48, (11) The block shown in Fig. 4-43 has mass m = 7.0 kg and lies on a fixed sm

Question

48, (11) The block shown in Fig. 4-43 has mass m = 7.0 kg and lies on a fixed smooth frictionless plane tilted at an angle 22.0° to the horizontal. (a) Determine the acceleration of the block as it slides down the plane. (b) If the block starts from rest 12.0 m up the plane from its base, what will be the block's speed when it reaches the bottom of the incline? .y FIGURE 4-43 Block on inclined plane. Problems 48 and 49 49. (II) A block is given an initial speed of 4.5 m/s up the 22° plane shown in Fig. 4-43. (a) How far up the plane will it go? (b) How much time elapses before it returns to its starting point? Ignore friction.

Explanation / Answer

48a] Force along the incline = mg sin theta

acceleration along the incline a = g sin theta

= 9.8* sin 22 degree = 3.671 m/s^2

b] using third equation of motion,

v = sqrt(2as) = sqrt(2*3.671*12)

= 9.386 m/s answer

49a] using third equation of motion,

s = u^2/2a

= 4.5^2/(2*3.671)

= 2.758 m answer

b) using second equation of motion,

0 = 4.5t - 0.5*3.671*t^2

t = 4.5/(0.5*3.671)

= 2.452 s answer

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