Why is the following situation impossible? Two identical dust particles of mass 1.00 µg are floating in empty space, far from an
1 answer:
Answer:
This is a conceptual problem so I will try my best to explain the impossible scenario. First of all the two dust particles ara virtually exempt from any external forces and at rest with respect to each other. This could theoretically happen even if it's difficult for that to happen. The problem is that each of the particles have an electric charge which are equal in magnitude and sign. Thus each particle should feel the presence of the other via a force. The forces felt by the particles are equal and opposite facing away from each other so both charges have a net acceleration according to Newton's second law because of the presence of a force in each particle:
Having seen Newton's second law it should be clear that the particles are actually moving away from each other and will not remain at rest with respect to each other. This is in contradiction with the last statement in the problem.
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A) Zero
The motion of the shot is a projectile's motion: this means that there is only one force acting on the projectile, which is gravity. However, gravity only acts in the vertical direction: so, there are no forces acting in the horizontal direction. Therefore, the x-component of the acceleration is zero.
B) -9.8 m/s^2
The vertical acceleration is given by the only force acting in the vertical direction, which is gravity:
where m is the projectile's mass and g is the gravitational acceleration. Therefore, the y-component of the shot's acceleration is equal to the acceleration due to gravity:
where the negative sign means it points downward.
C) 7.6 m/s
The x-component of the shot's velocity is given by:
where
is the initial velocity
is the angle of the shot
Substituting into the equation, we find
D) 9.3 m/s
The y-component of the shot's velocity is given by:
where
is the initial velocity
is the angle of the shot
Substituting into the equation, we find
E) 7.6 m/s
We said at point A) that the acceleration along the x-direction is zero: therefore, the velocity along the x-direction does not change, so the x-component of the velocity at the end of the trajectory is equal to the x-velocity at the beginning:
F) -11.1 m/s
The y-component of the velocity at time t is given by:
where
is the initial y-velocity
a = g = -9.8 m/s^2 is the vertical acceleration
t is the time
Since the total time of the motion is t=2.08 s, we can substitute this value into the equation, and we find:
where the negative sign means the vertical velocity is now downward.
Answer:
14160 kg/m^3
Explanation:
First of all, we need to find the volume of the cylinder.
The volume of the cylinder is given by:
where:
is the radius
is the height
Substituting, we find
And the density is given by
where m = 1 kg is the mass. Substituting, we find