In Fig. 6-62, a 5.0 kg block is sent sliding up a plane inclined at θ=37^∘ while a horizontal fo

step 1 Hello and welcome to this video solution of numerate. So here we are given a block of mass m Tha

In Fig. 6-62, a 5.0 kg block is sent sliding up a plane...

In Fig. $6-62,$ a 5.0 kg block is sent sliding up a plane inclined at $\theta=37^{\circ}$ while a horizontal force $\vec{F}$ of magnitude 50 $\mathrm{N}$ acts on it. The coefficient of kinetic friction between block and plane is $0.30 .$ What are the (a) magnitude and (b) direction (up or down the plane) of the block's acceleration? The block's initial speed is 4.0 $\mathrm{m} / \mathrm{s}$ . (c) How far up the plane does the block go? (d) When it reaches its highest point, does it remain at rest or slide back down the plane?

In Fig. $6-62,$ a 5.0 kg block is sent sliding up a plane inclined at
$\theta=37^{\circ}$ while a horizontal force $\vec{F}$ of magnitude 50 $\mathrm{N}$ acts on it.
The coefficient of kinetic friction between block and plane is $0.30 .$
What are the (a) magnitude and (b) direction (up or down the
plane) of the block's acceleration? The block's initial speed is 4.0
$\mathrm{m} / \mathrm{s}$ . (c) How far up the plane does the block go? (d) When it
reaches its highest point, does it remain at rest or slide back down
the plane?

Key Concepts

Force Decomposition on Inclined Planes

When analyzing an object on an inclined plane, it is crucial to break down all forces into components that are parallel and perpendicular to the plane. This technique simplifies the problem by isolating the effects of gravity, applied forces, and friction, allowing for easier application of the equations of motion.

Newton's Second Law of Motion

Newton's second law, which states that the net force acting on an object is equal to its mass times its acceleration, is fundamental in determining the acceleration of objects on an incline. By summing the forces along the direction of motion and setting them equal to mass times acceleration, one can solve for the unknown quantities like acceleration.

Kinetic Friction

Kinetic friction is the resistive force that acts opposite to the direction of motion when there is relative sliding between surfaces. It is generally calculated by multiplying the coefficient of kinetic friction by the normal force. On an inclined plane, the normal force is determined by the component of gravity perpendicular to the surface, modified by any other forces affecting the surface contact.

Work-Energy Principle with Non-Conservative Forces

In problems where energy methods are applied, the work-energy principle accounts for changes in kinetic energy due to work done by conservative forces (like gravity) and non-conservative forces (like friction). This approach is useful in determining quantities such as the maximum distance an object travels up an incline by equating the initial kinetic energy to the work done against gravity and friction.

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