A block of mass 2 ·0 kg is pushed down an inclined plane of...

A block of mass $2 \cdot 0 \mathrm{~kg}$ is pushed down an inclined plane of inclination $37^{\circ}$ with a force of $20 \mathrm{~N}$ acting parallel to the incline. It is found that the block moves on the incline with an acceleration of $10 \mathrm{~m} / \mathrm{s}^{2}$. If the block started from rest, find the work done (a) by the applied force in the first second, (b) by the weight of the block in the first second and (c) by the frictional force acting on the block in the first second. Take $g=10 \mathrm{~m} / \mathrm{s}^{2}$.

Key Concepts

Frictional Forces

Friction is a non-conservative force that opposes the motion of an object. On an inclined plane, friction acts opposite to the direction of motion and does negative work. Analyzing friction involves understanding how it counteracts other forces (such as gravity and applied forces) and affects the net force and acceleration of an object.

Newton’s Second Law of Motion

Newton’s Second Law, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F_net = ma), is a cornerstone principle in dynamics. It allows for the determination of unknown forces when the mass and acceleration of an object are known, linking kinematics and force analysis.

Force Decomposition on an Inclined Plane

When analyzing forces on an inclined plane, it is essential to decompose the gravitational force into components parallel and perpendicular to the plane. The parallel component (mg sin?) influences the object's motion along the incline, and this decomposition is fundamental in solving problems that involve motion on slopes.

Work and Energy

Work is defined as the transfer of energy when a force is applied over a distance. In physics, calculated as the product of the force component in the direction of displacement and the displacement itself, work is a key concept for determining how forces affect the energy state of an object.

Kinematics Under Constant Acceleration

Kinematics under constant acceleration involves using equations of motion that relate displacement, velocity, acceleration, and time. These equations, such as s = ut + ½at², are crucial in analyzing the distance traveled by an object starting from rest or with a known initial speed.

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