Answer:
Furthermore, the Pythagorean theorem works when the two added vectors are at right angles to one another - such as for adding a north vector and an east vector.
Answer:
a = -7.29 m / s²
Explanation:
For this exercise we must use Newton's second law,
F -W = m a
Force is electrical force
F = k q₁ q₂ / r²
k q₁ q₂ / r² -mg = m a
indicate that the charge of the two spheres is equal
q₁ = q₂ = q
a = (k q² / r² - m g) / m
a = k q² / m r² - g
Let's reduce the magnitudes to the SI system
m = 0.19 g (1kg / 1000 g) = 1.9 10⁻⁴ kg
q1 = q2 = q = -23.0 nC (1C / 10⁹ nC) = -23.0 10⁻⁹ C
r = 10.0 cm (1m / 100cm) = 0.1000 m
let's calculate
a = 9 10⁹ (23.0 10⁻⁹)² / (0.1000² 1.9 10⁻⁴) - 9.8
a = -7.29 m / s²
The negative sign indicates that the direction of this acceleration is downward
Answer:
0.20kg-m^2
Explanation:
Let the linear velocity of the rope(=of pulley) is v m/s
Using kinematic equation
=> v = u + at
=>v = 0 + 4.9a
=>v = 4.9a ------------ eq1
By v^2 = u^2 + 2as
=>v^2 = 0 + 2 x v/4.9 x 1.2
=>4.9v^2 - 2.4v = 0
=>v(4.9v - 2.4) = 0
=>v = 2.4/4.9 = 0.49 m/s
Thus by v = r x omega
=>omega = v/r = 0.49/0.02 = 24.49 rad/sec
BY W = F x s = 50 x 1.2 = 60 J
=>KE(rotational) = W = 1/2 x I x omega^2
=>60 = 1/2 x I x (24.49)^2
=>I = 0.20 kg-m^2
Speed = (acceleration) x (time)
Velocity = (speed) in (direction of the speed)
Speed = (-3 m/s²) x (5 s) = 15 m/s
Velocity =
(15 m/s) in the direction opposite to the direction you call positive.
Displacement = (distance between start-point and end-point)
in the direction from start-point to end-point.
Distance = (1/2) (acceleration) (time)²
Distance = (1/2) (3 m/s²) (5 s)²
= (1/2) (3 m/s²) (25 s²) = 37.5 meters
Displacement =
37.5 meters in the direction opposite to the direction you call positive.
