Starting from rest, a body slides down a 45^∘ inclined plane in twice the time it takes to slide

step 1 Hello students in this question we have given that starting from the rest a body slides down the

Starting from rest, a body slides down a 45^∘ inclined plane...

Starting from rest, a body slides down a $45^{\circ}$ inclined plane in twice the time it takes to slide the same distance in the absence of friction. What is the coefficient of friction between the body and the inclined plane?
a. $\sqrt{3} / 2$
b. $3 / 4$
c. $1 / 2$
d. $1 / 4$

Key Concepts

Newton's Second Law

This principle states that the net force acting on an object equals the mass of the object multiplied by its acceleration (F = ma). It is fundamental in analyzing the dynamics of objects on inclined planes by relating the various forces (gravity, friction, normal force) to the acceleration of the body.

Components of Gravitational Force on an Incline

When dealing with an inclined plane, the gravitational force is resolved into two components: one parallel to the plane, which drives the motion, and one perpendicular to the plane, which is balanced by the normal force. This resolution is essential for calculating the acceleration of a body down the slope and the frictional force acting against that motion.

Friction and Its Coefficient

Friction is the resistive force that opposes the motion of a body sliding over a surface. The coefficient of friction (typically denoted as ?) is a dimensionless number that quantifies the ratio of the frictional force to the normal force. In motion on an inclined plane, friction reduces the net force acting on the body, impacting its acceleration and the time taken to travel a given distance.

Kinematics in Uniformly Accelerated Motion

Kinematic equations describe the motion of bodies under constant acceleration, such as those sliding down an inclined plane. The equation s = 1/2 at² (where s is displacement, a is acceleration, and t is time) is particularly important for relating the distance traveled by the body to its acceleration and the time of travel, and is crucial when comparing motion under different forces.

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