Analysis: 1. Derived the formula for the height as a function of speed square without the presence of non-conservative force, and show that the relation should be given by h(v²) = -–v² + 2g mg Where cis constant number corresponding to the total mechanical energy.

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?

1] A 20kg mass hangs at rest at end of a pendulum rope. Assume that you push it up at 0.6m above initial level and keep it there. Identify forces on the mass, use work- energy theorem in 3D and find: a) How much work do you spend for this operation... If it takes 0.6 sec to bring it from "A" to "B",... b) What average power you have exerted... c) How much work do you spend for this operation... If you keep it at rest at "B" for 2 minutes, Then, you leave free. •.. d) What is its speed when it arrives at A?... B 0.6m A

A crane at a construction site lifts a concrete block with a mass of m = 482 kg from the ground to the top of a building with a height of h = 23.9 m. How much work did the motor of the crane do? (Assume zero energy loss in the lifting mechanism due to friction.) -112894 J moter If the duration of the lift was 1.35 minutes, then what was the average power performed by the crane?

Q3. An aircraft having a take-off mass of 36500 kg and a wing area of 95 m² fitted with turboprop engines of total power 10000 kW, assumed not to vary with speed, and propellers of 87 per cent efficiency. The drag polar for the aircraft is: C₂-0.0145+0.052C₂² At sea level: (a) Calculate the coefficient of lift at minimum required power, associated speed and the minimum power required for steady level flight. (b) Calculate the maximum rate of climb and angle of climb available to the pilot.

A 600-kg roller coaster car starts at a height of 35.0 m.  Assuming negligible energy losses to friction and air resistance, determine the PE, KE, and speed of the car at the carious locations (Start, A, B, C, D, E, and F) along the track.   Round your answers to the nearest whole number.

5. All the ramps below are 5 meters high. We know that the KE of the block at the bottom of each ramp will be equal to the loss of PE (conservation of energy). Find the speed of the block at ground level in each case. [Hint: Do you recall from earlier chapters how much time it takes something to fall a vertical distance of 5 m from a position of rest (assume = g 10 m/s²)? And how much speed a falling object acquires in this time?] This gives you the answer to Case 1. Discuss with your classmates how energy conservation provides the answers to Cases 2 and 3. 5m Case 1 Speed: = m/s Case 2 Speed = m/s Case 3 Speed m/s

Thanks to recent satellite data, we know that the North American continent is drifting westward at a speed of about 1cm/yr. We can assume that the solid part of a continent is about 50 kilometers thick. Estimate the kinetic energy that the continental US has as a result of this motion.

A conservative force of 22.5 N moves a particle of 1 gram along a circular path, oriented vertically, of diameter 50 cm. What is the work done by the conservative force, in Joules, in one cycle? Assume g = 10 ms ². Round to one decimal.

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