Can two spheres of different diameters and different<br> masses have the same moment of inertia?

A cannon fires a cannonball forward at a velocity of 48.1 m/s horizontally. If the cannon is on a mounted wagon 1.5 m tall, how

GalinKa [24]

Answer: 473.640 m

Explanation:

This situation is related to projectile motion or parabolic motion, in which the travel of the cannonball has two components: x-component and y-component. Being their main equations as follows:

x-component:

$x=V_{o}cos\theta t$ (1)

Where:

$V_{o}=48.1 m/s$ is the cannonball's initial velocity

$\theta=0$ because we are told the cannonball is shot horizontally

$t$ is the time since the cannonball is shot until it hits the ground

y-component:

$y=y_{o}+V_{o}sin\theta t-\frac{gt^{2}}{2}$ (2)

Where:

$y_{o}=1.5m$ is the initial height of the cannonball

$y=0$ is the final height of the cannonball (when it finally hits the ground)

$g=9.8m/s^{2}$ is the acceleration due gravity

We need to find how far (horizontally) the cannonball has traveled before landing. This means we need to find the maximum distance in the x-component, let's call it $X_{max}$ and this occurs when $y=0$ .

So, firstly we will find the time with (2):

$0=1.5 m+48. 1 m/s sin(0\°) t-(4.9 m/s^{2})t^2$ (3)

Rearranging the equation:

$0=-(4.9 m/s^{2})t^2+48. 1 m/s sin(0\°) t+1.5 m$ (4)

$-(4.9 m/s^{2})t^2+(48. 1 m/s) t+1.5 m=0$ (5)

This is a <u>quadratic equation</u> (also called <u>equation of the second degree</u>) of the form $at^{2}+bt+c=0$ , which can be solved with the following formula:

$t=\frac{-b \pm \sqrt{b^{2}-4ac}}{2a}$ (6)

Where:

$a=-4.9 m/s^{2}$

$b=48.1 m/s$

$c=1.5 m$

Substituting the known values:

$t=\frac{-48.1 \pm \sqrt{48.1^{2}-4(-4.9)(1.5)}}{2(-4.9)}$ (7)

Solving (7) we find the positive result is:

$t=9.847 s$ (8)

Substituting this value in (1):

$x=(48.1 m/s)cos(0\°) (9.847 s)$ (9)

$x=473.640 m$ This is the horizontal distance the cannonball traveled before it landed on the ground.

3 0

3 years ago

An astronaut of mass 65kg in training rides in a seat that is moved in uniform circular motion by a radial arm 5.10 meters long.

ikadub [295]

<h3><u>Answer;</u></h3>

= 2868 Newtons

<h3><u>Explanation;</u></h3>

Centripetal force is a force that acts on an object or a body in circular path and is directed towards the center of the circular path.

Centripetal force is given by the formula;

mv²/r ; where m is the mass of the body, r is the radius of the circular path and v is the velocity of a body;

mass = 65 kg, velocity = 15 m/s and r = 5.1 m

Therefore;

Centripetal force = (65 × 15²)/ 5.10

= 2867.65 Newtons

= 2868 N

7 0

4 years ago

A mixture can be classified as a solution, suspension, or colloid based on the

atroni [7]

The best answer choice here is B. =)

8 0

3 years ago

An electric car accelerates for 8.0 s by drawing energy from its 320-V battery pack. During this time, 1300 C worth of electrons

kati45 [8]

(a) $8.13\cdot 10^{-21}$

The magnitude of the charge of one electron is

$q=1.6\cdot 10^{-19}C$

Here the total amount of charge that passed through the battery pack is

Q = 1300 C

So this total charge is given by

Q = Nq

where

N is the number of electrons that has moved through the battery

Solving for N,

$N=\frac{Q}{q}=\frac{1300 C}{1.6\cdot 10^{-19} C}=8.13\cdot 10^{-21}$

(b) $4.16\cdot 10^5 J$

First, we can find the current through the battery, which is given by the ratio between the total charge (Q = 1300 C) and the time interval (t = 8.0 s):

$I=\frac{Q}{t}=\frac{1300 C}{8.0 s}=162.5 A$

Now we can find the power, which is given by:

$P=VI$

where

V = 320 V is the voltage

I = 162.5 A is the current

Subsituting,

$P=(320 V)(162.5 A)=52,000 W$

And now we can find the total energy transferred, which is the product between the power and the time:

$E=Pt = (52,000 W)(8.0 s)=4.16\cdot 10^5 J$

(c) 69.7 hp

Now we have to convert the power from Watt to horsepower.

We know that

1 hp = 746 W

So we can set up the following proportion:

1 hp : 746 W = x : 52,000 W

And by solving for x, we find the power in horsepower:

$x=\frac{1 hp \cdot 52,000 W}{746 W}=69.7 hp$

5 0

4 years ago

How much power is used by 4 A appliance that is plugged into a 120 V circuit for 4 minutes

Sever21 [200]

Answer:

Power, P = 480 W

Explanation:

It is required to find the power used by 4 A appliance that is plugged into a 120 V circuit for 4 minutes. Power used by an appliance is given by the formula as follows :

$P=VI$

Plugging all the values we get :

$P=120\times 4\\\\P=480\ W$

So, the power used by the appliance is 480 W.

8 0

3 years ago

Can two spheres of different diameters and different masses have the same moment of inertia?