Two blocks of masses m1 = 4.5kg and m2 = 6.5kg resting on a frictionless area connected by light inextensible chord as shown. A horizontal force F of 33.0 N directed to the right is applied to m1 as shown. Find (A) acceleration and (B) tension of the chord?
So this gives you the mass and force of m1, use Newton's second law (F=m*a) to get the acceleration.... 33.0/4.5kg=7.33 m/s^2
I drew this situation as
[m1]----[m2] since the applied force was to the right the --- tension force becomes limp and should =0
[m1]>~~_[m2] it's easier to imagine pulling a rope, if you take a step inward the rope becomes limp and has no tension force present anymore.
Hope this helps!!
To find the acceleration and tension, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
Let's start by finding the acceleration of the system:
1. We'll assume that the positive direction is to the right. Therefore, the force applied (F) is positive, and the tension in the chord is also positive.
2. The net force acting on m1 is F - T, where T is the tension in the chord.
3. The net force acting on m2 is T (since the mass m2 is not being acted upon by any other force).
4. According to Newton's second law, we have:
(F - T) = m1 * a --> equation 1
T = m2 * a --> equation 2
Now, let's solve these equations simultaneously to find the acceleration (a) and the tension (T):
From equation 1, we have:
F - T = m1 * a
From equation 2, we have:
T = m2 * a
Substituting the value of T from equation 2 into equation 1, we get:
F - (m2 * a) = m1 * a
Rearranging the equation to solve for acceleration:
F = (m1 + m2) * a
Now, we can substitute the given values into the equation to calculate the acceleration:
F = 33.0 N (given)
m1 = 4.5 kg (given)
m2 = 6.5 kg (given)
Plugging in these values, we have:
33.0 N = (4.5 kg + 6.5 kg) * a
Simplifying:
33.0 N = 11 kg * a
Now, we can solve for a:
a = 33.0 N / 11 kg
a ≈ 3.0 m/s²
So, the acceleration of the system is approximately 3.0 m/s².
To find the tension (T) in the chord, we can substitute the calculated acceleration (a) into either equation 1 or 2.
Using equation 2:
T = m2 * a = 6.5 kg * 3.0 m/s²
T = 19.5 N
So, the tension in the chord is 19.5 N.