What is an object doing at the moment its instantaneous acceleration is zero?
1 answer:
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Answer:
μsmín = 0.1
Explanation:
- There are three external forces acting on the riders, two in the vertical direction that oppose each other, the force due to gravity (which we call weight) and the friction force.
- This friction force has a maximum value, that can be written as follows:
where μs is the coefficient of static friction, and Fn is the normal force,
perpendicular to the wall and aiming to the center of rotation.
- This force is the only force acting in the horizontal direction, but, at the same time, is the force that keeps the riders rotating, which is the centripetal force.
- This force has the following general expression:
where ω is the angular velocity of the riders, and r the distance to the
center of rotation (the radius of the circle), and m the mass of the
riders.
Since Fc is actually Fn, we can replace the right side of (2) in (1), as
follows:
- When the riders are on the verge of sliding down, this force must be equal to the weight Fg, so we can write the following equation:
- (The coefficient of static friction is the minimum possible, due to any value less than it would cause the riders to slide down)
- Cancelling the masses on both sides of (4), we get:
- Prior to solve (5) we need to convert ω from rev/min to rad/sec, as follows:
- Replacing by the givens in (5), we can solve for μsmín, as follows:
Answer:
The maximum length during the motion is
Explanation:
From the question we are told that
The mass is
The vertical spring length is
The unstretched length is
The initial speed is
The new length of the spring
The spring constant k is mathematically represented as
Where F is the force applied
y is the difference in weight which is
The negative sign is because the displacement of the spring (i.e its extension occurs against the force F)
Now substituting values accordingly
The elastic potential energy is given as
where D is this the is the displacement
Since Energy is conserved the total elastic potential energy would be
Substituting value accordingly
So to obtain total length we would add the unstretched length
So we have