Lecture 17. Act 1 Statics A 1kg ball is hung at the end of a rod 1m long. The system balances at a point on the rod 0. 25m from the end holding the mass What is the mass of the rod (a)0.5kg )1Kg (c)2 kg 1m 1kg Physics 121: Lecture 17, Pg 11
Physics 121: Lecture 17, Pg 11 Lecture 17, Act 1 Statics A 1kg ball is hung at the end of a rod 1m long. The system balances at a point on the rod 0.25m from the end holding the mass. What is the mass of the rod ? (a) 0.5 kg (b) 1 kg (c) 2 kg 1kg 1m
Example Problem: Hanging Lamp Your folks are making you help out on fixing up your house They have always been worried that the walk around back is just too dark, so they want to hang a lamp. You go to the hardware store and try to put together a decorative light fixture. At the store you find a bunch of massless string (kind of a surprising find? ) a lamp of mass 2 kg, a plank of mass 1 kg and length 2 m, and a hinge to hold the plank to the wall. Your design is for the lamp to hang off one end of the plank and the other to be held to a wall by a hinge. The lamp end is supported by a massless string that makes an angle of300 with the plank. (The hinge supplies a force to string and the hinge be for this design to work?ust the hold the end of the plank in place. How strong Physics 121: Lecture 17, Pg 12
Physics 121: Lecture 17, Pg 12 Example Problem: Hanging Lamp Your folks are making you help out on fixing up your house. They have always been worried that the walk around back is just too dark, so they want to hang a lamp. You go to the hardware store and try to put together a decorative light fixture. At the store you find a bunch of massless string (kind of a surprising find?), a lamp of mass 2 kg, a plank of mass 1 kg and length 2 m, and a hinge to hold the plank to the wall. Your design is for the lamp to hang off one end of the plank and the other to be held to a wall by a hinge. The lamp end is supported by a massless string that makes an angle of 30o with the plank. (The hinge supplies a force to hold the end of the plank in place.) How strong must the string and the hinge be for this design to work ?
Example: Hanging Lamp 1. You need to solve for the forces on the string and the hinge Use statics equations m hinge L M Physics 121: Lecture 17, Pg 13
Physics 121: Lecture 17, Pg 13 Example: Hanging Lamp 1. You need to solve for the forces on the string and the hinge Use statics equations. hinge M m L
Example: Hanging Lamp 2. You need to solve for t and components of F UseΣF= O in x and y Use∑τ=oinz. T m L2→+L2 mg Physics 121: Lecture 17, Pg 14
Physics 121: Lecture 17, Pg 14 Example: Hanging Lamp 2. You need to solve for T and components of FH. Use SF = 0 in x and y. Use S = 0 in z. m T FH y Mg mg L/2 L/2 FHx
Hanging Lamp. 3. First use the fact that >F=0 in both x and y directions y xy Tcosφ 0 T sin Fy-Mg-mg=0 Now uset=0 in the z direction If we choose the rotation axis to be through the hinge then the hinge forces F and f will not enter into the torque equation L2 L2 LMg+mg-LTsind=0 M mg Physics 121: Lecture 17, Pg 15
Physics 121: Lecture 17, Pg 15 Hanging Lamp... 3. First use the fact that in both x and y directions: M m L/2 Fx Fy T L/2 Mg mg y x F = 0 x: T cos - Fx = 0 y: T sin + Fy - Mg - mg = 0 Now use = 0 in the z direction. If we choose the rotation axis to be through the hinge then the hinge forces Fx and Fy will not enter into the torque equation: mg - LTsin 0 2 L LMg + =