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3. Show that the kinetic energy of a two-particle system is given by 12 where mm...
I. Show that the angular momentum of a two-particle system is given by where m- mi...
I. Show that the angular momentum of a two-particle system is given by where m- mi + m2. v is the relative velocity (the velocity of one of the particles with respect to the other), is the relative position, and μ is the reduced mass. Q7- CM
Two particles are moving along the x axis. Particle 1 has a mass m1 and a...
Two particles are moving along the x axis. Particle 1 has a mass m1 and a velocity v1 = +4.5 m/s. Particle 2 has a mass m2 and a velocity v2 = -7.3 m/s. The velocity of the center of mass of these two particles is zero. In other words, the center of mass of the particles remains stationary, even though each particle is moving. Find the ratio m1/m2 of the masses of the particles.
3. (i) Find the kinetic energy of a particle of mass m with position given by...
3. (i) Find the kinetic energy of a particle of mass m with position given by the coordinates (s, u, v), related to the ordinary Cartesian coordinates by y z = 2s + 3 + u = 2u + v = 0+03 (ii) Find the kinetic energy of a particle of mass m whose position is given in cylindrical coordinates = = r cos r sine y (iii) Find the kinetic energy of a particle of mass m with position...
A system consists of two particles of mass mi and m2 interacting with an interaction potential...
A system consists of two particles of mass mi and m2 interacting with an interaction potential V(r) that depends only on the relative distancer- Iri-r2l between the particles, where r- (ri,/i,21) and r2 22,ひ2,22 are the coordinates of the two particles in three dimensions (3D) (a) /3 pointsl Show that for such an interaction potential, the Hamiltonian of the system H- am▽ri _ 2m2 ▽22 + V(r) can be, put in the form 2M where ▽ and ▽ are the...
Consider a system consisting of three particles: m1 = 5 kg, v1 = <11, -8, 12>m/s
Consider a system consisting of three particles: m1 = 5 kg, v1 = <11, -8, 12>m/s m2 = 2 kg, v2 = < -13, 4, -5 > m/s m3 = 2 kg, v2 = < -22, 38, 20 > m/s (a) What is the total momentum of this system? (b) What is the velocity of the center of mass of this system? (c) What is the total kinetic energy of this system? (d) What is the translational kinetic energy of this system? (e) What is the kinetic energy...
answer this question with steps: 3. In special relativity, the kinetic energy of a particle of...
answer this question with
steps:
3. In special relativity, the kinetic energy of a particle of mass m and velocity v is given byKE=yme-me, where γ = 1/ and c is the speed of light. (a) (2 points) Find the first three non-zero terms of the Taylor series expansion of γ, in the non-relativistic limit u/c 1. Hint: You can expand in either v/c orv/c2 (b) (1 point) What is the first non-zero term for the kinetic energy KE in...
Solve for v1 and v2 given conservation of kinetic energy Search this book n, in this...
Solve for v1 and v2 given conservation of kinetic
energy
Search this book n, in this case, reads Pi = Pf | M2V2,i = mjº18+ m2V2,f. ergy reads K; = K mavzi = {m101s+ mauz.s. lons in two unknowns. The algebra is tedious but not terribly difficult; you de (mi-m2)+1,i+2m2 U2, mi + m2 (m2-mi U2,+2m, V1, mi +m2 U2f numbers, we obtain V1,8 V2,1 = = 2.22 m -0.28 m
7. The kinetic energy, k, of a particle of mass m is given below, where the...
7. The kinetic energy, k, of a particle of mass m is given below, where the velocity, v, of the particle is constrained to [-1,1] Suppose that a particular particle is known to have mass m - 2 and that the probability that its velocity is in [a,b] is given below. Let K denote the random variable that characterizes the particle's kinetic energy. What is the probability that the kinetic energy is greater than one half? That is, find P[K...
Consider two masses sliding across a frictionless surface about to undergo a head-on collision as shown...
