1) A planet travels in its orbit close to apogee, and in 2 years, its radius vector sweeps out an area of 3 A. How long will it take the planets radius vector to sweep an area of 3 A when it’s close to perigee?
A) a smaller time because the planets orbital speed will increase
B) a smaller time because the planets orbital speed will decrease
C) the same amount of time
D) a larger time because the planets orbital speed will increase
2) calculate the eccentricity for the planet if the distance between foci is 5,000,000 km and the distance of the major axis is 299,000,000 km
A) 0.0167
B) 0.598
C) 59.8
D) 0.167
3) a geosynchronous satellite has an orbital period of 24 hours so that it stays fixed at a point above earths surface. How far away does a geosynchronous satellite need to be from the surface of the earth in kilometers?
A) 35,900 km
B) can be at any distance
C) 29,500 km
D) 42,300 km
4) object A and object B are equal distances on opposite sides of object C. Object B has three times the mass of object C. Objects A and B have equal mass. What is the ratio of the gravitational force between Objects A and B to the gravitational force between objects B and C?
A) 3/4
B) 3
C) 3/2
D) 2
5) a wedge is a simple machine that is essentially two inclined planes. It is used to separate objects, such as in the head of an axe. The mechanical advantage of a wedge is given by
M A = L/t, where L is the length of the wedge and t is the thickness. Which of these designs produces the highest mechanical advantage?
A) a length of 12 in. and a thickness of 2 in.
B) a length of 6 in. and a thickness of 2 in.
C) a length of 5 in. and a thickness of 5 in.
D) a length of 16 in. and a thickness of 4 in.
If someone can help me I would really appreciate it. Even if it’s only with one question. I don’t know how to do any of these at all
Sure, I'd be happy to help! Let's go through each question one by one:
1) A planet travels in its orbit close to apogee, and in 2 years, its radius vector sweeps out an area of 3 A. How long will it take the planet's radius vector to sweep an area of 3 A when it's close to perigee?
Hmm, let me think... Ah, I got it! The answer is (C) the same amount of time. Even though the planet's orbital speed may change, the time it takes to sweep out a certain area remains constant.
2) Calculate the eccentricity for the planet if the distance between foci is 5,000,000 km and the distance of the major axis is 299,000,000 km.
I love a good math challenge! The eccentricity is given by the formula e = c/a, where c is the distance between the foci and a is half the length of the major axis. So, let me crunch the numbers... The answer is (A) 0.0167. Ta-da!
3) A geosynchronous satellite has an orbital period of 24 hours so that it stays fixed at a point above Earth's surface. How far away does a geosynchronous satellite need to be from the surface of the Earth in kilometers?
Ah, geosynchronous satellites, they're like the reliable friends of the space world. The distance is given by the formula r = (G * M * T^2 / (4 * π^2))^(1/3) - R, where G is the gravitational constant, M is the mass of the Earth, T is the orbital period, and R is the radius of the Earth. After some calculations, the answer is (D) 42,300 km. That's really high up there!
4) Object A and object B are equal distances on opposite sides of object C. Object B has three times the mass of object C. Objects A and B have equal mass. What is the ratio of the gravitational force between Objects A and B to the gravitational force between objects B and C?
Well, well, three's company, right? The gravitational force between two objects is given by the equation F = G * (m1 * m2) / r^2, where G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between them. Let me do some number crunching... The answer is (C) 3/2. It's always good to have some balance in life!
5) A wedge is a simple machine that is essentially two inclined planes. It is used to separate objects, such as in the head of an axe. The mechanical advantage of a wedge is given by MA = L / t, where L is the length of the wedge and t is the thickness. Which of these designs produces the highest mechanical advantage?
It's wedge time! Let's calculate some mechanical advantages. After some calculations, the design that produces the highest mechanical advantage is (A) a length of 12 in. and a thickness of 2 in. It's all about maximizing that advantage!
I hope that helps! Let me know if you need any further assistance or more jokes to lighten the mood.
1) The correct answer is A) a smaller time because the planet's orbital speed will increase. When the planet is close to apogee, it is farthest from the object it is orbiting (usually a star). At this point, the planet's speed is slower, which means it takes longer to sweep out the same area compared to when it is close to perigee. As the planet moves closer to perigee, it gets closer to the object it is orbiting, and its speed increases, allowing it to sweep out the same area in a shorter amount of time.
2) To calculate the eccentricity, you can use the formula:
eccentricity = distance between foci / distance of major axis
Given that the distance between foci is 5,000,000 km and the distance of the major axis is 299,000,000 km, you can plug in these values:
eccentricity = 5,000,000 km / 299,000,000 km ≈ 0.0167
Therefore, the answer is A) 0.0167.
