A balanced lever has two weights on it, the first with mass #8 kg # and the second with mass #24 kg#. If the first weight is # 2 m# from the fulcrum, how far is the second weight from the fulcrum?

1 Answer
Mar 20, 2016

Answer:

Since the lever is balanced, the sum of torques is equal to 0

Answer is:

#r_2=0.bar(66)m#

Explanation:

Since the lever is balanced, the sum of torques is equal to 0:

#Στ=0#

About the sign, obviously for the lever to be balanced if the first weight tends to rotate the object with a certain torque, the other weight will have opposite torque. Let the masses be:

#m_1=8kg#

#m_2=24kg#

#τ_(m_1)-τ_(m_2)=0#

#τ_(m_1)=τ_(m_2)#

#F_1*r_1=F_2*r_2#

#m_1*cancel(g)*r_1=m_2*cancel(g)*r_2#

#r_2=m_1/m_2*r_1#

#r_2=8/24*2# #cancel((kg)/(kg))*m#

#r_2=2/3 m# or #r_2=0.bar(66)m#