A spherical ball of mass 15 kg stationary at the top of a hill of height 82 m . It slides down

step 1 a spherical ball of mass 15 kg stationary at the top of a hill of height 82 meter so initial hei

A spherical ball of mass 15 kg stationary at the top of a...

A spherical ball of mass $15 \mathrm{~kg}$ stationary at the top of a hill of height $82 \mathrm{~m} .$ It slides down a smooth surface to the ground, then climbs up another hill of height $32 \mathrm{~m}$ and finally slides down to horizontal base at a height of $10 \mathrm{~m}$ above the ground. The velocity attained by the ball is (A) $30 \sqrt{10 \mathrm{~m} / \mathrm{s}}$ (B) $10 \sqrt{30 \mathrm{~m} / \mathrm{s}}$ (C) $12 \sqrt{10} \mathrm{~m} / \mathrm{s}$ (D) $10 \sqrt{12} \mathrm{~m} / \mathrm{s}$

A spherical ball of mass $15 \mathrm{~kg}$ stationary at the top of a hill of height $82 \mathrm{~m} .$ It slides down a smooth surface to the ground, then climbs up another hill of height $32 \mathrm{~m}$ and finally slides down to horizontal base at a height of $10 \mathrm{~m}$ above the ground. The velocity attained by the ball is
(A) $30 \sqrt{10 \mathrm{~m} / \mathrm{s}}$
(B) $10 \sqrt{30 \mathrm{~m} / \mathrm{s}}$
(C) $12 \sqrt{10} \mathrm{~m} / \mathrm{s}$
(D) $10 \sqrt{12} \mathrm{~m} / \mathrm{s}$

Key Concepts

Conservation of Energy

This principle states that within a closed system free of non-conservative forces like friction, the total energy remains constant. It allows the analysis of problems by equating the loss in gravitational potential energy to the gain in kinetic energy, or vice versa, ensuring that energy is neither created nor destroyed.

Gravitational Potential Energy

Gravitational potential energy is the energy stored in an object due to its position in a gravitational field. It is given by the formula mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height above a reference point. Changes in height translate directly into changes in energy, which are then converted during motion.

Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion, calculated by the formula 1/2 mv². When an object moves and accelerates as a result of converting stored gravitational potential energy, this energy becomes kinetic energy, which can be used to determine the object's speed at various points in its motion.

Energy Conversion in Mechanical Systems

This concept involves the transformation of energy from one form to another, such as from gravitational potential energy to kinetic energy in a frictionless system. It is crucial for solving problems where an object moves under the influence of gravity, allowing the prediction of parameters like velocity using energy conservation equations.

Transcript

Please give Ace some feedback