Ask question

Ask question

All categories

2 years ago

15

A particle of mass moves under a force given bywhere and are unit vectors in the and directions. The particle is placed at the o

rigin with an initial velocity After how much time will the particle first return to the origin

1 answer:

krek1111 [17]2 years ago

4 0

The elapsed time when the particle returns to the origin is determined from the ratio of initial velocity and acceleration of the particle.

<h3>Time of motion of the particle</h3>

The time of motion of the particle is calculated by applying Newton's second law of motion.

F = ma

F = m(v)/t

where;

t is time of motion of the particle
m is mass of the particle
v is velocity of the particle

a = v - u/t

v = u + at

when the particle returns to the origin, direction of u, = negative.

final velocity = 0

0 = -u + at

at = u

t = u/a

Learn more about force here: brainly.com/question/12970081

#SPJ11

You might be interested in

In a flying ski jump, the skier acquires a speed of 110 km/h by racing down a steep hill and then lifts off into the air from a

matrenka [14]

Answer:

Approximately $\displaystyle\rm \left[ \begin{array}{c}\rm191\; m\\\rm-191\; m\end{array}\right]$ .

Explanation:

Consider this $45^{\circ}$ slope and the trajectory of the skier in a cartesian plane. Since the problem is asking for the displacement vector relative to the point of "lift off", let that particular point be the origin $(0, 0)$ .

Assume that the skier is running in the positive x-direction. The line that represents the slope shall point downwards at $45^{\circ}$ to the x-axis. Since this slope is connected to the ramp, it should also go through the origin. Based on these conditions, this line should be represented as $y = -x$ .

Convert the initial speed of this diver to SI units:

$\displaystyle v = \rm 110\; km\cdot h^{-1} = 110 \times \frac{1}{3.6} = 30.556\; m\cdot s^{-1}$ .

The question assumes that the skier is in a free-fall motion. In other words, the skier travels with a constant horizontal velocity and accelerates downwards at $g$ ( $g \approx \rm -9.81\; m\cdot s^{-2}$ near the surface of the earth.) At $t$ seconds after the skier goes beyond the edge of the ramp, the position of the skier will be:

$x$ -coordinate: $30.556t$ meters (constant velocity;)
$y$ -coordinate: $\displaystyle -\frac{1}{2}g\cdot t^{2} = -\frac{9.81}{2}\cdot t^{2}$ meters (constant acceleration with an initial vertical velocity of zero.)

To eliminate $t$ from this expression, solve the equation between $t$ and $x$ for $t$ . That is: express $t$ as a function of $x$ .

$x = 30.556\;t\implies \displaystyle t = \frac{x}{30.556}$ .

Replace the $t$ in the equation of $y$ with this expression:

$\begin{aligned} y = &-\frac{9.81}{2}\cdot t^{2}\\ &= -\frac{9.81}{2} \cdot \left(\frac{x}{30.556}\right)^{2}\\&= -0.0052535\;x^{2}\end{aligned}$ .

Plot the two functions:

$y = -x$ ,
$\displaystyle y= -0.0052535\;x^{2}$ ,

and look for their intersection. Refer to the diagram attached.

Alternatively, equate the two expressions of $y$ (right-hand side of the equation, the part where $y$ is expressed as a function of $x$ .)

$-0.0052535\;x^{2} = -x$ ,

$\implies x = 190.35$ .

The value of $y$ can be found by evaluating either equation at this particular $x$ -value: $x = 190.35$ .

$y = -190.35$ .

The position vector of a point $(x, y)$ on a cartesian plane is $\displaystyle \left[\begin{array}{l}x \\ y\end{array}\right]$ . The coordinates of this skier is approximately $(190.35, -190.35)$ . The position vector of this skier will be $\displaystyle\rm \left[ \begin{array}{c}\rm191\\\rm-191\end{array}\right]$ . Keep in mind that both numbers in this vectors are in meters.

4 0

3 years ago

.3.3: Populating a vector with a for loop. Write a for loop to populate vector userGuesses with NUM_GUESSES integers. Read integ

Reptile [31]

Answer:

#include <iostream>

#include <vector>

using namespace std;

int main() {

const int NUM_GUESSES = 3;

vector<int> userGuesses(NUM_GUESSES);

int i = 0;

int uGuess = 0;

for(i = 0; i <= userGuesses.size() - 1; i++){

cin >> uGuess;

userGuesses.at(i) = uGuess;

}

cout << endl;

return 0;

}

Explanation:

First inbuilt library were imported. Then inside the main( ) function, 3 was assigned to NUM_GUESSES meaning the user is to guess 3 numbers. Next, a vector was defined with a size of NUM_GUESSES.

Then a for-loop is use to receive user guess via cin and each guess is assigned to the vector.

8 0

3 years ago

What is Newton's Second Law?

Rudiy27

Answer:

An object's acceleration depends on its mass and on the net force acting on it.

Explanation:

Newton's second law states that the acceleration of an object is directly related to the net force and inversely related to its mass. Acceleration of an object depends on two things, force and mass.

8 0

3 years ago

Read 2 more answers

Force F acts between two charges, q1 and q2, separated by a distance d. If q1 is increased to twice its original value and the d

Step2247 [10]

Okay, haven't done physics in years, let's see if I remember this.

So Coulomb's Law states that $F = k \frac{Q_1Q_2}{d^2}$ so if we double the charge on $Q_1$ and double the distance to $(2d)$ we plug these into the equation to find

<span> $F_{new} = k \frac{2Q_1Q_2}{(2d)^2}=k \frac{2Q_1Q_2}{4d^2} = \frac{2}{4} \cdot k \frac{Q_1Q_2}{d^2} = \frac{1}{2} \cdot F_{old}$ </span>

So we see the new force is exactly 1/2 of the old force so your answer should be $\frac{1}{2}F$ if I can remember my physics correctly.

9 0

3 years ago

Read 2 more answers

Max discovered a beaker full of transparent liquid in the science lab. He hypothesized that since the liquid is transparent like

egoroff_w [7]

Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

8 0

3 years ago