10. Particles P₁, P2, P3 and Q form a rectangle as indicated in the diagram given below. Q (a) 79 kg (b) 77 kg (c) 81 kg (d) 67 kg (e) 75 kg ilm 0 FQ 3 m P3 P₁ P2 If particle P₁ has mass 61 kg, particle P3 has mass 57 kg and the resultant gravitational force Fo acting on particle Q due to the particles P₁, P₂ and P3 makes an angle 0= 78° with the straight line that passes through the particles P3 and Q, then the mass of particle P2 (rounded to the nearest kilogram) is equal to:
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- An intergalactic spaceship arrives at a distant planet that rotates on its axis with a period of T = 31 hours. The mass of the planet is M = 2.1 • 1025 kg. The spaceship enters a circular orbit with an orbital period that is equal to the planet's period for the rotation about its axis, T. a. Enter an expression for the radius of the spaceship’s orbit. b. Calculate the orbital radius in meters.8. At an amusement park there is a ride in which cylindrically shaped chambers spin around a central axis. People sit in seats facing the axis, their backs against the outer wall. At one instant the outer wall moves at a speed of 3.60 m/s, and an 87.0-kg person feels a 590-N force pressing against his back. What is the radius of the chamber? m11) Newton's Law of Gravity says that the force of gravity between any two objects is G d2 where the m's are the masses of the objects and, d is the distance between them, and G is a constant that depends on your choice of units. This includes big things like planets and small things like you and your pets. We don't need to know the values of the masses to think about what happens as two objects approach each other! lim G d--0+ d? If you think too long about your answer, it may be a bit troubling. What does it say about the force of gravity when you actually touch your pets?
- 3. Two astronauts in space, each will a mass of 100 kg, are 2 meters apart from one another. a) What is the gravitational force between them? b) Both astronauts are initially at rest, but the force of gravity between them will cause them to accelerate toward one another. At what rate will they accelerate toward one another? (a = F/m.) ans. a) 1.67 x 10-7 N %3Dm1 m2 In the picture above assume the only objects of interest are those shown. There is no Earth below them. The humanoid figures have zero mass but the balls do have mass. 1. Draw the FBD of Ball 1 2. Draw the FBD of Ball 2Gravitational field vector
- G = 6.67 ×10 -11 m 3 /kg/s 2 Some people claim that the location of Jupiter can have dramatic consequences on human events on Earth. For comparison to the last problem, what is the force of gravity due to a 100 kg person hugging a 60.0kg ASTR 110 student. Assume the distance between the students is 0.3 meters.5. A ball is thrown with an initial velocity of 8.5 m/s at an angle of 30.0⁰ from the horizontal. How long the ball is in flight? (assume g = 9.81 m/s²) 6. The planet A has a mass of 1.972-1024 kg and the planet B has a mass of 5.348-1024 kg. What is the distance between the planet A and planet B if the force of gravity between them is 2.111-1022 N?. (assume G = 6.670-10-¹¹ Nm²/kg²) 1770You are in charge of a cannon that exerts a force 17100 N on a cannon ball while the ball is in the barrel of the cannon. The length of the cannon barrel is 2.37 m and the cannon is aimed at a 36.7 ◦ angle from the ground. The acceleration of gravity is 9.8 m/s 2 . If you want the ball to leave the cannon with speed v0 = 89 m/s, what mass cannon ball must you use? Answer in units of kg. Answer in units of kg.
- 2-D star cluster puzzle Find the net gravitational force for III) Pentagon Let m=mass of the star = 1.99 x 10^30 kg, l=earth to star distance=149.6 x 10^6 km, G=6.67 x10^-11 N m^2/kg^2. Note that the masses of each star are the same. Also, it is advised to use vectors and components. And you can just find the gravitational net force of one of the stars in the shape3. The Earth has a mass of 5.97 X 10²4 kg, and the Moon has a mass of 7.36 × 102 kg. The Moon orbits the Earth at a distance of 384,000 km; that is, the center of the Moon is a distance of 384,000 km from the center of the Earth, as shown below. How far from the center of the Earth is the center of mass of the Earth-Moon system? Earth -5.97-104 kg 384,000 km -7.36 102 kg MoonThe Moon is 60 Earth radii (i.e. 60 rEarth) from the center of the Earth and has a mass of 0.012 Earth masses (i.e. 0.012 mEarth) a. How many Earth radii is the center of mass (the “barycenter”) of the Earth-Moon system from the center of the Earth? b. Is the center of mass inside the Earth or outside the Earth? c. What point along the line from the center of the Earth to the center of the Moon orbits the barycenter of the Solar System in a (nearly) circular orbit (e.g. the center of the Earth, the barycenter of the Earth-Moon system, the midpoint, the center of the Moon)?