5. An experiment is performed in deep space with two uniform spheres, one with mass 26.0 kg and the other with mass 106.0 kg. They have equal radii, r = 0.25 m. The spheres are released from rest with their centers a distance 41.0 m apart. They accelerate toward each other because of their mutual gravitational attraction. You can ignore all gravitational forces other than that between the two spheres. (a) When their centers are a distance 28.0 m apart, find the speed of the 26.0 kg sphere. (b) Find the speed of the sphere with mass 106.0 kg. [(a) 1.13 x 10-5 m/s, (b)2.78x10-6 m/s]
5. An experiment is performed in deep space with two uniform spheres, one with mass 26.0 kg and the other with mass 106.0 kg. They have equal radii, r = 0.25 m. The spheres are released from rest with their centers a distance 41.0 m apart. They accelerate toward each other because of their mutual gravitational attraction. You can ignore all gravitational forces other than that between the two spheres. (a) When their centers are a distance 28.0 m apart, find the speed of the 26.0 kg sphere. (b) Find the speed of the sphere with mass 106.0 kg. [(a) 1.13 x 10-5 m/s, (b)2.78x10-6 m/s]
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Gravitational force
In nature, every object is attracted by every other object. This phenomenon is called gravity. The force associated with gravity is called gravitational force. The gravitational force is the weakest force that exists in nature. The gravitational force is always attractive.
Acceleration Due to Gravity
In fundamental physics, gravity or gravitational force is the universal attractive force acting between all the matters that exist or exhibit. It is the weakest known force. Therefore no internal changes in an object occurs due to this force. On the other hand, it has control over the trajectories of bodies in the solar system and in the universe due to its vast scope and universal action. The free fall of objects on Earth and the motions of celestial bodies, according to Newton, are both determined by the same force. It was Newton who put forward that the moon is held by a strong attractive force exerted by the Earth which makes it revolve in a straight line. He was sure that this force is similar to the downward force which Earth exerts on all the objects on it.
Question
PLEASE CNA YOU SOLVE NUMBER 5 SHOWING STEP BY STEP ON A PICTURE. JUST POST THE PICTURE OF YOUR WORK, PLEASE.
![1.
A hollow plastic sphere is held below the surface of a freshwater lake by a cord anchored to the bottom of the
lake. The sphere has a volume of 0.650 m³ and the tension in the cord is 900 N. (a) Calculate the buoyant force
exerted by the water on the sphere. (b) What is the mass of the sphere? (c) The cord breaks and the sphere rises
to the surface. When the sphere comes to rest, what fraction of its volume will be submerged? [(a) 6370 N, (b)
558 kg, (c) 85.9%]
2. The pipe shown carries water, and it is given that A₁ 2.0A2. The fluid
heights in the vertical tubes are h₁ = 1.20m and h₂ = 0.80 m. (a) Find
the ratio of the flow speeds 2. (b) Find the gauge pressures P₁ and P₂. (c)
Tube 1
Tube 2
V1
Find the flow speed v₁ in the pipe. [(a) 2.00, (b) 11.9kPa and 7.8kPa, (c)
1.6 m/s.
A₂
F
3. The point masses m and 2m lie along the x-axis, with m at the origin and
2m at x = L. A third point mass M is moved along the x-axis. At what
point is the net gravitational force on M due to the other two masses
equal to zero? [x=0.414L]
4. The planet Uranus has a radius of 25,360 km and a surface acceleration due to gravity of 9.0 m/s² at its poles. Its
moon Miranda (discovered by Kuiper in 1948) is in a circular orbit about Uranus at an altitude of 104,000 km
above the planet's surface. Miranda has a mass of 6.6 x 10¹⁹ kg and a radius of 236 km. (a) Calculate the mass of
Uranus from the above data. (b) Calculate the magnitude of Miranda's acceleration due to its orbital motion
about Uranus. (c) Calculate the acceleration due to Miranda's gravity at the surface of Miranda. [(a) 8.7 x 10²5 kg,
(b) 0.35 m/s², (c) 0.079 m/s²]
5. An experiment is performed in deep space with two uniform spheres, one with mass 26.0 kg and the other with
mass 106.0 kg. They have equal radii, r = 0.25 m. The spheres are released from rest with their centers a
distance 41.0 m apart. They accelerate toward each other because of their mutual gravitational attraction. You
can ignore all gravitational forces other than that between the two spheres. (a) When their centers are a
distance 28.0 m apart, find the speed of the 26.0 kg sphere. (b) Find the speed of the sphere with mass 106.0 kg.
