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Question 1 (10 marks) (a) (4 marks) Recall that the gravitational potential energy for two masses...
Problem 4 In 1933 Fritz Zwiky used the virial theorem to demonstrate the existence of dark...
Problem 4 In 1933 Fritz Zwiky used the virial theorem to demonstrate the existence of dark matter (even though nobody believed him for the subsequent 40 years) in the Coma cluster of galaxies. The demonstration assumes that the Coma galaxies have a random spherical distribution around the center of gravity of the cluster, and that their velocity is also distributed randomly. With these hypothesis the average potential energy of the cluster can be approximated with the potential energy of a...
cosmology (1) 1. (10 points] In a simple model for a spherically symmetric dark matter halo,...
cosmology
(1) 1. (10 points] In a simple model for a spherically symmetric dark matter halo, the dark matter density is given by M PDM = 4ar, where M, is the enclosed mass at the virial radius r. Let v(r) be the velocity of a dark matter particle that is executing a circular orbit in the halo with radius r centered at r=0. Show that v(r) is independent of radius and obtain its value in terms of M, and ty....
2. The potential energy of two masses, m, and m, separated by a distance r is...
2. The potential energy of two masses, m, and m, separated by a distance r is given by: Gm.my VO) --- G 6.67X10" J m ka? Suppose a particle of mass m has a velocity v perpendicular to the earth's surface. Show that the minimum velocity that the particle must have in order to escape the earths surface 2GM. von Roth Then, considering that Mon = 5.98x1024 kg and Ron = 6.36x10m is its mean radius, calculate the escape velocity...
4. The equation mgy for gravitational potential energy is valid only for objects near the surface...
4. The equation mgy for gravitational potential energy is valid only for objects near the surface of a planet. Consider two very large objects of mass m1 and m2, such as stars or planets, whose centers are separated by the large distance r. These two large objects exert gravitational forces on each other.The gravitational potential energy is U = − Gm1m2 r where G = 6.67 × 10−11Nm2/kg2 is the gravitational constant. (a) Sketch a graph of U versus r....
Parallel Axis Theorem: I = ICM + Md Kinetic Energy: K = 2m202 Gravitational Potential Energy:...
Parallel Axis Theorem: I = ICM + Md Kinetic Energy: K = 2m202 Gravitational Potential Energy: AU = mgay Conservation of Mechanical Energy: 2 mv2 + u = žmo+ U Rotational Work: W = TO Rotational Power: P = TO Are Length (angle in radians, where 360º = 2a radians): S = re = wt (in general, not limited to constant acceleration) Tangential & angular speeds: V = ro Frequency & Period: Work-Energy Theorem (rotational): Weet = {102 - 10...
Question 2 (10 marks) Gears A and B have a mass of 4 kg and a...
Question 2 (10 marks) Gears A and B have a mass of 4 kg and a radius of gyration (k) of 300 mm, and ae 2017-2018 m, and are which has a mass of 15 kg and a radius of gyration (k of 0.5 m. A motor is attache both meshea switched on while the system is initially at rest and provides a constant moment oed so gear c a) Determine the # of revolutions of gear C before it...
Please use the formulate sheet and show all steps to make sure the question is worth...
Please use the formulate sheet and show all steps to make sure
the question is worth any points
a) The initial ratio of deuterium (D) to hydrogen (H) in a planet's atmosphere was 175000; however, the present ratio is 1/1500 and the initial and final abundances of D are 5 x 10° atoms per m3 and 9 x 106 atoms per m2, respectively. What fraction of deuterium has been lost, and what fraction of hydrogen has been lost in this...
PHYSICS: FINAL PAPER, August Entry Program 2009 Question 1 (5+10 marks) In a physics experiment, two...
PHYSICS: FINAL PAPER, August Entry Program 2009 Question 1 (5+10 marks) In a physics experiment, two masses m and M are connected together via some fric- tionless pulleys and massless wires. The larger mass M is released from rest. Assume that there is friction between the smaller mass and the surface of the slope. The system set-up is as shown in Figure 1. Figure 1: Question 1 (a) Draw all the forces acting on both the masses in separate free-body...
QUESTION 1 In pole vaulting, a jumper achieves great height by converting their kinetic energy of running in to gravita...
