A force of 8480 N is applied to a cart or decelerate is at a rate of 32.0 m/s2. What is the mass of the cart?

A mass weighing 4 lb stretches a spring 2 in. Suppose that the mass is given an additional 6-in displacement in the positive dir

givi [52]

Answer:

$\frac{1}{8} y'' + 2y' + 24y=0$

Explanation:

The standard form of the 2nd order differential equation governing the motion of mass-spring system is given by

$my'' + \zeta y' + ky=0$

Where m is the mass, ζ is the damping constant, and k is the spring constant.

The spring constant k can be found by

$w - kL=0$

$mg - kL=0$

$4 - k\frac{1}{6}=0$

$k = 4\times 6 =24$

The damping constant can be found by

$F = -\zeta y'$

$6 = 3\zeta$

$\zeta = \frac{6}{3} = 2$

Finally, the mass m can be found by

$w = 4$

$mg=4$

$m = \frac{4}{g}$

Where g is approximately 32 ft/s²

$m = \frac{4}{32} = \frac{1}{8}$

Therefore, the required differential equation is

$my'' + \zeta y' + ky=0$

$\frac{1}{8} y'' + 2y' + 24y=0$

The initial position is

$y(0) = \frac{1}{2}$

The initial velocity is

$y'(0) = 0$

6 0

3 years ago

A car slows down uniformly from a speed of 30.0 m/s to rest in 7.20 s

Ede4ka [16]

When acceleration is constant, the average velocity is given by

$\bar v=\dfrac{v+v_0}2$

where $v$ and $v_0$ are the final and initial velocities, respectively. By definition, we also have that the average velocity is given by

$\bar v=\dfrac{\Delta x}{\Delta t}=\dfrac{x-x_0}{t-t_0}$

where $x,x_0$ are the final/initial displacements, and $t,t_0$ are the final/initial times, respectively.

Take the car's starting position to be at $t_0=0\,\mathrm s$ . Then

$\dfrac{v+v_0}2=\dfrac{x-x_0}t\implies x=x_0+\dfrac12(v+v_0)t$

So we have

$x=0\,\mathrm m+\dfrac12\left(0\,\dfrac{\mathrm m}{\mathrm s}+30.0\,\dfrac{\mathrm m}{\mathrm s}\right)(7.20\,\mathrm s)=108\,\mathrm m$

You also could have first found the acceleration using the equation

$v=v_0+at$

then solve for $x$ via

$x=x_0+v_0t+\dfrac12at^2$

but that would have involved a bit more work, and it turns out we didn't need to know the precise value of $a$ anyway.

7 0

3 years ago

The "Giant Swing" at a county fair consists of a vertical central shaft with a number of horizontal arms attached at its upper e

Mashcka [7]

Answer:

Explanation:

When the central shaft rotates , the seat along with passenger also rotates . Their rotation requires a centripetal force of mw²R where m is mass of the passenger and w is the angular velocity and R is radius of the circle in which the passenger rotates.

This force is provided by a component of T , the tension in the rope from which the passenger hangs . If θ be the angle the rope makes with horizontal ,

T cos θ will provide the centripetal force . So

Tcosθ = mw²R

Tsinθ component will balance the weight .

Tsinθ = mg

Dividing the two equation

Tanθ = $\frac{g}{\omega^2R}$

Hence for a given w , θ depends upon g or weight .

8 0

3 years ago

Read 2 more answers

What is the correct order of the layers' density from lowest density to highest?

Orlov [11]

Answer:

C. crust, mantle, core

Explanation:

density increases as you travel from the crust to the inner core

the crust is on top

next is the mantle

and then the core

6 0

3 years ago

Read 2 more answers

Daltons theory was identified using

Margaret [11]

<h2>Answer with Explanation </h2>

Dalton’s theory can be classified by the following hypotheses:

1) All material was formed of particles, unbreakable and strong construction segments.

2) All particles of a given component are indistinguishable in volume and characteristics

3) Compounds are determined by a mixture of two or more distinct kinds of atoms.

4) Chemical responses appeared in the rearrangement of the reacting atoms.

This theory was to explain all matter in terms of atoms and their characteristics, the law of conservation of volume and the law of constant composition.

7 0

3 years ago