[(a) 1.13 x 10-5 m/s, (b)2.78x10-6 m/s]
6. A 0.250 kg toy is undergoing SHM on the end of a horizontal spring with force constant 300 N/m. When the toy
is 0.0160 m from its equilibrium position, it is observed to have a speed of 0.400 m/s. (a) What is the toy's total
energy at any point of its motion? (b) What is the toy's amplitude of the motion? (c)What is the toy's maximum
speed during its motion? [(a) 5.48 x 10-2 J, (b) 1.97 x 10-2 m, (c) 0.684 m/s]
7. A particle moves in simple harmonic motion according to x = 20cos(5t), where x is in centimeters and t is in
seconds. (a) What is the period? (b) What is the amplitude? (c) What is the maximum velocity? (d) At what value
of x does the maximum velocity occur? (e) What is the maximum acceleration? (f) At what value of x does the
maximum acceleration occur? (g) Write an equation for velocity as a function of time. [a) 1.26 sec, b) 0.2 m, c) 1
m/s, d) x = 0, e) 5 m/s², f) x = 0.20 m, g) v = -100sin(5t)]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0655393b-8df3-4633-b13c-e0d6983d2306%2Fdf43c8ac-9e94-4704-870d-0b16fb3027b9%2F9apcf8_processed.png&w=3840&q=75)
Transcribed Image Text:1.
A hollow plastic sphere is held below the surface of a freshwater lake by a cord anchored to the bottom of the
lake. The sphere has a volume of 0.650 m³ and the tension in the cord is 900 N. (a) Calculate the buoyant force
exerted by the water on the sphere. (b) What is the mass of the sphere? (c) The cord breaks and the sphere rises
to the surface. When the sphere comes to rest, what fraction of its volume will be submerged? [(a) 6370 N, (b)
558 kg, (c) 85.9%]
2. The pipe shown carries water, and it is given that A₁ 2.0A2. The fluid
heights in the vertical tubes are h₁ = 1.20m and h₂ = 0.80 m. (a) Find
the ratio of the flow speeds 2. (b) Find the gauge pressures P₁ and P₂. (c)
Tube 1
Tube 2
V1
Find the flow speed v₁ in the pipe. [(a) 2.00, (b) 11.9kPa and 7.8kPa, (c)
1.6 m/s.
A₂
F
3. The point masses m and 2m lie along the x-axis, with m at the origin and
2m at x = L. A third point mass M is moved along the x-axis. At what
point is the net gravitational force on M due to the other two masses
equal to zero? [x=0.414L]
4. The planet Uranus has a radius of 25,360 km and a surface acceleration due to gravity of 9.0 m/s² at its poles. Its
moon Miranda (discovered by Kuiper in 1948) is in a circular orbit about Uranus at an altitude of 104,000 km
above the planet's surface. Miranda has a mass of 6.6 x 10¹⁹ kg and a radius of 236 km. (a) Calculate the mass of
Uranus from the above data. (b) Calculate the magnitude of Miranda's acceleration due to its orbital motion
about Uranus. (c) Calculate the acceleration due to Miranda's gravity at the surface of Miranda. [(a) 8.7 x 10²5 kg,
(b) 0.35 m/s², (c) 0.079 m/s²]
5. An experiment is performed in deep space with two uniform spheres, one with mass 26.0 kg and the other with
mass 106.0 kg. They have equal radii, r = 0.25 m. The spheres are released from rest with their centers a
distance 41.0 m apart. They accelerate toward each other because of their mutual gravitational attraction. You
can ignore all gravitational forces other than that between the two spheres. (a) When their centers are a
distance 28.0 m apart, find the speed of the 26.0 kg sphere. (b) Find the speed of the sphere with mass 106.0 kg.
[(a) 1.13 x 10-5 m/s, (b)2.78x10-6 m/s]
6. A 0.250 kg toy is undergoing SHM on the end of a horizontal spring with force constant 300 N/m. When the toy
is 0.0160 m from its equilibrium position, it is observed to have a speed of 0.400 m/s. (a) What is the toy's total
energy at any point of its motion? (b) What is the toy's amplitude of the motion? (c)What is the toy's maximum
speed during its motion? [(a) 5.48 x 10-2 J, (b) 1.97 x 10-2 m, (c) 0.684 m/s]
7. A particle moves in simple harmonic motion according to x = 20cos(5t), where x is in centimeters and t is in
seconds. (a) What is the period? (b) What is the amplitude? (c) What is the maximum velocity? (d) At what value
of x does the maximum velocity occur? (e) What is the maximum acceleration? (f) At what value of x does the
maximum acceleration occur? (g) Write an equation for velocity as a function of time. [a) 1.26 sec, b) 0.2 m, c) 1
m/s, d) x = 0, e) 5 m/s², f) x = 0.20 m, g) v = -100sin(5t)]
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