Find the force corresponding to the potential energy U(x) (Use the following as necessary: a, b, and x. Express your answer in vector form.) Fx) =

(a) Check all of the following that are correct statements, where E stands for ymc². Read each statement very carefully to make sure that it is exactly correct. O At speeds close to the speed of light, kinetic energy is approximately equal to (1/2)mv². O The energy principle can be written AEsys Wsurr. %3D O The definition of work is W = |I. %3D O The definition K = E - mc² is valid even for speeds near the speed of light. O The definition of work is W = . O The definition of work is W = FxAx + F,AY + F;Az. %3D O The energy principle can be written Esys,f = Esys,i + Wsurr (b) An object with mass 120 kg moved in outer space. When it was at location its speed was 18 m/s. A single constant force N acted on the object while the object moved to location m. What is the speed of the object at this final location? final speed m/s %3D

A box with weight of magnitude FG=2.00N is lowered by a rope down a smooth plane that is inclined at an angle ϕ = 30.0 ∘ above the horizontal, as shown in (Figure 1) at left. The normal force acting on the box has a magnitude n=1.73N the tension force is 1.00 N, and the displacement Δr of the box is 1.80 m down the inclined plane. The work done on the box by gravity is 1.8 J What is the work Wn done on the box by the normal force? What is the work WT done by the tension force?

Show clearly all working with detailed explanations

a.) A particle with mass m is dropped with zero initial velocity a height h above the ground, under the action of the gravitational field (acceration constant g), such that it reaches the ground (z=0) with zero potential energy and velocity v>0. Determine h, in terms of the other quantities given. b.) Another particle moves with Simple Harmonic Motion with centre O.The particle has velocity 13ms–1 when it is 3m from O and 5ms–1 when it is 5m from O.(i) Find the period and amplitude of the motion

is the vector foeld conservative? prove it.

In a downhill ski race, your final velocity is not affected very much by getting a running start, because the initial kinetic energy is compared with the gain in gravitational potential energy on even small hillsHowever, you will finish the race much faster (which is more important ) To demonstrate this, find the final speed and the time taken for a skier who skies 82.5 m along a slope that is 19 degrees measured from horizontal , in the following situations (you may neglect friction ) A find the final speed in m/s lf the skier starting from rest B how long (in s) does it take for the skier to reach the bottom of this hill starting from rest C find the final speed in (m/s) of the skier with speed of 2.50 m/s D how long in (s) does it take for the skier to reach the bottom of this hill with a starting speed of 2.50 m/s