5th Grade. Please help! SC standards

An irregular object of mass 3 kg rotates about an axis, about which it has a radius of gyration of 0.2 m, with an angular accele

Artemon [7]

Answer:

0.06 Nm

Explanation:

mass of object, m = 3 kg

radius of gyration, k = 0.2 m

angular acceleration, α = 0.5 rad/s^2

Moment of inertia of the object

$I = mK^{2}$

I = 3 x 0.2 x 0.2 = 0.12 kg m^2

The relaton between the torque and teh moment off inertia is

τ = I α

Wheree, τ is torque and α be the angular acceleration and I be the moemnt of inertia

τ = 0.12 x 0.5 = 0.06 Nm

6 0

3 years ago

A bicyclist starting from rest applies a force of F = 454 N to ride his bicycle across flat ground for a distance of d = 250 m b

frutty [35]

Answer:

1.) 113500J

2.) 237m

Explanation:

Hello!

To solve this exercise follow the following steps, the description and complete process is in the attached image

1. Draw the full sketch of the problem.

2. The work is defined as the product of the trajectory by the force that is parallel to this direction, for this reason to find the work done we multiply the horizontal distance (250m) by the applied force (454N)

3. The potential energy is equal to the product of mass, gravity and height and is equal to the work done by the force applied by the cyclist, of this relationship and using algebra we can find the height that the cyclist climbed

4. We use the sine function to find the diagonal distance using the height and angle of the slope

7 0

3 years ago

PLeAsE hElp What is the kinetic energy of 14 Kg traveling at a velocity of 3m/s east

harkovskaia [24]

Answer:

Please see the given attachment.

Explanation:

Stay safe, stay healthy and be blessed.

Thank you.

<h2>PLEASE MARK ME AS BRAINLEST.</h2>

4 0

3 years ago

10 POINTS!!! Determine the pressure of your book in pascals (Pa). Show your work! (the pressure of the book in psi is 0.03 psi)

Musya8 [376]

You've listed a lot of data here, in both metric and customary units,
and I'm not even sure it's all needed. Let me try and boil it down:

Pressure on a surface =
   (total force on a surface) divided by (area of the surface).

The answer to the question is the pressure expressed in pascals.
There's actually enough information here to answer the question
in 2 different ways. We could ...

-- simply convert (0.03 pound per inch²) to pascals, or
-- go through the whole calculation of force, area, and then their quotient.

To me, converting 0.03 psi to Pa looks easier.

-- 1 pascal = 1 newton / 1 meter²

-- On Earth, 1 kilogram of mass weighs 9.8 Newtons and 2.2 pounds.
From this, we can calculate that

2.2 pounds of force = 9.8 newtons of force.

   1 pound = 4.45 newtons

(0.03 pound/inch²) x (4.45 newton/pound) x (1inch/2.54cm)² x (100cm/1m)² =

(0.03 x 4.45 x 1² x 100²) / (2.54² x 1²)    newton/meter² = 206.9 Pa .

7 0

4 years ago

An astronaut goes out for a space walk. Her mass (including space suit, oxygen tank, etc.) is 100 kg. Suddenly, disaster strikes

Marina CMI [18]

Answer:

Part A:

Unknown variables:

velocity of the astronaut after throwing the tank.

maximum distance the astronaut can be away from the spacecraft to make it back before she runs out of oxygen.

Known variables:

velocity and mass of the tank.

mass of the astronaut after and before throwing the tank.

maximum time it can take the astronaut to return to the spacecraft.

Part B:

To obtain the velocity of the astronaut we use this equation:

-(momentum of the oxygen tank) = momentum of the astronaut

-mt · vt = ma · vt

Where:

mt = mass of the tank

vt = velocity of the tank

ma = mass of the astronaut

va = velocity of the astronaut

To obtain the maximum distance the astronaut can be away from the spacecraft we use this equation:

x = x0 + v · t

Where:

x = position of the astronaut at time t.

x0 = initial position.

v = velocity.

t = time.

Part C:

The maximum distance the astronaut can be away from the spacecraft is 162 m.

Explanation:

Hi there!

Due to conservation of momentum, the momentum of the oxygen tank when it is thrown away must be equal to the momentum of the astronaut but in opposite direction. In other words, the momentum of the system astronaut-oxygen tank is the same before and after throwing the tank.

The momentum of the system before throwing the tank is zero because the astronaut is at rest:

Initial momentum = m · v

Where m is the mass of the astronaut plus the equipment (100 kg) and v is its velocity (0 m/s).

Then:

initial momentum = 0

After throwing the tank, the momentum of the system is the sum of the momentums of the astronaut plus the momentum of the tank.

final momentum = mt · vt + ma · va

Where:

mt = mass of the tank

vt = velocity of the tank

ma = mass of the astronaut

va = velocity of the astronaut

Since the initial momentum is equal to final momentum:

initial momentum = final momentum

0 = mt · vt + ma · va

- mt · vt = ma · va

Now, we have proved that the momentum of the tank must be equal to the momentum of the astronaut but in opposite direction.

Solving that equation for the velocity of the astronaut (va):

- (mt · vt)/ma = va

mt = 15 kg

vt = 10 m/s

ma = 100 kg - 15 kg = 85 kg

-(15 kg · 10 m/s)/ 85 kg = -1.8 m/s

The velocity of the astronaut is 1.8 m/s in direction to the spacecraft.

Let´s place the origin of the frame of reference at the spacecraft. The equation of position for an object moving in a straight line at constant velocity is the following:

x = x0 + v · t

where:

x = position of the object at time t.

x0 = initial position.

v = velocity.

t = time.

Initially, the astronaut is at a distance x away from the spacecraft so that

the initial position of the astronaut, x0, is equal to x.

Since the origin of the frame of reference is located at the spacecraft, the position of the spacecraft will be 0 m.

The velocity of the astronaut is directed towards the spacecraft (the origin of the frame of reference), then, v = -1.8 m/s

The maximum time it can take the astronaut to reach the position of the spacecraft is 1.5 min = 90 s.

Then:

x = x0 + v · t

0 m = x - 1.8 m/s · 90 s

Solving for x:

1.8 m/s · 90 s = x

x = 162 m

The maximum distance the astronaut can be away from the spacecraft is 162 m.

6 0

3 years ago