Two horizontal forces act on a 1.0 kg chopping block that can slide over a frict

Question

Two horizontal forces act on a 1.0 kg chopping block that can slide over a frictionless kitchen counter, which lies in an xy plane...

Two horizontal forces act on a 1.0 kg chopping block that can slide over a frictionless kitchen counter which lies in an xy plane. One force is F (3.2 N) i (3.0 N) j. Find the acceleration of the chopping block in unit-vector notation for each of the following second forces. (a) 2 (-3.2 N) i (-3 N) j m/s2) i m/s2) j (b) F2 (-3.2 N) i (3.0 N) j m/s2) i m/s2) j (c) F2 (3.2 N) i (-3 N) j m/s2) i m/s2) j

Explanation / Answer

F1 = 3.2i + 3 j where i and j are the unit vectors in the x and y direction



a) F1+F2=3.21+3j-3.2i-3j=0

   a = 0


b) F1+F2=3.2i+3j-3.2i+3j = 6j

the resultant force is in the direction of the y axis

a=F/m= 6 j / 1 kg = 6 (m/s^2) j meaning the mass accelerates at 6m/s^2 along the +y axis

c) F1+F2=3.2i+3j+3.2i-3j=6.4i

the total force is 6.4N along the +X axis

the acceleration = 6.4i/1 kg = 6.4(m/s^2)i meaning the acceleration is 6.4 m/s^2 along the +X axis

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