-kx³. The work required to stretch the 0 to the stretched length x = l is Wo. In terms of A "stiff" spring has a force law given by F spring from the relaxed state x Wo, how much work is required to extend the spring from the stretched length l to the length 2l?

Imagine a spring that doesn't follow Hooke's Law, but instead requires a force F(x)=kln(x+1)F(x)=kln⁡(x+1), where F is in newtons, x is the stretch length in meters and k = 150.0 N. An engine pulls and stretches the spring at a constant power output. If the engine pulls the spring so it stretches a distance of 10 meters in 5 seconds, what is the engine's power output, in watts? Justify your answer using your equations and rationale used.

Nilo phi

Steven carefully places a m = 1.45 kg wooden block on a frictionless ramp so that the block begins to slide down the ramp from rest. The ramp makes an angle of 0 = 53.3° up from the horizontal. Which forces do nonzero work on the block as it slides down the ramp? ☐ gravity How much total work Wnet has been done on the block after it slides down along the ramp a distance of 1.87 m? Nancy measures the speed of the wooden block after it has gone the 1.87 m down the ramp. Predict what speed u she should measure. Now, Steven again places the wooden block back at the top of the ramp, but this time he jokingly gives the block a big push before it slides down the ramp. If the block's initial speed is 2.00 m/s and the block again slides down the ramp 1.87 m, what should Nancy measure for the speed v of the block this time? ☐ spring friction normal J Wnet = v = m/s v = m/s

In the figure below an object of mass m starts from rest on a roller coaster with negligible friction. A hA B hB C hc Ꭰ hp (a) What terms are present in the object's mechanical energy? Choose from E O Gravitational potential energy, Spring potential energy, Kinetic energy, Work done against friction O Gravitational potential energy, Spring potential energy, Kinetic energy Spring potential energy, Kinetic energy, Work done against friction, Gravitational potential energy, Kinetic energy because, there is no friction (b) Mechanical energy is conserved Only conservative forces ◆ act. (c) Calculate the speed of the object at point D (VD) in terms of the following variables: (g, ha, hD)

Suppose that a certain spring has spring constant k = 0.08 N/m (that’s Newtons per meter). How much work must be done to stretch the spring by 0.5 m past its equilibrium point?  Your answer will end up in units of N*m .

If a spring compressed by 76 cm contains 2.4 J of potential energy, what is the spring constant (k) for that spring? Express your answer in N/m.

A box of mass 'm' is pushed into a spring with spring constant 'k'. The spring is displaced a total length of Δx, and then we let go of the box. From the work-energy theorem, what is the final velocity of the box after we let go?

1) A constant horizontal force of F = 200.0 N pushes a crate of mass m = 25.0 kg, initially at rest, along a rough horizontal surface. The crate travels a total distance of 8.00 m, and the coefficient of kinetic friction between the crate and the surface is 0.250. a) What is the work done on the crate by the force F? b) How much does friction increase the internal energy of the crate-surface system ?

A child of mass m = 16 kg slides down a slide of height h = 2.7 m without friction. Let gravitational potential energy be zero at ground level. a)Write an expression for the child's total mechanical energy, E, at the top of the slide, in terms of the variables in the problem and the acceleration due to gravity g.  b)Calculate the change in the child's potential energy, ΔU in joules, from the top to the bottom of the slide at ground level (i.e. ΔU = Uground - Utop).  c)What is the child's final speed, vf in m/s?