Problem 1: Calculating Work
A force of 10 N is applied to push a box across a horizontal surface. The displacement of the box is 5 m, and the angle between the force and displacement is 30°. Find the work done.
The chapter "Work and Energy" in HC Verma's Physics textbook for Class 11 is one of the foundational topics in mechanics. It introduces students to the concepts of work, energy, and power, which are crucial for understanding advanced physics topics. Solving HC Verma problems helps students build a strong conceptual foundation while enhancing problem-solving skills.
Work (W) = F * d * cos(θ)
Where:
KE = 1/2 * m * v2
Where:
PE = m * g * h
Where:
W = ΔKE
Power (P) = Work / Time
HC Verma's problems are designed to help students grasp concepts practically and improve their numerical skills. By solving problems, students gain the following benefits:
A force of 10 N is applied to push a box across a horizontal surface. The displacement of the box is 5 m, and the angle between the force and displacement is 30°. Find the work done.
Solution:
Work (W) = F * d * cos(θ) = 10 * 5 * cos(30°) = 10 * 5 * (√3/2) = 25√3 J
The work done is 25√3 Joules.
A body of mass 2 kg is moving with a velocity of 3 m/s. Calculate its kinetic energy.
Solution:
KE = 1/2 * m * v2 = 1/2 * 2 * 32 = 1 * 9 = 9 J
The kinetic energy of the body is 9 Joules.
The work-energy theory is also known as the kinetic energy hypothesis or the principle of work. The hypothesis states that the effort done by all powers going to follow up on a component results in the adjustment of the component.
The work-energy theorem has the advantage that the work done on an item may be computed by integrating the area that is applied as a force and multiplying it by the work done if it moves from point A to point B.