Two celestial objects are in space: one with a mass of 8.22 x 109 kg and one with a mass of 1.38 x 108 kg. If they are separated
1 answer:
Answer: Two celestial objects are in space: one with a mass of 8.22 x 109 kg and one with a mass of 1.38 x 108 kg. If they are separated by a distance of 1.43 km, then, the magnitude of the force of attraction (in newtons) between the objects will be 52.9kN
Explanation: To find the answer we need to know more about the Newton's law of gravitation.
<h3>What is Newton's law of gravitation?</h3>- Gravitation is the force of attraction between any two bodies.
- Every body in the universe attracts every other body with a force.
- This force is directly proportional to the product of their masses and inversely proportional to the square of the distance between these two masses.
- Mathematically we can expressed it as,
- Here, we have given with the data's,
- Thus, the force of attraction between these two bodies will be,
Thus, if two celestial objects are in space: one with a mass of 8.22 x 109 kg and one with a mass of 1.38 x 108 kg and, If they are separated by a distance of 1.43 km, then, the magnitude of the force of attraction (in newtons) between the objects will be 52.9kN.
Learn more about the Newton's law of gravitation here:
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Answer:
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Explanation:
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The image is missing, so i have attached it;
Answer:
A) V_rel = [-(2.711)i - (0.2588)j] m/s
B) a_rel = (0.8637i + 0.0642j) m/s²
Explanation:
We are given;
the cruise ship velocity; V_b = 1 m/s
Angular velocity; ω = 1 deg/s = 1° × π/180 rad = 0.01745 rad/s
Angular acceleration;α = -0.5 deg/s² = 0.5 x π/180 rad = -0.008727 rad/s²
Now, let's write Velocity (V_a) at A in terms of the velocity at B(V_b) with r_ba being the position vector from B to A and relative velocity (V_rel)
Thus,
V_a = V_b + (ω•r_ba) + V_rel
Now, V_a = 0. Thus;
0 = V_b + (ω•r_ba) + V_rel
V_rel = -V_b - (ω•r_ba)
From the image and plugging in relevant values, we have;
V_rel = -1[(cos15)i + (sin15)j] - (0.01745k * -100j)
V_rel = - (cos15)i - (sin15)j - 1.745i
Note that; k x j = - i
V_rel = [-(2.711)i - (0.2588)j] m/s
B) Let's write the acceleration at A with respect to B in terms of a_b.
Thus,
a_a = a_b + (α*r_ba) + (ω(ω•r_ba)) + (2ω*v_rel) + a_rel
a_a and a_b = 0.
Thus;
0 = (α*r_ba) + (ω(ω•r_ba)) + (2ω*v_rel) + a_rel
a_rel = - (α*r_ba) - (ω(ω•r_ba)) - (2ω*v_rel)
Plugging in the relevant values with their respective position vectors, we have;
a_rel = - (-0.008727k * -100j) - (0.01745k(0.01745k * -100j)) - (2*0.01745k * [-(2.711)i - (0.2588)j])
a_rel = 0.8727i - (0.01745² x 100)j + 0.0946j - 0.009i
Note that; k x j = - i and k x i = j
Thus,simplifying further ;
a_rel = 0.8637i + 0.0642j m/s²
