The potential energy of an interaction is given by U(x)=ax², where a = +6.4 J/m². Initial speed of a 0.79-kg object in this system is 2.63 m/s at x = 0. A. How far does the object travel before it reaches a speed of v = 0? Express your answer with the appropriate units. B. Does your answer in the previous part depend on whether the object is traveling in the positive or negative direction? Yes, the answer in the previous part is for the object traveling in the negative x� direction, the distance for the object traveling in the positive x� direction is greater than the obtained result. Yes, the answer in the previous part is for the object traveling in the positive x� direction, the distance for the object traveling in the negative x� direction is greater than the obtained result. No, it does not depend on whether the object is traveling in the positive or negative x� direction.

A 55 kg snowboarder begins his run at the top of a 50.0 m tall hill with a speed of 0.5 m/s. What is the speed of the snowboarder at the bottom of the hill?

What is the gravitational potential energy of a ball with a weight of 69 N when it is sitting on a shelf 1.6 m above the floor?J What assumption do you need to make to get your answer?

8. A ball has a 17 J of kinetic energy and its mechanical energy is 25 J. Find the potential energy of the ball. a. b. If the ball has a mass of 3.2 kg, what is its height above the ground? c. What is the speed of the ball?

While leaning out a window that is 6.4 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. b) the gravitational potential energy (in J) of the ball-earth system, relative to the ground when it is released. c) the gravitational potential energy (in J) of the ball-earth system, relative to the ground when it is caught. 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

Q 1

Q1. a. Distinguish between homogeneous and non-homogeneous equation. b.Find the work done in moving an object along a straight line from (3, 2, -1) to (2, -1, 4) in a forcefield given by F = 4i – 3j + 2k .

a. A 10.0 kg object has an initial velocity of (5.0i + 3.0j) m/s. What is its kinetic energy at this time? KE = ½ mv² where v² = V.V

A diver of mass 68 kg stands on a diving board 5.0 m above a pool. At the moment of the jump, the diving board transfers its 3400 J of energy to the diver, who leaves the board at an angle of 35°. a. What is the speed of the diver just before they enter the water? b. Suppose that when the diver enters the water, they experience an acceleration of a->water= +4 m/ss J. What is the minimum depth of the pool necessary so that this diver comes to rest exactly at the bottom of the pool

A 260 g particle in a semi-spherical bowl of radius 0.6 m is released from rest at point A at the level of the center of the bowl, and the surface of the bowl is rough. The speed of the particle at B is 2 m/s. The acceleration of gravity is 9.8 m/s2 . a)What is its kinetic energy at B? b)What is the magnitude of the energy lost due to friction as the particle moves from A to B?