A 2.00 kg object is subjected to three forces that give acceleration ( ) ( )j sms ima rrr 22 /6/8 += − . If two of the three forces are ( ) ( )j NN iF rrr 16.030.01 += and ( ) ( )j NN iF rrr 8.012.02 += − , find the third force.
See Similar Questions (and their answers) below.
To find the third force acting on the object, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. We are given the mass of the object as 2.00 kg and the acceleration as (−2) i + (2/6) j.
Let's calculate the net force acting on the object using the given forces. We have two forces given:
Force 1: F1 = 16.03 N i + 0.01 N j
Force 2: F2 = 8.01 N i + 2.02 N j
To calculate the net force, we add these two forces together:
Net Force = F1 + F2 = (16.03 N i + 0.01 N j) + (8.01 N i + 2.02 N j)
Net Force = (16.03 N + 8.01 N) i + (0.01 N + 2.02 N) j
Net Force = 24.04 N i + 2.03 N j
Now, we can equate the net force to the mass of the object multiplied by its acceleration:
Net Force = mass × acceleration
24.04 N i + 2.03 N j = 2.00 kg × (−2) i + (2/6) j
By comparing the i and j components separately, we can find the third force:
For the i component:
24.04 N = 2.00 kg × (−2)
24.04 N = −4.00 kg m/s^2
Dividing both sides by −4.00 kg:
24.04 N ÷ (−4.00 kg) = 6.01 N
For the j component:
2.03 N = 2.00 kg × (2/6)
2.03 N = 0.67 kg m/s^2
Dividing both sides by 0.67 kg:
2.03 N ÷ 0.67 kg ≈ 3.03 N
So, the third force is approximately 6.01 N i + 3.03 N j.