1) a) Define what is meant by mechanical work. b) Explain how the principle of conservation of energy applies to a man sliding from rest down  a vertical pole, if there is a constant force of friction acting on him. c) A man slides down a pole and reaches the ground after falling a distance h = 15 m. His  potential energy at the top of the pole is 1000 J. Sketch a graph to show how his  gravitational potential energy Ep varies with h. Add to your graph a line to show the  variation of his kinetic energy Ek with h.

A sledder has 500 J of potential energy and 230 J of kinetic energy at one point on a steep hill.  How much kinetic energy will the sledder have at the bottom of the hill? (Assume negligible air resistance and friction.) b. As the sledder goes down the hill and picks up speed will their potential and kinetic energy increase or decrease.

A 1.5 kg ball is thrown upward with a velocity of 6 m/s. a). What is the kinetic energy of the ball as it is thrown upward? b). What is the gravitational potential energy of the ball when it reaches its highest point? c). To what height above the thrower’s hand will the ball rise? (for c only, round answer to nearest hundredth).

1. A roller-coaster car with a mass of 1200 kg starts at rest from a point 20 m above the ground. At point B, it is 9 m above the ground. [Express your answers in kilojoules (kJ).] a. What is the initial potential energy of the car? b. What is the potential energy at point B? c. If the initial kinetic energy was zero and the work done against friction between the starting point and point B is 40 000 J (40 kJ), what is the kinetic energy of the car at point B 2. The time required for one complete cycle of a mass oscillating at the end of a spring is 0.80 s. What is the frequency of oscillation?

A. Calculate the work done by the force of gravity when a 5.0kg object is lifted to a height of 30.0m above the ground B. Calculate the velocity with which the object strikes the ground if dropped from that height, using the principle of conservation of energy C. Calculate the kinetic energy and the potential energy of the object at a halfway on the path after it is dropped. To do this part, you need to find the velocity of the object at that position using an equation of motion. What is the total energy of the object at that point? Does this verify the principle of conservation of energy?

Conservation and Energy Q5: please answer all parts and explain reasoning (even if minor)

Suppose you are biking at a constant speed up a road inclined at 5° above the horizontal. You need to bike up this hill for 200 m in 2 minutes or less. There is an average drag force of 25 N as well. Calculate the minimum amount of power in hp your body must provide in order to make it up this hill in time. Assume 80 kg total mass of yourself and bike and 25% energy efficiency in your body. Define a system and draw energy state diagrams as part of your solution. Draw any necessary FBDs for forces. B

Q 3. Three cars are traveling at 30km/h, 50km/h and 200km/h, respectively. Each speed corresponds to a certain kinetic energy. a)  Note down the expression for the kinetic energy of a moving object with a velocity v. b)  Note down the potential energy for an object lifted up from the ground to height h. c)  Based on a) and b) find an expression for the height as a function of velocity by assuming that the kinetic energy equals the potential energy of the same object. In other words find h(v) from which the object would need to be dropped and calculate the height so it has a speed of 30 km/h, 50 km/h or 200 km/h on impact with the ground. Assume free fall without air resistance d)  Comment on your chances of survival if you are involved in head-on collisions for the three different speeds.

An object moves along the x axis, subject to the potential energy shown in the figure. (Figure 1) The object has a mass of 2.4 kg and starts at rest at point A. A) What is the object's speed at point B? B) What is the object's speed at point C? C) What is the object's speed at point D? D) What are the turning points for this object? Check all that apply. Point A Point B Point C Point D Point E