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Two spherical objects have masses of 3.1 x 10^5 kg and 6.5 x 10^3 kg. The gravitational attraction between them is 65 N. How far

nata0808 [166]

Answer:

4.55 x 10⁹m

Explanation:

Given parameters:

Mass of object 1 = 3.1 x 10⁵kg

Mass of object 2 = 6.5 x 10³kg

Gravitational force = 65N

Unknown:

Distance between them = ?

Solution:

To solve this problem, we use the expression below from the universal gravitational law;

Fg = $\frac{G mass 1 x mass 2}{distance ^{2} }$

G = 6.67 x 10⁻¹¹

65 = $\frac{6.67 x 10^{11} x 3.1 x 10^{5} x 6.5 x 10^{3} }{distance^{2} }$

Distance = 4.55 x 10⁹m

3 0

3 years ago

A car moves in a circular motion and it is subject to a centripetal acceleration of 24 m/s2. If the radius of the circular path

Softa [21]

Answer:

Explanation:

Centripetal acceleration is given by:

$a_{c} = v^{2}/r$

Thus, centripetal acceleration is inversely proportional to the radius. Thus, when radius will double, the centripetal acceleration will be halved.

3 0

3 years ago

A 0.43 kg hammer is moving horizontally at 5.2 m/s when it strikes a nail and comes to rest after driving the nail 0.014 m into

vagabundo [1.1K]

Answer:

The duration of the impact is 0.005384 seconds

Explanation:

Given

m = 0.43 kg

v = 5.2 m/s

x = 0.014 m

Knowing the formulas

$v^{2}_{f} = v^{2}_{i} + 2ax\\0 = 5.2^{2} + 2a*0.014\\a = - 965.71 m/s^{2} \\\\vf = vi + at\\0 = 5.2 + (965.71)t\\t = 0.005384 s$

5 0

3 years ago

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Find the angle formed by two forces of 7N and 15N respectively if its result is worth 20N

nadezda [96]

First, you need to make certain assumptions before solving this question. Why? Because there are no information given about the direction of these forces. In such questions as above, ALWAYS make the following assumptions:

1) Take first force, say $F_{1}$ , and assume that it is pointing towards the x-direction.

Let us take the 7N force! By keeping the above assumption in our minds, the force vector would be like:
$F_{1}$ = $7i$ , where $i$ = Unit vector in the x-direction.

2) Take the second force, say $F_{2}$ , and assume that it is making an angle $\alpha$ with the first force $F_{1}$ .

Let us take the 15N force! By keeping the above assumption in our minds, the forces vector would be like:

$F_{2} = (15*cos \alpha)i + (15*sin \alpha )j$

Now from simple vector addition, we know that,
$F_{R} = F_{1} + F_{2}$ --- (A)

Where $F_{R}$ = Resultant vector.
NOTE: In equation (A), all forces are in vector notation. Assume that there is an arrow head on top of them.

Let us find $F_{1}+F_{2}$ first!
$F_{1}+F_{2}$ =   $7i+(15*cos \alpha)i + (15*sin \alpha )j$

=> $F_{1}+F_{2}$ =   $(7+15*cos \alpha)i + (15*sin \alpha )j$

Now the magnitude of $F_{1}+F_{2}$ is,
| $F_{1}+F_{2}$ | = $\sqrt{ (7+ 15*cos \alpha)^{2} + (15*sin \alpha )^{2}}$

=> | $F_{1}+F_{2}$ | = $\sqrt{ 49 + 225*(cos \alpha)^{2} + 210*(cos \alpha)+ 255*(sin \alpha )^{2}}$

Since $(sin \alpha)^{2} + (cos \alpha)^{2} = 1$ , therefore,

=> | $F_{1}+F_{2}$ | = $\sqrt{ 49 + 225 + 210*(cos \alpha)}$

Since  | $F_{1}+F_{2}$ | = | $F_{R}$ |, and the magnitude of the resultant force is 20N, therefore,

| $F_{R}$ | = | $F_{1}+F_{2}$ |
20 = $\sqrt{ 49 + 225 + 210*(cos \alpha)}$

Take square on both sides,
400 = $49 + 225 + 210*(cos \alpha)$
$(cos \alpha) = \frac{3}{5}$

$\alpha = 53.13^{o}$

Ans: Angle formed by the two forces, 7N and 15N, is: 53.13°

-israr

4 0

2 years ago

In 2-3 complete sentences, explain why the needle on a compass always points in the direction of magnetic north.

Alex17521 [72]

The needle on a compass always points in the direction of magnetic north because of the magnetic poles of earth. the compass is essentially a magnet itself, so the southern pole of the compass is attracted to the northern pole of earth.

8 0

3 years ago

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