Consider two masses sliding across a frictionless surface about to undergo a head-on collision as shown in the figure. The first mass (m1 = 3 kg) is travelling to the right with a speed of V1 = 8 m/s. The speed of the second mass (m2 = 5 kg) is unknown. After the masses collide, m1 rebounds moving off at a speed of v = 2 m/s in the opposite direction, while m2 is motionless. a)(10 pts.) At what velocity,...
Given the formula of the kinetic energy of a particle m with speed v: KE =...
Given the formula of the kinetic energy of a particle m
with
speed v:
KE = 1⁄2mv2 ,
and the formula of the gravitational potential energy:
PE = -GMEm/R,
where G is gravitational constant and ME and R=6378 km are the
mass and the radius of Earth. Now the particle is shot from Earth
surface to space. Find the minimum required initial speed for this
particle to completely escape the influence of Earth gravity (i.e.
PE=0). Notice that the gravitational...
I. Show that the angular momentum of a two-particle system is given by where m- mi + m2. v is the relative velocity (the velocity of one of the particles with respect to the other), is the relative position, and μ is the reduced mass. Q7- CM
3. (i) Find the kinetic energy of a particle of mass m with position given by the coordinates (s, u, v), related to the ordinary Cartesian coordinates by y z = 2s + 3 + u = 2u + v = 0+03 (ii) Find the kinetic energy of a particle of mass m whose position is given in cylindrical coordinates = = r cos r sine y (iii) Find the kinetic energy of a particle of mass m with position...
A system consists of two particles of mass mi and m2 interacting with an interaction potential V(r) that depends only on the relative distancer- Iri-r2l between the particles, where r- (ri,/i,21) and r2 22,ひ2,22 are the coordinates of the two particles in three dimensions (3D) (a) /3 pointsl Show that for such an interaction potential, the Hamiltonian of the system H- am▽ri _ 2m2 ▽22 + V(r) can be, put in the form 2M where ▽ and ▽ are the...
answer this question with
steps:
3. In special relativity, the kinetic energy of a particle of mass m and velocity v is given byKE=yme-me, where γ = 1/ and c is the speed of light. (a) (2 points) Find the first three non-zero terms of the Taylor series expansion of γ, in the non-relativistic limit u/c 1. Hint: You can expand in either v/c orv/c2 (b) (1 point) What is the first non-zero term for the kinetic energy KE in...
Solve for v1 and v2 given conservation of kinetic
energy
Search this book n, in this case, reads Pi = Pf | M2V2,i = mjº18+ m2V2,f. ergy reads K; = K mavzi = {m101s+ mauz.s. lons in two unknowns. The algebra is tedious but not terribly difficult; you de (mi-m2)+1,i+2m2 U2, mi + m2 (m2-mi U2,+2m, V1, mi +m2 U2f numbers, we obtain V1,8 V2,1 = = 2.22 m -0.28 m
7. The kinetic energy, k, of a particle of mass m is given below, where the velocity, v, of the particle is constrained to [-1,1] Suppose that a particular particle is known to have mass m - 2 and that the probability that its velocity is in [a,b] is given below. Let K denote the random variable that characterizes the particle's kinetic energy. What is the probability that the kinetic energy is greater than one half? That is, find P[K...
Consider two masses sliding across a frictionless surface about to undergo a head-on collision as shown in the figure. The first mass (m1 = 3 kg) is travelling to the right with a speed of V1 = 8 m/s. The speed of the second mass (m2 = 5 kg) is unknown. After the masses collide, m1 rebounds moving off at a speed of v = 2 m/s in the opposite direction, while m2 is motionless. a)(10 pts.) At what velocity,...
Given the formula of the kinetic energy of a particle m
with
speed v:
KE = 1⁄2mv2 ,
and the formula of the gravitational potential energy:
PE = -GMEm/R,
where G is gravitational constant and ME and R=6378 km are the
mass and the radius of Earth. Now the particle is shot from Earth
surface to space. Find the minimum required initial speed for this
particle to completely escape the influence of Earth gravity (i.e.
PE=0). Notice that the gravitational...
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