A 5 kg ball and a 2 kg ball are placed at opposite ends of a massless beam so that the system is in equilibrium. What is the ratio of the length of the beam to the distance from the heavier ball to the pivot

L/x = 3.5 (The ratio of length of beam to the distance from heavier ball to pivot).

Explanation:

In order for the system to be in equilibrium, the moment created by both masses about the pivot point must be equal:

m₁x = m₂y

where,

m₁ = 5 kg

m₂ = 2 kg

x = distance of 5 kg ball from pivot

y = distance of 2 kg ball from pivot

Therefore,

(5 kg)x = (2 kg)y

y = (5kg/2kg)x

y = 2.5 x

but,

x + y = L

where,

L = length of beam

using the value of y from the previous equation:

x + 2.5 x = L

3.5 x = L

L/x = 3.5 (The ratio of length of beam to the distance from heavier ball to pivot).

the small 0.38-kg slider is known to move from position a to position b along the vertical-plane slot. determine (a) the work done on the body by its weight and (b) the work done on the body by the spring. the distance r = 0.70 m, the spring modulus k = 154 n/m, and the unstretched length of the spring is 0.53 m

explanation:

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