Problem 4: (use energy methods) When s = 0, the spring on the firing mechanism is unstretched. If the spring is pulled back to s
= 100mm and released. The mass of the ball is 0.3kg. Determine: 1. The speed of the ball as it leaves the spring and is about to start moving on the circular track. 2. The maximum angle θ the ball will travel without loosing contact with the circular track. Assume all contact surfaces to be s
1 answer:
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The magnitude of the friction force is 25 N
Explanation:
To solve this problem, we just have to analyze the forces acting on the block along the horizontal direction. We have:
- The horizontal component of the pulling force,
, where F = 50 N is the magnitude and
is the angle between the direction of the force and the horizontal; this force acts in the forward direction
- The force of friction,
, acting in the backward direction
According to Newton's second law, the net force acting on the block in the horizontal direction must be equal to the product between the mass of the block and its acceleration:
where
m is the mass of the block
is the horizontal acceleration
However, the block is moving at constant speed, so the acceleration is zero:
So the equation becomes
(1)
The net force here is given by
(2)
And so, by combining (1) and (2), we find the magnitude of the friction force:
Learn more about force of friction:
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Answer:
The position for mass is
Explanation:
Let x(t) donate the position of mass at time t,Then x satisfies the differential equation
The general solution is
It follows
thus the position of mass is