-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?
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- A 36.0 kg box initially at rest is pushed 5.45 m along a rough, horizontal floor with a constant applied horizontal force of 150 N. If the coefficient of friction between box and floor is 0.300, find the following. (a) the work done by the applied force (b) the increase in internal energy in the box-floor system due to friction (c) the work done by the normal force (d) the work done by the gravitational force (e) the change in kinetic energy of the box (f) the final speed of the box m/sthe mass of the object is m=0.2kg the spring is compressed at a distance of X=4cm when the mass is released it slides up to the height of 10cm. and then it turns around and slides back down. find the spring constant, K of the spring? WwwM A note: that the equation for spring potential energy is (1/2*k*x2). and gravitational potential energy is m*g*h. also, the conservation of mechanical energy is MEi=MEf.In the figure, a 4.2 kg block is accelerated from rest by a compressed spring of spring constant 650 N/m. The block leaves the spring at the spring's relaxed length and then travels over a horizontal floor with a coefficient of kinetic friction k = 0.229. The frictional force stops the block in distance D = 8.3 m. What are (a) the increase in the thermal energy of the block-floor system, (b) the maximum kinetic energy of the block, and (c) the original compression distance of the spring? - No friction (a) Number i Units (b) Number Units (c) Number i Units > > >
- 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 phiSteven 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?