A packing crate with mass 80.0 kg is at rest on a horizontal, frictionless surface. At t=0 a ne

step 1 Here in this given problem mass of packing rate that is given as 80 .0 kilogram then using the d

A packing crate with mass 80.0 kg is at rest on a...

A packing crate with mass $80.0 \mathrm{~kg}$ is at rest on a horizontal, frictionless surface. At $t=0$ a net horizontal force in the $+x$ -direction is applied to the crate. The force has a constant value of $80.0 \mathrm{~N}$ for $12.0 \mathrm{~s}$ and then decreases linearly with time so it becomes zero after an additional $6.00 \mathrm{~s}$. What is the final speed of the crate, $18.0 \mathrm{~s}$ after the force was first applied?

Key Concepts

Newton's Second Law

Newton’s Second Law connects the net force acting on an object with its acceleration and mass. It provides the principle that an object’s acceleration is directly proportional to the net force applied and inversely proportional to its mass, serving as the basis for analyzing changes in motion under various forces.

Impulse and Momentum

Impulse is the cumulative effect of a force acting over a period of time, mathematically defined as the integral of the force with respect to time. This concept is fundamental in relating forces that vary with time to the resulting change in an object's momentum, regardless of the instantaneous force values.

Integration of Time-Dependent Forces

When dealing with forces that vary over time, such as linearly changing forces, integration is required to calculate the total impulse. By integrating the force function over the time interval during which it acts, one determines the overall change in momentum, which is essential for solving problems involving variable acceleration.

Frictionless Surface Dynamics

Examining motion on a frictionless surface simplifies the analysis by removing resistive forces like friction. This idealization allows a focus on the direct impact of applied forces on the object's motion, enabling a clearer application of Newtonian mechanics and impulse-momentum relationships.

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