While leaning out a window that is 5.8 m above the ground, you drop a 0.60 kg basketball to a friend at ground level. Your friend catches the ball at a height of 1.9 m above the ground. Determine the following. (a) the amount of work done (in J) by the force of gravity on the ball J (b) the gravitational potential energy (in J) of the ball-earth system, relative to the ground when it is released J (c) the gravitational potential energy (in J) of the ball-earth system, relative to the ground when it is caught J (d) the ratio of the change (PEf − PE0) in the gravitational potential energy of the ball-earth system to the work done on the ball by the force of gravity ΔPE W

A block of mass m = 7.30 kg is released from rest from point h₂ m 3.20 m 2.00 m (i) (a) Determine the block's speed at points B and C point B m/s m/s point C and slides on the frictionless track shown in the figure below. (Assume h₂ = 7.80 m.) (b) Determine the net work done by the gravitational force on the block as it moves from point to point

The energy needed to increase the speed of a certain car from 22 m/s to 54 m/s is 2900 kJ. A) What is the mass of the car? B) At what speed is the cars kinetic energy equal to 1500 kJ? C) The car is driven up pikes Peak, an elevation gain of 5500 feet from the base. What is the change of potential energy of the car? give the answer in Joules. 

A 1.80 kg snowball is fired from a cliff 12.0 m high. The snowball's initial velocity is 16.4 m/s, directed 27.0° above the horizontal. (a) How much work is done on the snowball by the gravitational force during its flight to the flat ground below the cliff? (b) What is the change in the gravitational potential energy of the snowball-Earth system during the flight? (c) If that gravitational potential energy is taken to be zero at the height of the cliff, what is its value when the snowball reaches the ground? (a) Number (b) Number (c) Number Units Units Units

A center throws a basketball m = 1 kg straight up with an initial speed of vo = 9.5 m's. He releases the ball at shoulder | height ho = 1.9 m. Let gravitational potential energy be zero at ground level. Give the total mechanical energy of the ball E in terms of maximum height h it reaches, the mass m, and the gravitational acceleration g. E= What is the height, hm in meters? 9 HOME

A baby is free to move on a horizontal frictionless table and is attracted to the origin by a mysterious force with magnitude F(r) = ar+Br². (i) Find the potential energy function associated with the mysterious force. (ii) If the baby is released from rest at the location (r, 0) = (a, π/4), what will be his speed when he reaches the origin? Law Application a X

A roller coaster car travels with a speed of 2.29 m/s at point A, located 10.7m above the ground. Calculate how fast the roller coaster is moving when it reaches point D, 10.7m below point A. Assume the roller coaster is ideal and loses no energy to friction.

Problem 4: A 2.00 kg object moving in the x-y plane is under the influence of a force describe by the potential energy U (x,y) = (4.00 J/m³)x3 – (2.00 J/m4)y“. What is the magnitude and direction (angle) of the acceleration of the object at a point x=1 m and y = 2 m?

just part (d)

Problem 2: Suppose a car approaches a hill and has an initial speed of 108 km/h at the bottom of the hill. The driver takes her foot off of the gas pedal and allows the car to coast up the hill. a) If the car has the initial speed stated at a height of h = 0, how high, in meters, can the car coast up a hill if work done by friction is negligible?  b) If, in actuality, a 770-kg car with an initial speed of 108 km/h is observed to coast up a hill and stops at a height 20.5m above its starting point, how much thermal energy was generated by friction in J?