Application of Newton s Laws. F fr
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1 Application of ewton Law. A hocey puc on a frozen pond i given an initial peed of 0.0/. It lide 5 before coing to ret. Deterine the coefficient of inetic friction ( μ between the puc and ice. The total force acting on the puc i + + g a ( fr a ( x fr x g 0 (3 y fr Solution ro (3, g. The μg μg a a μ g (4 μ μg Subtituting thi in (, we get fr Before we can find μ, we need to find a. x xi + vixt + a xt (4 By replacing acceleration with Eq. (4, we get Δ x x f xi vixt μ gt (5 And fro velocity to acceleration relationhip, we obtain tie, t, a v 0 v μ gt f i v (6 i t μ g Replacing t in Eq. (5 with Eq. (6 and uing the total ditance the puc traveled before topping, one get vi vi vi 5 μ g μ g μ g 400 μ Two bloc are in contact on a frictionle urface. A horizontal force i applied to the larger bloc, a hown below.
2 a. If,, and bloc..3 g. g 3., find the noral force between the two b. ind the noral force between the bloc if the ae force i applied to. a. or a a ( or a a ( (+ ( give ( + a + a.i (3.0 b. Interchange and.3i ind the acceleration of the yte and the tenion in the tring. M Aue that the urface i frictionle and the pulley
3 and tring are ale. a. ree body diagra T T Mg g Becaue the cord length i fixed, a a a. Alo, the pulley i ale and frictionle. Thu, T T T. Uing ewton econd law T Ma g T a ( ( Add ( and ( g ( M + a a M + g T Mg M + 4. A all bloc lide on an inclined plane. ind the acceleration of the bloc if a. the urface i frictionle b. the urface i rough, with a coefficient of liding friction μ. g θ
4 P BB a. The force that act on the bloc are the weight g and the noral force. We elect the coordinate yte, a hown in the figure below. y f g co θ θ g g in θ θ x Becaue f 0, by ewton econd law, + g a. y: y g y -g co θ a y 0 - g co θ 0 g co θ x: x 0 g x g inθ a x a g inθ a a g inθ b. By ewton econd law, + g+ f a. y: y fy 0 g y -g co θ a y 0 - g co θ 0 g co θ ( x: x 0 fx - f g x g inθ a x a g inθ - f. a f μ. ro ( g co θ. Thu, f μ g coθ. g inθ - μ g coθ a a g inθ - μ g coθ 5. Two bloc are connected by a tring, a hown in the figure. The yte i in equilibriu. The inclined plane ae an angle of 4 o. Auing that the plane i frictionle, what i the a of the hanging bloc? 6.7 g 4P o
5 The free-body diagra of the bloc and are hown below. T T g g The down-plane coponent of the 6.7-g a i given by o o g in 4 (6.7 g(9.8 in T g in4 o g 4 o g co 4 o or the yte to be otionle, at equilibriu, thi force ut be balanced by the tenion of the tring. On the other hand, the hanging bloc i alo in equilibriu, o it weight g ut balance the tenion force. Thu, 4.48 g g A bloc of a 30 g i upported by two wire attached to the ceiling, a hown in the figure below. ind the tenion in the wire.
6 T y T x T 3 x ax 0 -T co 0 +T co 50 (i y ax 0 +T in 0 +T in 50 - g (ii Solve (i for T : 0 -T co 0 +T co 50 >>> T co 0 T co 50 T T Subtitute in (ii co 0 co 50 (.469 T 0 +T in 0 +T in 50 - g >>> 0 +T in 0 +(.469 T in 50 - g 0 T (in 0 + in 50 ( g T ( (.469 T g 94 T 94/ T 0 T (.469 T A bloc of a 7.96 g ret on a plane inclined at to the horizontal. The coefficient of tatic friction i 0.5 and the coefficient of inetic friction i 0.5. a. What i the iniu force, parallel to the plane, which can prevent the bloc fro lipping down the plane? b. What i the iniu force that will tart the bloc oving up the plane? c. What force i required to ove the bloc up the plane at contant velocity?
7 o g a. When i at it iniu, the force of tatic friction f i directed up and i equal to it axiu value: f, ax μ μ g coθ. Thu, g inθ in μ g coθ 0. Then, in g( inθ μ coθ ( ( in co b. To tart oving the bloc up the plane, we ut have g inθ μ g coθ 0. The iniu value i achieved when in g( inθ + μ coθ ( ( in co c. Becaue the bloc i already in otion, the frictional force acting on it i that of inetic friction. We replace μ with μ, and the force of friction becoe f, ax μ μ gcoθ. Thu, g in θ μ g coθ a 0, and 40. ( inθ + μ co ( ( in co g θ
8 8. A force i exerted on the axle of the pulley, a hown in the figure below. The pulley and tring are ale and there i no friction. Two object,. g and.9 g, are attached a hown to the oppoite end of the tring. The object i at ret on the floor. a. What i the larget value the force ay have o that will reain at ret on the floor? b. What i the tenion in the tring if the upward force i 0? c. Referring to (b above, what i the acceleration of? a. When T >, leave the floor. Thu, the larget value of force for to reain at ret on the floor i b. The net force acting on the pulley i T 0 T 0 T 55 c. et force acting T g Acceleration of a 43.4 /. 36.0
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