When a particle of mass m is at (x, 0), it is attracted toward the origin with a force whose magnitude is k/x2. If the particle starts from rest at x = b and is acted on by no other forces, find the work done on it by the time it reaches x = a, 0< a< b.A particle of mass m is moving under the force of attraction of another particle of mass m1 at a distance r , find the mathmatical model that describe the problemIn conclusion, state the relationship between the mass of the spherical object and the distances they were let to roll with reference to the ramp to the knock-back distance of catcher 1. What implications do these relationships give concerning the magnitude of the force which causes the knocking-back of catcher 1?
- Work of 2 Joules is done in stretching a spring from its natural length to 20 cmcm beyond its natural length. What is the force (in Newtons) that holds the spring stretched at the same distance (20 cmcm)?Consider the curve y = 10 + 4x − x^(2) at (x, y) = (3, 13). Find a vector, v, that has length 4 and is parallel to the tangent line to y = 10 + 4x−x^(2) at x = 3.Suppose ƒ is differentiable at (9, 9), ∇ƒ(9, 9) = ⟨3, 1⟩, and w = (1, -1). Compute the directional derivative of ƒ at ⟨9, 9⟩ in the direction of the vector w.
- Find the work done by a force F = 5i (mag-nitude 5 N) in moving an object along the line from the origin to the point (1, 1) (distance in meters).Suppose that an object moves in the positive direction along a coordinate line over the interval [a, b]. The work performed on the object by a variable force F(x) applied in the direction of motion is W =Determine the force being experienced by a 2-microcoulomb charge at (-2,4,6) m due to another point charge 3 mC located at (2,0,-1) m. Assume the charges are in vacuum.
- Work of 2 Joules is done in stretching a spring from its natural length to 15 cm beyond its natural length. What is the force (in Newtons) that holds the spring stretched at the same distance (15 cm)?A mass m moves along the x-axis subject to an attractive force given by 19mx/2 and a retarding force given by , where x is its distance from the origin and is a constant. A driving force given by , where A is a constant, is applied to the particle along the x-axis. D)what is the Q value?Two blocks, with masses 4.00 kg and 8.00 kg, are connected by a string and slide down a 30.0oinclined plane (Figure 1). The coefficient of kinetic friction between the 4.00 kg block and the plane is 0.250; that between the 8.00 kg block and the plane is 0.350. (A) What happens if the positions of the blocks are reversed, so that the 4.00 kg block is uphill from the 8.00 kg block? Calculate the acceleration of the smaller block in this case. (Express your answer with the appropriate units.) (B) Calculate the acceleration of the larger block in this case. (Express your answer with the appropriate units.)