A uniform metre rule of mass 90g is pivoted at the 40cm mark. If the rule is in equilibrum with an unknown mass, M placed at the 10cm mark and 72g mass at the 70cm mark, determine M.
Please help me urgently!!
sum moments about the piviot;
90(50-40)+72(70-40)+M(10-40)=0
solve for M
Please explain how and why bobpursley
To determine the unknown mass M, we can use the principle of moments, which states that the sum of clockwise moments about a pivot point is equal to the sum of anti-clockwise moments about the same point when an object is in equilibrium.
In this case, the metre rule is in equilibrium, so the sum of the clockwise moments is equal to the sum of the anti-clockwise moments.
Clockwise moments = Mass1 * Distance1
Anti-clockwise moments = Mass2 * Distance2 + Mass3 * Distance3
Given:
Mass1 = 90g (the metre rule itself)
Distance1 = Distance from the pivot to Mass1 = 40cm
Mass2 = 72g (the 72g mass)
Distance2 = Distance from the pivot to Mass2 = 70cm
Distance3 = Distance from the pivot to the unknown mass M = 10cm
Using the principle of moments, we can set up the equation:
Mass1 * Distance1 = Mass2 * Distance2 + Mass3 * Distance3
Substituting the given values:
90g * 40cm = 72g * 70cm + M * 10cm
To solve for M, we can rearrange the equation:
M * 10cm = (90g * 40cm) - (72g * 70cm)
M = [(90g * 40cm) - (72g * 70cm)] / 10cm
Now, let's calculate the value of M:
M = [(3600g∙cm) - (5040g∙cm)] / 10cm
M = (-1440g∙cm) / 10cm
M = -144g
From the calculations, we found that the value of M is -144g. However, a negative mass does not make physical sense. Therefore, there might be a mistake in the calculation or the given values. Please double-check the values and calculations to find the correct mass of M.