Un crucero con una masa de 1,00 ×10^7 kg choca contra un muelle a una velocidad de 0,750 m / s

Un crucero con una masa de 1,00 ×10^7 kg choca contra un...

Un crucero con una masa de $1,00 \times 10^7 \mathrm{~kg}$ choca contra un muelle a una velocidad de $0,750 \mathrm{~m} / \mathrm{s}$. Se detiene tras recorrer $6,00 \mathrm{~m}$, lo que daña el barco, el muelle y las finanzas del capitán del remolcador. Calcule la fuerza media ejercida sobre el muelle; utilice el concepto de impulso. (FIGURE CAN'T COPY)

Key Concepts

Average Force

The average force is a simplified concept where a varying force over an interval is replaced by a constant force that produces the same overall change in momentum. It is calculated by dividing the total impulse by the time over which the force is applied, serving as an effective measure in collision analyses.

Impulse-Momentum Theorem

The impulse-momentum theorem states that the impulse acting on an object is equal to the change in its momentum. This theorem bridges the concepts of force and motion by relating the time-integrated force to the resulting change in velocity of the object.

Kinematics in Uniformly Accelerated Motion

Kinematics provides the equations that relate displacement, velocity, acceleration, and time under the assumption of constant acceleration. These equations are essential for determining the time interval during which an object decelerates, which is required for calculating the average force using the impulse-momentum approach.

Impulse

Impulse is defined as the product of force and the time interval over which the force is applied. It represents how much the momentum of an object changes due to the force, and it is foundational in analyzing situations where forces are applied over short time spans, such as collisions.

Momentum

Momentum is the product of an object's mass and its velocity. It is a measure of the quantity of motion that an object has and is central to understanding dynamics, particularly through conservation laws and change induced by applied forces.

Transcript

00:01 All right, so it's a cruise ship with a very large mass, right? the mass of this cruise ship is 1 .00 times 10 to the seventh kilograms, right? strikes up here at a speed of three quarters of a meter per second.

00:17 This is bad, right? so our change in velocity is going to be 0 .750 meters per second.

00:25 And it travels six meters, i guess, into the pier or the, yeah, six meters, right? so the distance over which it stops is 6 .0 meters, right? and what they want to know is they want to know the average force exerted on the pier using the concept of impulse.

00:46 And you could use energy, you could use impulse.

00:49 Energy might be easier, but let's use their wishes here.

00:54 So if we want to get a force, right? force times time is going to be mass change in velocity.

01:00 So this is our impulse.

01:04 And what we're saying is that that is equal to the change in momentum.

01:06 So let's play by the rules here.

01:08 Right.

01:09 So the hint that they give us is calculate the time it took to, or the ship to stop, right? okay.

01:15 So the average velocity is going to be 0 .750 plus zero.

01:21 That's its final velocity divided by two.

01:23 And this is assuming, by the way, that it slows down uniformly has a uniform acceleration.

01:29 And they do say average, so let's go for it, right? okay, so this average is 0 .75 divided by 2, which is 0 .375 meters per second.

01:43 So therefore, the time it takes the thing to stop is going to be the distance divided by the average velocity.

01:51 Right? so i'm doing six meters that it travels, right, divided by the average velocity.

01:58 That would give us the time it takes.

02:00 And there's other ways, by the way, to find the time.

02:01 I'm just doing this.

02:03 So six divided by that answer is 16.

02:08 It's going to take 16 seconds...

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