When the object is at the top of the hill it has the most potential energy. If it is sitting still, it has no kinetic energy. As the object begins to roll down the hill, it loses potential energy, but gains kinetic energy. The potential energy of the position of the object at the top of the hill is getting converted into kinetic energy. Hope this helped. :)
Answer:
A+B; 5√5 units, 341.57°
A-B; 5√5 units, 198.43°
B-A; 5√5 units, 18.43°
Explanation:
Given A = 5 units
By vector notation and the axis of A, it is represented as -5j
B = 3 × 5 = 15 units
Using the vector notations and the axis, B is +15i. The following vectors ate taking as the coordinates of A and B
(a) A + B = -5j + 15i
A+B = 15i -5j
|A+B| = √(15)²+(5)²
= 5√5 units
∆ = arctan(5/15) = 18.43°
The angle ∆ is generally used in the diagrams
∆= 18.43°
The direction of A+B is 341.57° based in the condition given (see attachment for diagrams
(b) A - B = -5j -15i
A-B = -15i -5j
|A-B|= √(15)²+(-5)²
|A-B| = √125
|A-B| = 5√5 units
The direction is 180+18.43°= 198.43°
See attachment for diagrams
(c) B-A = 15i -( -5j) = 15i + 5j
|B-A| = 5√5 units
The direction is 18.43°
See attachment for diagram
Gravity is universal. This force of gravitational attraction is directly dependent upon the masses of both objects and inversely proportional to the square of the distance that separates their centers. This means that as you move away from an object the gravitational force decreases.
The kinetic energy at the bottom of the swing is also 918 J.
Assume the origin of the coordinate system to be at the lowest point of the pendulum's swing. A pendulum, when raised to the highest point has potential energy since it is raised to a height h above the origin. At the highest point, the pendulum's velocity becomes zero, hence it has no kinetic energy. Its energy at the highest point is wholly potential.
When the pendulum swings down from its highest position, it gains velocity. Hence a part of its potential energy begins to convert itself into kinetic energy. If no dissipative forces such as air resistance exist, then, the law of conservation of energy can be applied to the swing.
Under the action of conservative forces, the total mechanical energy of a system remains constant.This means that the sum of the potential and kinetic energies of a body remains constant.
When the pendulum reaches the lowest point of its swing, it is at the origin of the chosen coordinate system. Its vertical displacement from the origin is zero, hence its potential energy with respect to the origin is zero. Therefore the entire potential energy of 918 J should have been converted into kinetic energy, according to the law of conservation of energy.
Thus, the kinetic energy of the pendulum at the lowest point of its swing is equal to the potential energy it had at its highest point, which is equal to <u>918 J.</u>
