Imagine you have a pendulum made of a mass hanging from a spring. Restrict all motion to take place in a vertical plane. At rest the pendulum has length l0. The spring constant is k. There are two degrees of freedom, which you can take as θ, the angle from the vertical of the pendulum, and x, the extension of the spring. Find the generalized force Fθ, and Fx using the principle of virtual work.

The force in Newtons on a particle directed along the -axis is given by F(x)-exp(-(a/4) +7) for x 0 where is in meters. The particle is constrained to move along the a-axis. Find the work done in Joules on the particle, W, in moving it from x 0 to x = 1 using the fact that F =dW/dx. For your reference, 1 Joule 1 Part A Express your answer to 3 significant figures. View Available Hint(s) Newton x 1 meter. ΑΣΦΦ Submit Request Answer

Current Attempt in Progress a In the figure, a horizontal force F of magnitude 18.0 N is applied to a 3.03 kg book as the book slides a distance d = 0.51 m up a frictionless ramp at angle 0 = 30°. (a) During the displacement, what is the net work done on the book by Fa, the gravitational force o the book, and the normal force on the book? (b) If the book has zero kinetic energy at the start of the displacement, what is its speed a the end of the displacement? Use g=9.81 m/s². ar (a) Number i (b) Number Units Units Psychology 8 +7

A A parent pulls a child in a wagon at a constant speed, exerting a force of F = 55N at an angle of 30° with respect to the horizontal sidewalk. (a) How much work do they do, if they pull the wagon for a distance of 30m? (b) What is the force of friction on the wagon?

A potential energy function for a system in which a two-dimensional force acts is of the form U = 3x5y − 2x.  Find the force that acts at the point (x, y). (Use the following as necessary: x and y.) F =

A person pushes a cart to the right with a force of 8 N at an angle of 0=40 degrees as shown in the diagram. The cart moves a horizontal distance by 10.0m, what is the work done by the force of gravity? (B) if the cart is moving at a constant velocity, determine the work done by the force of friction. C lastly, calculate the net work on the cart

applications of definite integrals

S 3 aluations What magnitude force is required to give a helicopter of mass M an acceleration of 0.10g upward? Express your answer in terms of the variable M and appropriate constants. F = Submit Part B 后 VE ΑΣΦ W = Request Answer MINNINMI MIXMM What work is done by this force as the helicopter moves a distance h upward? Express your answer in terms of the variables M, h, and appropriate constants. VG| ΑΣΦ ? WIKIN ?

A box slides down a plank of length d that makes an angle of θ with the horizontal as shown. μk is the kinetic coefficient of friction and μs is the static coefficient of friction. 1.Enter an expression for the minimum angle θ (in degrees) the box will begin to slide. 2.Enter an expression for the nonconservative work done by kinetic friction as the block slides down the plank. Assume the box starts from rest and θ is large enough that it will move down the plank.  3.For a plank of any length, at what angle θ (in degrees) will the final speed of the box at the bottom of the plank be 0.85 times the final speed of the box when there is no friction present? Assume μk = 0.39.

A 35 kg sled slides along a horizontal surface on which the coefficient of kinetic friction is 0.25. Its velocity at point A is 10.0 m/s, and its velocity at point B is 2.0 m/s. You must use Work/Energy methods (not Kinematics). (a) What is the frictional force acting on the sled? (b) How much work is done on the sled by friction over the displacement ∆x = xB − xA? (c) What is the distance the sled travels between A and B?