Answer:
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Explanation:
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Answer: 109.89 Nm
Explanation:
The maximum torque will be calculated as the force multiplied by the perpendicular distance. This will be:
Torque = force × perpendicular distance
torque = 333 × 0.33
= 109.89 Nm
Answer:
x(t) = 0.077cos(6.455t)
Explanation:
If the spring can be stretched 0.2 m by a force of 50 N, then the spring constant is:
k = 50 / 0.2 = 250 N/m
The equation of simple harmonic motion is as the following:
where 
We also know that the initial velocity is 0.5 m/s, which is also the maximum speed at the equilibrium:
is the initial phase
Therefore, the position of the mass after t seconds is
x(t) = 0.077cos(6.455t)
Explanation:
The object is moving along the parabola y = x² and is at the point (√2, 2). Because the object is changing directions, it has a centripetal acceleration towards the center of the circle of curvature.
First, we need to find the radius of curvature. This is given by the equation:
R = [1 + (y')²]^(³/₂) / |y"|
y' = 2x and y" = 2:
R = [1 + (2x)²]^(³/₂) / |2|
R = (1 + 4x²)^(³/₂) / 2
At x = √2:
R = (1 + 4(√2)²)^(³/₂) / 2
R = (9)^(³/₂) / 2
R = 27 / 2
R = 13.5
So the centripetal force is:
F = m v² / r
F = m (5)² / 13.5
F = 1.85 m
