Answer:
108.7 V
Explanation:
Two forces are acting on the particle:
- The external force, whose work is 
- The force of the electric field, whose work is equal to the change in electric potential energy of the charge: 
where
q is the charge
is the potential difference
The variation of kinetic energy of the charge is equal to the sum of the work done by the two forces:
and since the charge starts from rest, 
, so the formula becomes
In this problem, we have
is the work done by the external force
is the charge
is the final kinetic energy
Solving the formula for , we find
Answer:
Explanation:
The moment of inertia is the integral of the product of the squared distance by the mass differential. Is the mass equivalent in the rotational motion
a) True. When the moment of inertia is increased, more force is needed to reach acceleration, so it is more difficult to change the angular velocity that depends proportionally on the acceleration
b) True. The moment of inertia is part of the kinetic energy, which is composed of a linear and an angular part. Therefore, when applying the energy conservation theorem, the potential energy is transformed into kinetic energy, the rotational part increases with the moment of inertia, so there is less energy left for the linear part and consequently it falls slower
c) True. The moment of inertial proportional to the angular acceleration, when the acceleration decreases as well. Therefore, a smaller force can achieve the value of acceleration and the change in angular velocity. Consequently, less force is needed is easier
The two factors are mass and distance between them.
Weight of the child m = 50 kg
Radius of the merry -go-around r = 1.50 m
Angular speed w = 3.00 rad/s
(a)Child's centripetal acceleration will be a = w^2 x r = 3^2 x 1.50 => a = 9 x
1.5
Centripetal Acceleration a = 13.5m/sec^2
(b)The minimum force between her feet and the floor in circular path
Circular Path length C = 2 x 3.14 x 1.50 => c = 3 x 3.14 => C = 9.424
Time taken t = 2 x 3.14 / w => t = 6.28 / 3 => t = 2.09
Calculating velocity v = distance / time = 9.424 / 2.09 m/s => v = 4.5 m/s
Calculating force, from equation F x r = mv^2 => F = mv^2 / r => 50 x (4.5)^2
/ 1.5
F = 50 x 3 x 4.5 => F = 150 x 4.5 => F = 675 N
(c)Minimum coefficient of static friction u
F = u x m x g => u = F / m x g => u = 675/ 50 x 9.81 => 1.376
u = 1.376
Hence with the force and the friction coefficient she is likely to stay on merry-go-around.
