Two astronauts are playing catch in a zero gravitational field. Astronaut 1 of mass m1 is initially moving to the right with spe
1 answer:
The final velocity () of the first astronaut will be greater than the <em>final velocity</em> of the second astronaut (
) to ensure that the total initial momentum of both astronauts is equal to the total final momentum of both astronauts <em>after throwing the ball</em>.
The given parameters;
- Mass of the first astronaut, = m₁
- Mass of the second astronaut, = m₂
- Initial velocity of the first astronaut, = v₁
- Initial velocity of the second astronaut, = v₂ > v₁
- Mass of the ball, = m
- Speed of the ball, = u
- Final velocity of the first astronaut, =
- Final velocity of the second astronaut, =
The final velocity of the first astronaut relative to the second astronaut after throwing the ball is determined by applying the principle of conservation of linear momentum.
if v₂ > v₁, then , to conserve the linear momentum.
Thus, the final velocity () of the first astronaut will be greater than the <em>final velocity</em> of the second astronaut (
) to ensure that the total initial momentum of both astronauts is equal to the total final momentum of both astronauts after throwing the ball.
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Answer:
Part(a): The frequency is .
Part(b): The speed of the wave is .
Explanation:
Given:
The distance between the crests of the wave, .
The time required for the wave to laps against the pier,
The distance between any two crests of a wave is known as the wavelength of the wave. So the wavelength of the wave is .
Also, the time required for the wave for each laps is the time period of oscillation and it is given by .
Part(a):
The relation between the frequency and time period is given by
Substituting the value of in equation (1), we have
Part(b):
The relation between the velocity of a wave to its frequency is given by
Substituting the value of and
in equation (2), we have
Explanation:
It is given that,
The horizontal and vertical component of velocity of an electron is:
The magnetic field acting there is given by :
(a) The magnitude of the magnetic force on the electron is given by :
q = e
(b) We know that the charge on proton is :
The magnetic force as same as for electron but the direction is opposite i.e.
Hence, this is the required solution.
Complete question:
The 100-kg homogeneous cylindrical disk is at rest when the force F =500N is applied to a cord wrapped around it, causing the disk to roll. Use the principle of work and energy to determine the angular velocity of the disk when it has turned one revolution (radius of the disk = 300mm).
Answer:
The angular velocity of the disk when it has turned one revolution is 16.712 rad/s
Explanation:
From the principle of work and energy;
U = E₂ - E₁, since the disk is initially at rest, T₁ = 0
U = E₂
Work done, U = product of force and perpendicular distance
U = F × d
As the cord winds, force act through the cord at a distance of 2d
U = F × 2d
Distance of one complete revolution = 2πR = 2π(0.3) = 0.6π
U = 500 × 2(0.6π) = 1885.2 J
Kinetic energy E₂
Recall that U = E₂
1885.2 = 6.75ω²
ω² = 1885.2/6.75
ω² = 279.2889
ω = √279.2889
ω = 16.712 rad/s
Therefore, the angular velocity of the disk when it has turned one revolution is 16.712 rad/s