At a construction site a pipe wrench struck the ground with a speed of 24 m / s. (a) From what

At a construction site a pipe wrench struck the ground with...

Key Concepts

Kinematics under Constant Acceleration

This concept involves the study of motion where the acceleration remains constant, such as in free fall. It uses equations that relate displacement, initial velocity, time, and acceleration. These equations allow one to calculate unknown quantities when an object is dropped or thrown in a gravitational field, making them essential for solving problems like the one described.

Gravitational Acceleration

Gravitational acceleration is the constant acceleration experienced by objects due to Earth's gravity, typically approximated as 9.8 m/s². This constant plays a crucial role in kinematics problems involving free fall, where it is used to connect the time of fall, displacement, and final velocity. Understanding gravitational acceleration is fundamental for analyzing vertical motion under gravity.

Energy Conservation in Free Fall

Although not exclusively necessary for solving kinematics problems, energy conservation principles provide an alternative method to analyze free fall. This approach equates the loss in gravitational potential energy with the gain in kinetic energy, enabling calculations of velocity acquired during the fall, and thereby linking the energy perspective with kinematic equations.

Graphical Representations of Motion

Graphical analysis, such as sketching curves for position, velocity, and acceleration versus time, is vital for visualizing motion under gravity. The position-time graph is quadratic due to the acceleration, the velocity-time graph is linear with a constant slope equal to gravitational acceleration, and the acceleration-time graph is a horizontal line representing the constant gravitational force. These graphs help in understanding the relationships among the physical quantities during free fall.

Transcript

00:01 So for part a of this problem, we are trying to figure out how far this wrench fell before it struck the ground.

00:12 So at what was its maximum height when it was dropped? for this, we only know two things, really.

00:21 We know the final velocity.

00:23 And we also know the acceleration because this thing is in free fall.

00:28 It's going to accelerate downward at 9 .8 meters per second.

00:31 Squared and we are going to assume that a resistance is going to be negligible for our purposes.

00:45 So we can use this equation here, v squared, this is v final squared, is equal to v initial squared plus one, sorry, now one, plus two times the acceleration times the change in position.

01:08 And so this change in position here, this is our h, this is what we're looking for.

01:14 A is g, so that's 9 .8 meters per second squared in the downward direction.

01:23 V not is actually going to be zero.

01:25 So this initial velocity is going to be zero because we are dropping this wrench, which implies that it's beginning from rest.

01:34 So now if i rewrite this equation, i have v -final squared.

01:39 Equal to 2 times g times h where we are looking for h so to solve for h i'm going to solve for h i'm going to divide both sides by 2g so i get h equals v squared over 2g and if i plug my numbers into this i get 24 squared on top 2 times 9 .8 down here on the bottom or 9 .81 and you should end up with a value of 39 .4, sorry, 29 .4 meters.

02:21 Now for part b, we need to figure out how long it was in the air for.

02:28 Now there's several different ways you can go about doing this.

02:31 One of the ways is to use this equation here, where we have delta x is equal to v .0 times time, plus one half times acceleration times times squared.

02:45 You could use this where, of course, v0 is equal to 0.

02:50 And now we know this because we found it in part a.

02:54 So we can solve this for time because this goes away and can square that t...

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