The block B of mass 7.1 kg and cylinder A of mass 14.2 kg are connected to a light cord that passes through a hole in the center of the smooth table. If the block is given a speed v = 9.1 m/s, determine the radius r of the circular path along which it travels.
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![The block B of mass 7.1 kg and cylinder A of mass 14.2 kg are connected to a light cord that
passes through a hole in the center of the smooth table. If the block is given a speed v = 9.1
m/s, determine the radius r of the circular path along which it travels.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac88ceb3-c3f8-479a-871e-300ef42f6b1c%2F53ee50ff-8abb-45bc-b62d-e6893f820ca6%2Fisfybm6_processed.jpeg&w=3840&q=75)
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- A rocket, launched from the Earth, shuts off its engines when its speed is 5.10 km/s. It reaches a maximum altitude of 2600 km before it falls back to Earth. At what altitude did the rocket's engines shut off? The mass and radius of the Earth are 5.97 1024 kg and 6.37 106 m, respectively. kmIn 2014, the Rosetta space probe reached the comet Churyumov– Gerasimenko. Although the comet’s core is actually far from spherical, in this problem we’ll model it as a sphere with a mass of 1.0 x 1013 kg and a radius of 1.6 km. If a rock were dropped from a height of 1.0 m above the comet’s surface, how long would it take to hit the surface?A rotating star collapses under the influence of gravitational forces to form a pulsar. The radius of the pulsar is 5.00 × 10−4 times the radius of the star before collapse. There is no change in mass. In both cases, the mass of the star is uniformly distributed in a spherical shape. If the period of the star’s rotation before collapse is 4.00 × 104 s, what is its period after collapse?
- I whirl John (mass 0.27 kg) over my head in a circle. There is a spring scale between my hand and the string, so I can measure the force of tension in the string, which I find to be 2.12 N. I measure the length of the string (the radius of the circle) and find it to be 1.34 m. Assuming that John's speed is not changing, how fast is he going?A puck of mass m = 1.30 kg slides in a circle of radius r = 22.0 cm on a frictionless table while attached to a hanging cylinder of mass M= 2.30 kg by a cord through a hole in the table. What speed keeps the cylinder at rest? M Number i 2.227 Units m/sA bead of mass m slides without friction along a curved wire with shape z = f(r) where r = Vr2 + y², i.e. the distance from the z-axis. The wire is rotated around the z-axis at a constant angular velocity w. Gravity acts downward along the z-axis with a constant acceleration g. a) Using Newton's second law in an inertial frame, derive an expression for radius ro of a fixed circular orbit (i.e. a solution with r = ro = const.). What is the normal force the wire applies to the bead to keep it in a circular orbit? b) Show that the equation of motion for r(t) (general equation not the circular motion) is F(1 + f'(r)²) + i² f'(r)f"(r) + gf'(r) – w?r = 0. Using this verify your answer to part (a). c) Consider small displacements from the circular orbit, r = ro+e(t). Derive a condition on the function f(r) such that a circular orbit at r = ro is stable. d) Find the force on the bead in the o direction, i.e. perpendicular to the plane of wire. The angular velocity is w = . Obtain the answer…
- The proton is traveling at a constant speed of 5.5 × 105 m/s, and the radius of the kissing circle is 0.02 m. The mass of a proton is 1.7 × 10-27 kg. When the proton is at location A, what are the magnitude and direction (d|p→|/dt)(p^) of the parallel component of dp→/dt?Planet X is a sphere where a 0.5 kg block weighs 36 N when sitting on the surface. If an object is dropped from rest at a distance 9R from X's center it is observed to impact the surface at a speed of 16,000 m/s. Find a value for the radius of planet X.A meteoroid is moving towards a planet. It has mass m = 0.54×109 kg and speed v1 = 4.7×107 m/s at distance R1 = 1.6×107 m from the center of the planet. The radius of the planet is R = 0.78×107 m. The mass of the planet is M = 5.6×1025kg. There is no air around the planet. a)Enter an expression for the total energy E of the meteoroid at R, the surface of the planet, in terms of defined quantities and v, the meteoroid’s speed when it reaches the planet’s surface. Select from the variables below to write your expression. Note that all variables may not be required.α, β, θ, d, g, G, h, m, M, P, R, R1, t, v, v1 b)Enter an expression for v, the meteoroid’s speed at the planet’s surface, in terms of G, M, v1, R1, and R. c)Calculate the value of v in meters per second.
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