Gravity is given by g = 9.81 - 3.32 X 10-6 h m/s2, where h is the height above sea level. An airplane is travelling at 900 km/h at an elevation of 10 km. If its weight at sea level is 40 kN, determine (a) its kinetic energy and (b) its potential energy relative to sea level. Draw a figure of it.

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?

A child of mass m = 27 kg slides down a slide of height h = 2.1 m without friction. Let gravitational potential energy be zero at ground level. 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.  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).  What is the child's final speed, vf in m/s?

A car with a mass of 2000 kg starts at rest from a point 30 m above the ground. At point B, it is 15 m above the ground. If the initial kinetic energy was zero and the work done against friction between the starting point and point B is 20 000 J, what is the kinetic energy of the car at point B? (g= 10 m/s2).

As usual, Hampus is out cycling. He is driving at 30.0 km/ h when he comes to a small hill that is 11 m high and 350 m long. Hampus and the bike weigh 95 kg together. a) What kinetic energy does Hampus have just before the hill? b) How much extra energy must Hampus produce to maintain a constant speed (30.0 km/ h) throughout the hill? c) How long does it take him to drive up the hill? d) What effect must he develop on the hill? Once at the top of the hill, the ground is flat. Hampus is tired and stops pedaling. After 12s the cycle stops. e) How big is the coefficient of friction? You can assume that is constant throughout the deceleration and that it includes both drag and rolling resistance.

A 2.3 kg mass starts from rest at point A and moves along the x-axis subject to the potential energy shown in the figure below. PE 30 J 25 J 20 J 15 J D 10 J 5 J 2 m 4 m 6 m 8 m 10 m (a) Determine the speed (in m/s) of the mass at points B, C, D. (For each answer, enter a number.) point 4.7 m/s В X Is energy conserved? If so, how do you know it is conserved? How does the total energy at A compare to the total point energy at any other point. m/s X Is energy conserved? If so, how do you know it is conserved? How does the total energy at A compare to the total point energy at any other point. m/s

A point guard launches a basketball m = 1 kg straight up with an initial speed of v0 = 6.5 m/s. The ball leaves his hand at shoulder height h0 = 2.2 m. Let gravitational potential energy be zero at ground level. Give the total mechanical energy of the ball E in terms of maximum height hm it reaches, the mass m, and the gravitational acceleration g.