Answer:
t=1.87s
b. 9.74
Explanation:
First to find time set an equation for angular velocity:
Now to find the angle:
F_P + F_Q = M g
F_P = M g - F_Q
Torque, or moment of force:
∑ M_P = 0
∑ M_P = M g L - F_Q · 3 L
0 = M g L - 3 F_Q L / : L
0 = M g - 3 F_Q
3 F_Q = M g
F_Q = M g /3
Finally:
F_P = M g - M g/3
F_P = 4 M g / 3
Explanation:
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Answer: His acceleration is -18.66m/s^2
Explanation:
Ok, the initial speed is 2.8m/s. (we can define the initial direction as the positive direction).
And he wants to stop, so he must accelerate in the opposite direction as the initial movement, then we would have:
a(t) = -A.
So we have a constant, and negative acceleration.
Now, if we want to find the velocity we must integrate over time, and we will get:
v(t) = -A*t + V0
where V0 is the initial velocity, we know that it is 2.8m/s, and t is the time in seconds.
Then the velocity is:
v(t) = -A*t + 2.8m/s.
Now we know that John is brought to rest in 0.15 seconds after he starts slowing down, this means that at t = 0.15 seconds, his velocity is equal to zero.
v(0.15s) = 0m/s = -A*0.15s + 2.8m/s
2.8m/s = A*0.15s
2.8m/s/0.15s = 18.66m/s^2 = A.
So his acceleration is -A, then we have that:
His acceleration is -18.66m/s^2
The answer is 523.60 rounded. To get this use the formula: V=4/3 • π • r^3 = 4/3·π·(53) ≈ 523.59878. Which is four over three, multiplied by “pie” multiplied by the radius cubed. (Which is 5 • 5 • 5). To get the radius, you split the diameter in half. For you equation, “1/2 of ten is five” so the radius is five. Hope this helps!