? Is a quantity that measure how much a machine multiple force or distance

Physics

1 answer:

Afina-wow [57]3 years ago

5 0

Mechanical advantage is a quantity that measures how much a machine multiplies force or distance.

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Why do scientist use different types of models to represent compounds

nexus9112 [7]

Because they are different they all show different traits.

5 0

3 years ago

A stone that starts at rest free falls for 7.0 s. How far does the stone fall in this time?

vredina [299]

Gravitational acceleration is approx 9.8 m/s
Time is 7s

a=9.8 m/s
t=7s

a = d/t^2

therefore:

d = a * t^2

d = 9.8 * 7^2

d = 9.8 * 49

d = 480.2 [m]

7 0

3 years ago

If position vector r = bt^2i + ct^3j, where b and c are positive constants, when does the velocity vector make an angle of 450 w

vazorg [7]

$\vec r(t)=bt^2\,\vec\imath+ct^3\,\vec\jmath$

The velocity at time $t$ is

$\dfrac{\mathrm d\vec r(t)}{\mathrm dt}=2bt\,\vec\imath+3ct^2\,\vec\jmath$

Take two vectors that point in the positive $x$ and positive $y$ directions, such as $\vec\imath$ and $\vec\jmath$ . The dot products of the velocity vector with $\vec\imath$ and $\vec\jmath$ are

$\dfrac{\mathrm d\vec r(t)}{\mathrm dt}\cdot\vec\imath=2bt=\sqrt{4b^2t^2+9c^2t^4}\cos\theta$

and

$\dfrac{\mathrm d\vec r(t)}{\mathrm dt}\cdot\vec\jmath=3ct^2=\sqrt{4b^2t^2+9c^2t^4}\cos\theta$

We want the angles between these vectors to be 45º, for which we have $\cos45^\circ=\frac1{\sqrt2}$ . So

$\begin{cases}2\sqrt2\,bt=\sqrt{4b^2t^2+9c^2t^4}\\3\sqrt2\,ct^2=\sqrt{4b^2t^2+9c^2t^4}\end{cases}\implies3\sqrt2\,ct^2-2\sqrt2\,bt=0$

$\implies t(3ct-2b)=0$

$\implies t=0\text{ or }t=\dfrac{2b}{3c}$

When $t=0$ , the velocity vector is equal to the zero vector, which technically has no direction/doesn't make an angle with any other vector. So the only time this happens is for