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schepotkina [342]
2 years ago
7

Two masses, m1 & m2 are separated by a distance of 12 m between their centers. The gravitational force attraction between th

e two masses is measured to be 6.0 x 10-6 N. The masses are then moved closer to one another, to a distance of 4 m between centers, and the resulting gravitational force is measured again. According to the Universal Law of Gravitation, the second measurement is
Physics
1 answer:
Artemon [7]2 years ago
6 0

The universal law of gravitation says that the gravitational force between the two masses is

<em>F</em>₁ = <em>G</em> <em>m</em>₁ <em>m</em>₂ / <em>r</em> ² = 6.0 × 10⁻⁶ N

where <em>r</em> = 12 m. When the distance between the two masses is reduced to <em>R</em> = 4 m, i.e. 1/3 of the original distance <em>r</em>, we have

<em>F</em>₂ = <em>G</em> <em>m</em>₁ <em>m</em>₂ / <em>R </em>² = <em>G</em> <em>m</em>₁ <em>m</em>₂ / (<em>r</em>/3)² = 1/9 <em>G</em> <em>m</em>₁ <em>m</em>₂ / <em>r </em>² = 1/9 <em>F</em>₁

so that the resulting gravitational force has 1/9 the first magnitude, or

<em>F</em>₂ = 1/9 (6.0 × 10⁻⁶ N) ≈ 6.7 × 10⁻⁷ N

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One end of a rope is tied to the handle of a horizontally-oriented and uniform door. a force fis applied to the other end of the
sergeinik [125]
<span>Answer:The weight of the door creates a CCW torque given by Tccw = 145 N*3.13 m / 2 You need a CW torque that's equal to that Tcw = F*2.5 m*sin20</span>
4 0
3 years ago
Read 2 more answers
Determine the torque applied to the shaft of a car that transmits 225 hp
Arisa [49]

Incomplete question.The complete question is here

Determine the torque applied to the shaft of a car that transmits 225 hp and rotates at a rate of 3000 rpm.

Answer:

Torque=0.51 Btu

Explanation:

Given Data

Power=225 hp

Revolutions =3000 rpm

To find

T( torque )=?

Solution

As

T(Torque)=\frac{W(Work)}{2\pi n(Revolutions) }

As force moves an object through a distance, work is done on the object. Likewise, when a torque rotates an object through an angle, work is done.

So

T=\frac{225*42.207}{2\pi 3000}\\ T=0.51 Btu

8 0
2 years ago
the minute hand on a clock is 9 cm long and travels through an arc of 252 degrees every 42 minutes. To the nearest tenth of a ce
Tanzania [10]

Answer:

The minutes hand travels 39.60 cm.

Explanation:

Note: a clock has a shape of a circle, the minutes hand is the radius, and the travel of the minutes hand forms a arc.

Length of an arc = ∅/360(2πr)

L = ∅/360(2πr).................... Equation 1π

Where L = length of an arc, ∅ = angle formed by an arc, r = radius of the arc.

Given:  ∅ = 252°, r = 9 cm, π = 3.143.

Substituting these values into equation 1,

L = 252/360(2×3.143×9)

L = 0.7×2×3.143×9

L = 39.60 cm.

Thus the minutes hand travels 39.60 cm.

4 0
2 years ago
A material that has a fracture toughness of 33 MPa.m0.5 is to be made into a large panel that is 2000 mm long by 250 mm wide and
scoray [572]

Answer:

F_{allow} = 208.15kN

Explanation:

The word 'nun' for thickness, I will interpret in international units, that is, mm.

We will begin by defining the intensity factor for the steel through the relationship between the safety factor and the fracture resistance of the panel.

The equation is,

K_{allow} =\frac{K_c}{N}

We know that K_c is 33Mpa*m^{0.5} and our Safety factor is 2,

K_{allow} = \frac{33Mpa*m^{0.5}}{2} = 16.5MPa.m^{0.5}

Now we will need to find the average width of both the crack and the panel, these values are found by multiplying the measured values given by 1/2

<em>For the crack;</em>

\alpha = 0.5*L_c = 0.5*4mm = 2mm

<em>For the panel</em>

\gamma = 0.5*W = 0.5*250mm = 125mm

To find now the goemetry factor we need to use this equation

\beta = \sqrt{sec(\frac{\pi\alpha}{2\gamma})}\\\beta = \sqrt{sec(\frac{2\pi}{2*125mm})}\\\beta = 1

That allow us to determine the allowable nominal stress,

\sigma_{allow} = \frac{K_{allow}}{\beta \sqrt{\pi\alpha}}

\sigma_{allow} = \frac{16.5}{1*\sqrt{2*10^{-3} \pi}}

\sigma_{allow} = 208.15Mpa

So to get the force we need only to apply the equation of Force, where

F_{allow}=\sigma_{allow}*L_c*W

F_{allow} = 208.15*250*4

F_{allow} = 208.15kN

That is the maximum tensile load before a catastrophic failure.

4 0
2 years ago
Because the soles of your shoes have cleats, you can exert a forward force of 100 N even on slippery ice. A 10-kg picnic cooler
Brilliant_brown [7]

Answer:

you must throw 3 snowballs

Explanation:

We can solve this exercise using the concepts of conservation of the moment, let's define the system as formed by the refrigerator and all the snowballs. Let's write the moment

Initial. Before bumping that refrigerator

          p₀ = n m v₀

Where n is the snowball number

Final. When the refrigerator moves

         pf = (n m + M) v

The moment is preserved because the forces during the crash are internal

        n m v₀ = (n m + M) v

        n m (v₀ - v) = M v

        n = M/m    v/(vo-v)

Let's look for the initial velocity of the balls, suppose the person throws them with the maximum force if it slides in the snow (F = 100N), let's use the second law and Newton

          F = m a

          a = F / m

The distance the ball travels from zero speed to maximum speed is the extension of the arm (x = 1 m), let's look kinematically for the speed of the balls when leaving the arm

          v₁² = v₀² + 2 a x

          v₁² = 0+ 2 (100/1) 1

          v₁ = 14.14 m / s

This is the initial speed for the crash

         v₀ = v = 14.14 m / s

  Let's calculate

           n = M/m   v/ (v₀-v)

           n = 10/1   3 / (14.14 -3)

          n = 2.7 balls

you must throw 3 snowballs

7 0
2 years ago
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