An object with a mass of #3 kg# is acted on by two forces. The first is #F_1= < 7 N , -3 N># and the second is #F_2 = < -1 N, 6 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#
# \ \ \ \ = <<7,-3>> + <<-1,6>>#
# \ \ \ \ = <<6,3>>#
The magnitude,
# F = | vecF | #
# \ \ \ \= |<<6,3>>| #
# \ \ \ \= sqrt(6^2+3^2) #
# \ \ \ \= sqrt(36+9) #
# \ \ \ \= sqrt(45) #
# \ \ \ \= 6.71 \ N # (2dp)
Applying Newton's 2nd Law of Motion,
# :. 6.71=3a#
# :. a=2.24 \ ms^-2# (2dp)
The direction of the acceleration is the same as the direction of the resultant force
# tan theta = 3/6 #
# :. \ theta = arctan 0.5#
# :. \ theta = 26.6º# (1dp)
Hence,
The objects rate of acceleration is
#2.23 \ ms^-2# (2dp)
The direction of the acceleration is at an angle of#26.6º# (1dp)
