An object with a mass of #2 kg# is acted on by two forces. The first is #F_1= <4 N , 8 N># and the second is #F_2 = < 1 N, 7 N>#. What is the object's rate and direction of acceleration?
1 Answer
The objects rate of acceleration is
The direction of the acceleration is at an angle of
Explanation:
Let the resultant force acting on the object be
# vecF = vecF_1 + vecF_2#
# \ \ \ \ = <<4,8>> + <<1,7>>#
# \ \ \ \ = <<5,15>>#
The magnitude,
# F = | vecF | #
# \ \ \ \= |<<5,15>>| #
# \ \ \ \= sqrt(5^2+15^2) #
# \ \ \ \= sqrt(25+225) #
# \ \ \ \= sqrt(250) #
# \ \ \ \= 15.81 \ N # (2dp)
Applying Newton's 2nd Law of Motion,
# :. 15.81=2a#
# :. a=7.91 \ ms^-2# (2dp)
The direction of the acceleration is the same as the direction of the resultant force
# tan theta = 15/5 #
# :. \ theta = arctan 3#
# :. \ theta = 71.6º# (1dp)
Hence,
The objects rate of acceleration is
#7.91 \ ms^-2# (2dp)
The direction of the acceleration is at an angle of#71.6º#