Three smooth balls of iron of mass m and radius R are placed inside a tube of diameter 3R (see Figure). Find the magnitude of the forces (A, B, C and D) exerted by the sides of the container on each ball. Write your answers in terms of m, g and R.
A=
B=
C=
D=
A = 3*m*g
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c=3*m*g/sqrt(3)
d=(m*g)/sqrt(3)
B=2*(m*g)/sqrt(3)
To find the magnitude of the forces exerted by the sides of the container on each ball, we need to consider the forces acting on each ball individually.
Let's start with force A exerted by the side of the container on the top ball.
Force A is equal to the weight of the ball, which is given by the mass of the ball multiplied by the acceleration due to gravity (g). The mass of the ball is given as "m". Therefore, force A can be written as A = m * g.
Next, let's calculate force B exerted on the middle ball.
For the middle ball, it experiences two forces - the force exerted by the top ball and the force exerted by the bottom ball. Since all three balls are in contact and at rest, the forces between them are equal in magnitude and opposite in direction.
The force exerted by the bottom ball on the middle ball is equal to its weight, which is given by the mass of the bottom ball (m) multiplied by g. So, force C is equal to C = m * g.
Similarly, the force exerted by the top ball on the middle ball is also equal to its weight, which is given by the mass of the top ball (m) multiplied by g. So, force B = m * g.
Lastly, let's find the force exerted on the bottom ball, force D.
For the bottom ball, it only experiences the force exerted by the middle ball. This force is equal in magnitude and opposite in direction to force C. Therefore, force D = -C = -m * g.
To summarize:
A = m * g
B = m * g
C = m * g
D = -m * g
So, the magnitude of forces A, B, C, and D exerted by the sides of the container on each ball is equal to m * g, where m is the mass of the ball and g is the acceleration due to gravity.