1) Calculate the work that the spring does on the block as the spring expands from a length of 2.0 meters to its equilibrium length of 2.5 meters (in the time between diagram A and diagram B above). The sign of the work done by the spring (positive or negative) is important. joules Submit
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- Hi, can you please help me with this assignment A pendulum of length L. A ball that practically carries all the weightpendulum, has a velocity of velocity v1 at the moment when the cord makes an angle \phi_1 with the vertical direction.a) Derive the relation for the velocity of the ball at the lowest point of its trajectory (\phi = 0deg).What is the smallest possible value of velocity v1 for the pendulum tob) reach a position in which the massless cord is in horizontal position \phi=90deg,c) pass the highest point above the pivot so that the cord does not kink (\phi = 180deg+)? Thank YouShow your complete solution, including diagram.2. A linear spring of stiffness k is to be designed to atop a 20-Mg railroad car traveling at 8 km/h within 400 mm after impact. Find the smallest value of k that will produce the desired result.In the figure at the right is shown three graphs of the shapes of the same taut elastic string in three different circumstances, labeled A, B, and C. In some of the problems below, the string represents a guitar string, tied down at both ends, while in others, it is part of a very long telephone wire whose ends are not shown. Be careful to note which is which for each problem! The string is light enough that the effects of gravity can be ignored. In each case, the bit of string at the position x = 23 cm is painted blue.1. Suppose the three graphs all represent the same string, tied down at x = 0 and x = 70 cm, and at the same tension. What can you say about the three frequencies of oscillation? a. Situation A has the highest frequency. b. Situation B has the highest frequency. c. Situation C has the highest frequency. d. The three frequencies are all the same. e. You cant say anything from the information given. 2. Suppose the three graphs all represent the same string, tied down…
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- Consider a pair of masses m1 and m2 connected by a non-stretchable string that runs over a frictionless pulley as shown on the figure on the right. If the coefficient of the kinetic friction between m1 and on the horizontal surface on which it initially rest is μk, find its resulting acceleration magnitude in terms of m1, m2, and μk, when the system is released. Assume that air resistance is negligible and m2 > μk m1. Show the complete and thorough solution in a clean paperA projectile of mass m is launched with initial velocity Vo at angle (theta)from the +x direction. From the origin, the projectile is connected to a massless spring with force constant k, as shown. (1) Set-up the equations of motion of the projectile, both in the horizontal and vertical directions. Take note the presence of gravity and force by the spring (Hooke's law which is a vector).Use the worked example above to help you solve this problem. A block of mass m1 = 1.72 kg, initially moving to the right with a velocity of +3.95 m/s on a frictionless horizontal track, collides with a massless spring attached to a second block of mass m2 = 2.01 kg moving to the left with a velocity of −2.83 m/s. The spring has a spring constant of 6.33 x102 N/m. (a) Determine the velocity of block 2 at the instant when block 1 is moving to the right with a velocity of +3.00 m/s. (Indicate the direction with the sign of your answer.) (b) Find the compression of the spring.
- Use the worked example above to help you solve this problem. Two billiard balls of identical mass move toward each other as shown in the figure. Assume that the collision between them is perfectly elastic. If the initial velocities of the balls are v1i = +25.2 cm/s and v2i = −20.3 cm/s, what are the velocities of the balls after the collision? Assume friction and rotation are unimportant. (Indicate the direction with the sign of your answer.) v1f = v2f =For the system forces showed, calculate the magnitude of the resulting force from the forces F, P, and Q. In addition, determine in degrees the direction angles of this resultant force found. PROCESS:1. (25%) Decompose each of the shown forces into its rectangular components. For which use the method of projections with the force F and the two-point method of the line of action of the forces P and Q.A body P (shown in red) of mass m is at the base of a fixed rough inclined plane of inclination α to the horizontal and elevation h. A light inelastic string is attached to P and passes over a smooth pulley (shown in yellow) at the top of the plane where it is attached to a body Q (shown in white) of mass M initially adjacent to the pulley and able to move vertically downwards. Initially, the system is a rest, the body Q is next to the pulley at height h above the horizontal, and the plane has friction coefficient µ. The diagram below shows a snapshot of the system shortly after the body Q is released. Copy the diagram above, label the forces acting and formulate Newton’s equations of motion for the system. (b) Show that M > m(µ cos α + sin α). (c) Assuming the condition in part (b) above is satisfied, find in terms of m, M, µ, h, g and α, an expression for the speed of P when Q is level with the initial position of P.