A block of mass 2 kg is hanging over a smooth and light...

A block of mass $2 \mathrm{~kg}$ is hanging over a smooth and light pulley through a light string. The other end of the string is pulled by a constant force $F=40 \mathrm{~N}$. The kinetic energy of the particle increase $40 \mathrm{~J}$ in a given interval of time. Then: $\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$ (a) tension in the string is $40 \mathrm{~N}$ (b) displacement of the block in the given interval of time is $2 \mathrm{~m}$ (c) work done by gravity is $-20 \mathrm{~J}$ (d) work done by tension is $80 \mathrm{~J}$

A block of mass $2 \mathrm{~kg}$ is hanging over a smooth and light pulley through a light string. The other end of the string is pulled by a constant force $F=40 \mathrm{~N}$. The kinetic energy of the particle increase $40 \mathrm{~J}$ in a given interval of time. Then: $\left(g=10 \mathrm{~m} / \mathrm{s}^{2}\right)$
(a) tension in the string is $40 \mathrm{~N}$
(b) displacement of the block in the given interval of time is $2 \mathrm{~m}$
(c) work done by gravity is $-20 \mathrm{~J}$
(d) work done by tension is $80 \mathrm{~J}$

Key Concepts

Newton's Second Law

Newton's second law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). This fundamental law provides the basis for analyzing the dynamics of a system, including calculating acceleration, determining net force, and understanding how different forces interact.

Work-Energy Theorem

The work-energy theorem states that the net work done on an object equals its change in kinetic energy. This principle is used to relate the forces acting on an object over a displacement to the resulting change in its motion, making it fundamental for analyzing dynamic systems.

Work Done by a Force

Work done by a force is defined as the product of the force and the displacement in the direction of the force. It is an important concept in mechanics as it connects the force applied to an object with the energy change experienced by that object.

Tension in a String

Tension refers to the force transmitted through a string, rope, or cable when forces are applied at its ends. In idealized systems involving massless strings and frictionless pulleys, tension is uniformly distributed, though it may differ from the external force applied if other forces, such as gravity, are present.

Gravitational Work and Potential Energy

Gravity performs work on objects as they move vertically, and this work is directly linked to changes in gravitational potential energy. When an object moves against the direction of gravitational force, gravity does negative work, resulting in an increase in potential energy, while moving in the direction of gravity results in positive work.

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