Two astronauts (Fig. P8.80), each haring a mass of 75.0 kg, are connected by a 10.0-m rope of negligible mass. They are isolated in space, moving in circles around the point halfway between them at a speed of 5.00 m/s. Treating the astronauts as particles, calculate (a) the magnitude of the angular momentum and (b) the rotational energy of the system. By pulling on the rope, the astronauts shorten the distance between them to 5.00 m. (c) What is the new angular momentum of the system? (d) What are their new’ speeds? (e) What is the new rotational energy of the system? (f) How much work is done by the astronauts in shortening the rope? Figure P8.80 Problems 80 and 81
Two astronauts (Fig. P8.80), each haring a mass of 75.0 kg, are connected by a 10.0-m rope of negligible mass. They are isolated in space, moving in circles around the point halfway between them at a speed of 5.00 m/s. Treating the astronauts as particles, calculate (a) the magnitude of the angular momentum and (b) the rotational energy of the system. By pulling on the rope, the astronauts shorten the distance between them to 5.00 m. (c) What is the new angular momentum of the system? (d) What are their new’ speeds? (e) What is the new rotational energy of the system? (f) How much work is done by the astronauts in shortening the rope? Figure P8.80 Problems 80 and 81
Solution Summary: The author explains the formula to calculate the angular momentum of the astronauts.
Two astronauts (Fig. P8.80), each haring a mass of 75.0 kg, are connected by a 10.0-m rope of negligible mass. They are isolated in space, moving in circles around the point halfway between them at a speed of 5.00 m/s. Treating the astronauts as particles, calculate (a) the magnitude of the angular momentum and (b) the rotational energy of the system. By pulling on the rope, the astronauts shorten the distance between them to 5.00 m. (c) What is the new angular momentum of the system? (d) What are their new’ speeds? (e) What is the new rotational energy of the system? (f) How much work is done by the astronauts in shortening the rope?
Figure P8.80 Problems 80 and 81
Definition Definition Product of the moment of inertia and angular velocity of the rotating body: (L) = Iω Angular momentum is a vector quantity, and it has both magnitude and direction. The magnitude of angular momentum is represented by the length of the vector, and the direction is the same as the direction of angular velocity.
Assuming the normal angle for stairs in a house, 37.0˚ with the horizontal, what is Kevin’s acceleration down the stairs? The sled is always touching at least one stair so you can treat it the same as a ramp. The coefficient of kinetic friction between the sled and the carpeted stairs is 0.708.
A helicopter pulls up and back on the truck with a force of 5.78⋅10^4 N at an angle of 30.0˚ from the horizontal. The truck has a mass of 5.04⋅10^3 kg. The truck’s engine applies a force on the truck that is in the x direction causing the truck to accelerate at 2.09 m/s2 in x. A) What is the force the engine is exerting? B) What is the normal force acting on the truck? Assume no acceleration in y.
Mikasa and her allies, from Attack on Titan, uses omni-directional mobility gear (ODM gear) to move from place to place. The ODM gear launches out wires with grappling hooks they can use to swing through the city. Mikasa, who has a mass of 68.0 kg, holds herself in place not moving with two wires from the ODM gear, as shown below with θ1 = 39.3°. If the tension in the wire labeled T1 is 688 N, what tension, magnitude and direction, is needed in T2?
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