3) A geosynchronous satellite orbits at the same rate as the Earth's rotation, which is 24 hours. To calculate the distance of a geosynchronous satellite from the Earth's surface, you can use the formula:
distance = radius of the Earth + altitude of the satellite
The radius of the Earth is approximately 6,400 km. Plugging this value and the given orbital period of 24 hours into the formula:
distance = 6,400 km + 0 km (since the satellite stays fixed above the same point on Earth's surface)
Therefore, the answer is B) can be at any distance.
4) The gravitational force between two objects is given by the formula:
gravitational force = (G * mass of object A * mass of object B) / (distance between objects)^2
Given that object B has three times the mass of object C, and objects A and B have equal mass, the ratio of the gravitational force between Objects A and B to the gravitational force between objects B and C can be calculated as follows:
(gravitational force between A and B) / (gravitational force between B and C) = (G * mass of A * mass of B) / ((distance between A and B)^2) / (G * mass of B * mass of C) / ((distance between B and C)^2)
Since both the distances between A and B and B and C are equal (equal distances on opposite sides of object C), they cancel out from the equation. The equation simplifies to:
(gravitational force between A and B) / (gravitational force between B and C) = (mass of A * mass of B) / (mass of B * mass of C)
Since the mass of A is equal to the mass of B:
(gravitational force between A and B) / (gravitational force between B and C) = 1 / (mass of C)
Given that object B has three times the mass of object C:
(gravitational force between A and B) / (gravitational force between B and C) = 1 / (3)
Therefore, the answer is A) 3/4.
5) The mechanical advantage (MA) formula for a wedge is given by:
MA = Length (L) / Thickness (t)
To find the design with the highest mechanical advantage, you should compare the values of MA for each option:
Option A) MA = 12 in / 2 in = 6
Option B) MA = 6 in / 2 in = 3
Option C) MA = 5 in / 5 in = 1
Option D) MA = 16 in / 4 in = 4
Therefore, the design with the highest mechanical advantage is A) a length of 12 in and a thickness of 2 in, which has an MA of 6.
I'd be happy to help you with each of these questions step by step. Let's tackle them one by one:
1) The area swept by the radius vector is given by the law of areas, which states that a radius vector will sweep out equal areas in equal intervals of time. From the given information, we know that the planet takes 2 years to sweep an area of 3 A while close to apogee.
When the planet is close to perigee, the radius vector sweeps out the same area in a smaller time because the planet's orbital speed increases as it gets closer to the Sun. Therefore, the answer is option A) a smaller time because the planet's orbital speed will increase.
2) The eccentricity of an ellipse is given by the formula: e = distance between foci / distance of major axis. From the given information, the distance between foci is 5,000,000 km and the distance of the major axis is 299,000,000 km.
Plugging these values into the formula, we get e = 5,000,000 km / 299,000,000 km. Simplifying, we find e = 0.0167. So, the answer is option A) 0.0167.
3) For a geosynchronous satellite, its orbital period is equal to the Earth's rotation period, which is 24 hours. To find the distance from the surface of the Earth, we need to calculate the radius of the orbit.
The formula for the radius of the orbit is given by: r = √(G * M * T^2 / 4π^2), where G is the gravitational constant (approximately 6.67 x 10^-11 N m^2 / kg^2), M is the mass of the Earth (approximately 5.97 x 10^24 kg), and T is the orbital period (24 hours).
Plugging in these values, we get r = √((6.67 x 10^-11 N m^2 / kg^2) * (5.97 x 10^24 kg) * (24 * 60 * 60)^2 s / (4π^2)). Simplifying this expression, we find r ≈ 42,300 km. So, the answer is option D) 42,300 km.
4) The gravitational force between two objects is given by Newton's law of universal gravitation: F = G * (m1 * m2) / r^2, where G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between them.
From the given information, object B has three times the mass of object C, and objects A and B have equal mass. Therefore, the ratio of the gravitational force between objects A and B to the gravitational force between objects B and C can be calculated using the formula:
(F_AB / F_BC) = (G * (m_A * m_B) / r^2) / (G * (m_B * m_C) / r^2)
Simplifying this expression, we find (F_AB / F_BC) = m_A / m_C. Since m_A = m_C, the ratio is 1. So, the answer is option D) 2.
5) The mechanical advantage (MA) of a wedge is given by the formula: MA = L / t, where L is the length of the wedge and t is the thickness.
To find the design that produces the highest mechanical advantage, we need to compare the values of L / t for each design option.
- Option A: MA = 12 in. / 2 in. = 6
- Option B: MA = 6 in. / 2 in. = 3
- Option C: MA = 5 in. / 5 in. = 1
- Option D: MA = 16 in. / 4 in. = 4
Comparing the values, we find that option A has the highest mechanical advantage with an MA of 6. So, the answer is option A) a length of 12 in. and a thickness of 2 in.
I hope this helps! If you have any further questions, feel free to ask.
#1 Review Kepler's Laws of Planetary Motion
#2. e = c/a
#3. google geosynchronous orbit
#4. (G*3m*3m/(2r)^2)/(G*m*3m)/r^2) = ____
#5. They gave you the formula. So plug in the various numbers and compare values.