Only two horizontal forces act on a 3.0 kg body that can move over a frictionless floor. One force is 9.0 N, acting due east, and the other is 8.0 N, acting 62° north of west. What is the magnitude of the body's acceleration?

Question

Physics

Rigoberto Stevens

2 January, 02:33

Only two horizontal forces act on a 3.0 kg body that can move over a frictionless floor. One force is 9.0 N, acting due east, and the other is 8.0 N, acting 62° north of west. What is the magnitude of the body's acceleration?

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Johnny Weber · Answer 1

We can translate the given forces into their complex counterparts: 9.0 < 180 and 8.0 < 90-62. The mass of the object is converted to weight first by multiplying by 9.8 m/s2. The complex counterpart is 29.4 < 270. Adding the three forces, the resultant force is 25.7172 < - 94.32 degrees.

Using second law of motion, F = ma; a = 25. 7172 N / 3 kg = 8.5724 m/s2