QUESTION 1
In pole vaulting, a jumper achieves great height by converting
their kinetic energy of running in to gravitational potential
energy. The pole plays an intermediary role in this process.
Suppose that a jumper runs at a speed of 9.1 m s-1, use a simple
model to estimate how far the jumper's centre of mass will rise.
(For reference only, a new world record was set in early 2014 of
6.16 m.)
QUESTION 2
A hoist system (see figure...
could you please solve a and b? Chapier 2i. Note: you needn't derive Kepler's laws-but do...
could you please solve a and b?
Chapier 2i. Note: you needn't derive Kepler's laws-but do mention when you are using them, an describe the physical concepts involved and the meanings behind the variables. u) Consider two stars Mi and M; bound together by their mutual gravitational force (and isolated from other forces) moving in elliptical orbits (of eccentricity e and semi-major axes ai and az) at distances 11 in n and r from their center of mass located at...
cosmology
(1) 1. (10 points] In a simple model for a spherically symmetric dark matter halo, the dark matter density is given by M PDM = 4ar, where M, is the enclosed mass at the virial radius r. Let v(r) be the velocity of a dark matter particle that is executing a circular orbit in the halo with radius r centered at r=0. Show that v(r) is independent of radius and obtain its value in terms of M, and ty....
2. The potential energy of two masses, m, and m, separated by a distance r is given by: Gm.my VO) --- G 6.67X10" J m ka? Suppose a particle of mass m has a velocity v perpendicular to the earth's surface. Show that the minimum velocity that the particle must have in order to escape the earths surface 2GM. von Roth Then, considering that Mon = 5.98x1024 kg and Ron = 6.36x10m is its mean radius, calculate the escape velocity...
Parallel Axis Theorem: I = ICM + Md Kinetic Energy: K = 2m202 Gravitational Potential Energy: AU = mgay Conservation of Mechanical Energy: 2 mv2 + u = žmo+ U Rotational Work: W = TO Rotational Power: P = TO Are Length (angle in radians, where 360º = 2a radians): S = re = wt (in general, not limited to constant acceleration) Tangential & angular speeds: V = ro Frequency & Period: Work-Energy Theorem (rotational): Weet = {102 - 10...
Question 2 (10 marks) Gears A and B have a mass of 4 kg and a radius of gyration (k) of 300 mm, and ae 2017-2018 m, and are which has a mass of 15 kg and a radius of gyration (k of 0.5 m. A motor is attache both meshea switched on while the system is initially at rest and provides a constant moment oed so gear c a) Determine the # of revolutions of gear C before it...
Please use the formulate sheet and show all steps to make sure
the question is worth any points
a) The initial ratio of deuterium (D) to hydrogen (H) in a planet's atmosphere was 175000; however, the present ratio is 1/1500 and the initial and final abundances of D are 5 x 10° atoms per m3 and 9 x 106 atoms per m2, respectively. What fraction of deuterium has been lost, and what fraction of hydrogen has been lost in this...
PHYSICS: FINAL PAPER, August Entry Program 2009 Question 1 (5+10 marks) In a physics experiment, two masses m and M are connected together via some fric- tionless pulleys and massless wires. The larger mass M is released from rest. Assume that there is friction between the smaller mass and the surface of the slope. The system set-up is as shown in Figure 1. Figure 1: Question 1 (a) Draw all the forces acting on both the masses in separate free-body...
QUESTION 1
In pole vaulting, a jumper achieves great height by converting
their kinetic energy of running in to gravitational potential
energy. The pole plays an intermediary role in this process.
Suppose that a jumper runs at a speed of 9.1 m s-1, use a simple
model to estimate how far the jumper's centre of mass will rise.
(For reference only, a new world record was set in early 2014 of
6.16 m.)
QUESTION 2
A hoist system (see figure...
could you please solve a and b?
Chapier 2i. Note: you needn't derive Kepler's laws-but do mention when you are using them, an describe the physical concepts involved and the meanings behind the variables. u) Consider two stars Mi and M; bound together by their mutual gravitational force (and isolated from other forces) moving in elliptical orbits (of eccentricity e and semi-major axes ai and az) at distances 11 in n and r from their center of mass located at...
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