Unit-1. Force & Motion. Solutions 1.6 Energy & Motion page a) W 1. = F.x = 1. = F.cos60!.2x =F.x W 2. b) = W 2 = 2. 2.m.v 1.

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1 page Two objects K and L are stationary over frictionless horizontal surfaces. They are pulled as shown in the figure. The work done on object K when it reaches point A is W 1 and the work done on object L when it reaches point B is W 2. The speed of object K at point A is v 1 and the speed of object L at point B is v 2. a) W 1 = F.x W 2 = F.cos60!.2x =F.x W 1 W 2 = 1 b) W 1 = W 2 a) Calculate the ratio of W 1 to W 2. b) Calculate the ratio of v 1 to v m.v 1 2 = 1 2.2m.v 2 2 v 1 v 2 = 2

2 page The path given in the figure is frictionless. Object K of mass 2 kg is stationary at point A. Horizontal force F is applied to object K parallel to the path and it can merely reach point C. W F = F.x =F.20= 20F PE C =mgh C = PE =0 PE C = 120 J 20F = 120 What is the magnitude of force F? (AB=BC, g=10 m/s 2.) F =6 N

3 page Two boxes, X and Z, are tied by a rope as shown in the figure. The coefficient of friction of the surface of the table is 0,5. F f = 0,5.40= 20 N ME initial = ME final PE X = KE X + KE Z + W Ff (5.10.1,5)=( v 2 )+( v 2 )+(20.1,5) What is the speed of box X after it falls 1,5 m? (Pulley is supposed to be weightless and frictionless. g=10 m/s 2.) 90= 9.v 2 2 v = 10 m / s

4 page The object is released from point K, it can reach point M and it stops at point L as shown in the figure. PE KE ME K 5mgh 0 5mgh L mgh 0 mgh M mgh mgh PE =0 Both KL and LM parts of the path have friction. The work done by friction force between K and L is more than the work done by friction force between L and M. What can be said about the smoothness of the paths KL and LM?

5 page The path shown in the drawing has friction only between points L and M. An object of mass m=2 kg is thrown with a speed of v=4 m/s from point M. The object can reach point K. KE M W Ff = PE K PE =0 0,6 m 1 m 1 m ( )-(µ.20.1)=(2.10.0,6) 16-20µ = 12 If the length of the paths are related as KL=LM=1 m, then what is the coefficient of friction? (g=10 m/s 2.) 20µ = 4 µ = 0,2

6 page Deep in the forest, a 50 grams leaf falls from a tree and drops straight to the ground. PE top = m.g.h=0, = 1,5 J KE ground = 1 2.0, = 0,1 J W by air friction = 0,1-1,5 =-1,4 J PE =0 If it falls 3 meters and its speed on the landing was 2 m/s, how much work done on the leaf by the air resistance? (g=10 m/s 2.)

7 page The spring shown in the figure is compressed by 0,5 m and a block of mass m=2 kg is placed in front of the spring. After the spring is released, the object can reach point C, turns back and passes through the point B with a speed of 6 m/s. PE spring = 1 2.k.x 2 = ( 1 2 )2 = 100 J KE B = 1 2.m.v 2 = = 36 J W friction = =-64 J Calculate the friction force that acts on the object. ( O is the equilibrium position of the spring and only the inclined surface has friction. g=10 m/s 2.) -64=-2.F f.4 F f =8 N

8 page Spring constants of two massless springs are k 1 =k and k 2 =2k. They are placed over a horizontal surface. The spring at right is compressed by an amount of x, an object is placed in front of the spring and they are released. The object moves toward the spring at left and it compresses it by an amount of x/2. E initial = 1 2.k.x 2 E final = 1 2.2k. x 2 2 = 1 4.k.x 2 50 % of its initial energy is converted into heat energy. What percent of the initial energy is converted into heat energy?

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