A 0.5 kg ball moves in a circle that is 0.4 m in radius at a speed of 4.0 m/s. Calculate the centripetal force exerted on the ba
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1 answer:
M = 0.5 kg, the mass of the ball
r = 0.4 m. the radius from the center of the circle to the ball
v = 4.0 m/s, the tangential velocity of the ball as the ball rotates
counterclockwise about the center of the circle.
Refer to the diagram shown below.
By definition, the centripetal acceleration of the ball is
a = v²/r = (4 m/s)²/(0.4 m) = 40 m/s²
The centripetal force exerted on the ball is
F = m*a = (0.5 kg)*(40 m/s²) = 20 N
Answer: 20 N
r = 0.4 m. the radius from the center of the circle to the ball
v = 4.0 m/s, the tangential velocity of the ball as the ball rotates
counterclockwise about the center of the circle.
Refer to the diagram shown below.
By definition, the centripetal acceleration of the ball is
a = v²/r = (4 m/s)²/(0.4 m) = 40 m/s²
The centripetal force exerted on the ball is
F = m*a = (0.5 kg)*(40 m/s²) = 20 N
Answer: 20 N
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Question:
A particle moving along the x-axis has a position given by x=(24t - 2.0t³)m, where t is measured in s. What is the magnitude of the acceleration of the particle at the instant when its velocity is zero
Answer:
24 m/s
Explanation:
Given:
x=(24t - 2.0t³)m
First find velocity function v(t):
v(t) = ẋ(t) = 24 - 2*3t²
v(t) = ẋ(t) = 24 - 6t²
Find the acceleration function a(t):
a(t) = Ẍ(t) = V(t) = -6*2t
a(t) = Ẍ(t) = V(t) = -12t
At acceleration = 0, take time as T in velocity function.
0 =v(T) = 24 - 6T²
Solve for T
Substitute -2 for t in acceleration function:
a(t) = a(T) = a(-2) = -12(-2) = 24 m/s
Acceleration = 24m/s
Answer:
Reactance
Explanation:
In an AC circuit, the capacitive reactance of a capacitor is given by:
where
f is the frequency of the AC current
C is the capacitance of the capacitor
The reactance of the capacitor tells somehow the "resistance" of the capacitor to the passage of current through it. In fact:
- When the frequency of the AC current is zero (this means, we are in regime of DC current), the reactance becomes infinite, and this is true because the capacitor does not let the current pass through it)
- When the frequency of the AC current tends to infinite, the reactance becomes zero, and this is true because in this case the current changes direction so fast that the capacitor has not enough time to "block" the current, so the current almost no feels the presence of the capacitor.