SPH4U/SPH3UW Unit 2.3 Applying Newton s Law of Motion Page 1 of 7. Notes

Transcription

1 SPH4U/SPH3UW Unit.3 Appling Newton Law of Motion Page 1 of 7 Note Phic Tool Bo Solving Newton Law of Motion Proble o Read quetion to enure full undertanding o Draw and label a ree Bod Diagra o Separate each BD for each object a required o Calculate and Label the and coponent of each force o Write up the a and/or a for each group o Solve above equation eparatel o Check validit of our olution Tpe of Quetion o Static quetion, object eerting a force but not oving Object hanging fro rope o Kinetic quetion Object being pulled or puhed acro floor Gravit oving object down hill Hanging Weight Inclined Plane Eaple A gnat hang onto to eparate ring, attached to the ceiling b rope. If the peron i hanging otionle and each angle i 85, deterine the tenion in each rope if the gnat ha a a of 80kg. 80

2 SPH4U/SPH3UW Unit.3 Appling Newton Law of Motion Page of 7 We are given: 80 kg, g 9.8, 85, net 0,? T co co 85 in 85 in 85 Let u up force in the direction net co 85 1co 85 0 co85 1co85 But co 85 co Let u up the force in the direction net 1in85 in85 80kg 9.8 in T N but 0, therefore net in N T T 784N in N Therefore, the tenion in each rope i 390N Eaple ignificant digit A car engine with weight w hang fro a chain that i linked at ring O to two other chain, one fatened to the ceiling and the other to the wall. ind the tenion in each of the three chain, auing that w i the given weight and the ring and chain have no ignificant weight.

3 SPH4U/SPH3UW Unit.3 Appling Newton Law of Motion Page 3 of 7 Note: thi quetion i abtract, we do not know the actual weight of the engine. Note: becaue of the ring, the lanted chain do not eert force on the engine itelf, o we will have to eparate the force on the ring fro the force on the engine. Diagra b) repreent the BD for the engine, while c) the BD for the ring. 1 0 therefore T1 The force acting on the engine: T w Let calculate the force on the ring T co 60 T 0 3 T in 60 T 0 Since T w, we can rewrite the -direction a w T in 60 0 Now for w T3 in 60 T : T T3co 60 w co w Therefore T1 w T 0.577w T 1.155w w w

4 SPH4U/SPH3UW Unit.3 Appling Newton Law of Motion Page 4 of 7 Eaple A toboggan loaded with children lide down a now covered lope. The cobined a of the children and toboggan i 100kg. The angle of the hill i 30. What i the acceleration of the toboggan? w g 100kg N Let the weight The noral force ha onl a -coponent, but the a ha both an and coponent: Therefore w win 30 w wco 30. and The acceleration i purel in the + direction, o a 0. Then fro Newton Second Law we know win a a win g in 9.8 in n wco a 0 Note: we did not need the coponent to find the acceleration, which alo did not require the a of the object.

5 SPH4U/SPH3UW Unit.3 Appling Newton Law of Motion Page 5 of 7 Eaple: A ball of a 1 =0kg and a block of a 50kg are attached b a lightweight cord that pae over a frictionle pulle of negligible a. The block lie on a frictionle incline of angle 30. ind the agnitude of the acceleration of the two object and the tenion in the cord. Let draw free bod diagra for the two ae. We will attack thi proble b recogniing that the Tenion T in each free bod diagra will be the link that tie the two ae together. So we will let the algebra of Newton Law take u to the olution.

6 SPH4U/SPH3UW Unit.3 Appling Newton Law of Motion Page 6 of 7 Let look at Newton Law when applied to a 1 where we will decide that acceleration upward i poitive. a 1 g a 1 Tenion 1 Let look at Newton Law when applied to a where acceleration down i poitive baed on the connected oveent of the ae (up for hanging a and down for a on incline). ' 1 ' g in a Tenion a ' Now ince the ae are connected, the acceleration are the ae. Thi allow u to olve for the acceleration b adding the two equation (thi cancel the tenion force). g in a (1) Tenion 1g Tenion 1a () g in g a a g in a 1 1 g in g a N N in kg kg 50kg 0kg kg kg 49N 70kg 0.7 g We need onl plug in the acceleration into either of the equation and olve for the Tenion g a Therefore the acceleration i Tenion 1 a g Tenion 1 1 N N Tenion 0kg 0.7 0kg 9.8 kg kg 10N and the tenion in the rope i 10N.

7 SPH4U/SPH3UW Unit.3 Appling Newton Law of Motion Page 7 of 7 Etra Note and Coent