A balanced lever has two weights on it, the first with mass #3 kg # and the second with mass #4 kg#. If the first weight is # 8 m# from the fulcrum, how far is the second weight from the fulcrum?

Question

A balanced lever has two weights on it, the first with mass #3 kg # and the second with mass #4 kg#.  If the first weight is # 8 m# from the fulcrum, how far is the second weight from the fulcrum?

Adrian Ayala · Accepted Answer

6 m away from the fulcrum, opposite from the first weight.

For the lever to be "balanced", there must be no net torque on the system, or #tau_"net"=0# or #Sigma tau = 0# Assuming the fulcrum is at the center of mass of the lever (or the lever is massless), the torques created by each of the weights must be equal and opposite: #tau_1 + tau_2 = 0# #tau_1 = - tau_2# Torque is the force perpendicular to a point of rotation multiplied by the distance from that pivot point. Assuming the lever to be horizontal, the torque equation becomes: #F_1xxr_1 = -(F_2xxr_2)# #m_1gxxr_1=-(m_2gxxr_2)# Solving for #r_2# gives: #r_2=((m_1cancel(g))r_1)/(-m_2cancel(g))=-m_1/m_2r_1# Applying the given information, we get: #r_2=-(3"kg")/(4"kg")(8"m")=-6"m"# The fact that #r_2# is a negative value tells us that it is on the opposite side of the fulcrum from the first weight. The second weight must be positioned 6 m away from the fulcrum on the other side of the fulcrum.

Nora Arzate · Answer

undefined To find the distance of the second weight from the fulcrum, you can use the principle of moments. Moment = Force × Distance. Since the lever is balanced, the total clockwise moment equals the total anticlockwise moment. Let x be the distance of the second weight from the fulcrum. So, the moment of the first weight is 3 kg × 8 m, and the moment of the second weight is 4 kg × x. Setting these moments equal, we have 3 kg × 8 m = 4 kg × x. Solving for x, we get x = (3 kg × 8 m) / 4 kg = 6 m. Therefore, the second weight is 6 meters from the fulcrum.

Layla Ahmed · Answer

undefined The second weight, with a mass of 4 kg, is 6 meters away from the fulcrum.