A charged particle moves at 2.5 × 104 m/s at an angle of 25° to a magnetic field that has a field strength of 8.1 × 10–2 T. If t
2 answers:
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(a) +2.60 m/s
The motion of the fish dropped by the seagul is a projectile motion, which consists of two independent motions:
- a horizontal uniform motion, at constant speed
- a vertical motion, at constant acceleration (acceleration of gravity, , downward)
In this part we are only interested in the horizontal motion. As we said the horizontal component of the fish's velocity does not change, therefore its value when the fish reaches the ocean is equal to its initial value, which is the speed at which the seagull was flying (because it was flying horizontally):
(b) -17.2 m/s
The vertical component of the fish's velocity instead follows the equation:
where
is the initial vertical velocity, which is zero
is the acceleration of gravity
t is the time
Since the fish reaches the ocean at t = 1.75 s, we can substitute this time into the formula to find the final vertical velocity:
where the negative sign indicates the direction (downward).
(c)
The horizontal component of the fish's velocity would increase
The vertical component of the fish's velocity would stay the same.
As we said from part (a) and (b):
- The horizontal component of the fish's velocity is constant during the motion and it is equal to the initial velocity of the seagull -> so if the seagull's initial speed increases, the horizontal velocity of the fish will increase too
- The vertical component of the fish's velocity does not depend on the original speed of the seagull, therefore it is not affected.
(a) The force exerted by the electric field on the plastic sphere is equal to
where
is the charge of the sphere and E is the strength of the electric field. This force should balance the weight of the sphere:
where m is the mass of the sphere and g is the gravitational acceleration.
Since the two forces must be equal, we have:
and so we find the intensity of the electric field
(b) Now let's find the direction of the field. The electric force must balance the weight of the sphere, which is directed downward, so the electric force should be directed upward. Since the charge is negative, the force is opposite to the electric field direction, and so the direction of the electric field is downward.
where
where m is the mass of the sphere and g is the gravitational acceleration.
Since the two forces must be equal, we have:
and so we find the intensity of the electric field
(b) Now let's find the direction of the field. The electric force must balance the weight of the sphere, which is directed downward, so the electric force should be directed upward. Since the charge is negative, the force is opposite to the electric field direction, and so the direction of the electric field is downward.