Two blocks m1 = 9.1 kg and m2 = 5.6 kg are connected by a homogeneous rope that has a mass of mr = 1.50 kg. A constant vertical force, F = 193.0 N, is applied to the upper block. What is the magnitude of the acceleration of the system?What is the magnitude of the tension in the rope at the bottom end of the rope?
assume the rope does not stretch
total mass = 9.1+1.5+5.6 = 16.2
total weight = 16.2*9.81 = 158.9 N
acceleration of system = a
a = (193 -158.9)/16.2
a = 2.1 m/s^2
I do not know mass of lower block so call it m
force down = 9.81 m
force up = tension T
acceleration up = 2.1
T - 9.81 m = m (2.1)
T = m (2.1+9.81)
To find the magnitude of the acceleration of the system, 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. In this case, the net force is equal to the applied force minus the force of tension in the rope.
Let's calculate the acceleration first:
1. Calculate the total mass of the system. We can find this by adding up the masses of the two blocks and the mass of the rope:
Total mass (mtotal) = m1 + m2 + mr
= 9.1 kg + 5.6 kg + 1.50 kg
= 16.20 kg
2. Calculate the net force. The net force is the applied force minus the force of tension:
Net force (Fnet) = F - T
= 193.0 N - T
3. Apply Newton's second law to find the acceleration:
Fnet = mtotal * acceleration
Substituting the values, we have:
193.0 N - T = 16.20 kg * acceleration
Now, let's calculate the magnitude of the tension in the rope at the bottom end:
The tension in the rope is the force exerted by one block on the other through the rope. Since the rope is homogeneous, this tension is the same throughout the rope. The magnitude of the tension at the bottom end of the rope is the tension in the rope plus the force of gravity acting on the lower block, m2.
Let's calculate the tension:
1. Calculate the force of gravity acting on the lower block:
Force of gravity (Fgravity) = m2 * g
= 5.6 kg * 9.8 m/s^2 (acceleration due to gravity)
2. The magnitude of the tension at the bottom end is the sum of the tension and the force of gravity on the lower block:
Tbottom = T + Fgravity
Substituting the values we have and solving these equations will give us the magnitude of the acceleration of the system and the magnitude of the tension in the rope at the bottom end.