TWo blocks of massses 20 kg and 8 kg are connected together by a light string and rest on a frictionless level surface. Attached to the 8 kg mas is a second light string, which a person uses to pull both blocks horizontally. If the two-block system accelerates at .5 m/s squared, what is the tension in the second string attached to the 8 kg mass?
Use F=ma where m=mass of both blocks.
To find the tension in the second string attached to the 8 kg mass, we can use Newton's second law of motion:
F = m * a
Where:
F is the net force acting on the system,
m is the mass of the system, and
a is the acceleration of the system.
First, we need to find the net force acting on the system. The net force is equal to the force applied by the person pulling the blocks. Let's assume this force is denoted as F_pull.
For the 20 kg mass:
F_pull = 20 kg * a
For the 8 kg mass:
F_pull = 8 kg * a
Since both blocks are connected, the tension in the second string attached to the 8 kg mass is equal to the force pulling the 8 kg mass.
Therefore, the tension in the second string attached to the 8 kg mass is:
Tension = F_pull = 8 kg * a = 8 kg * 0.5 m/s² = 4 N
So, the tension in the second string attached to the 8 kg mass is 4 Newtons.
To find the tension in the second string attached to the 8 kg mass, we need to consider the forces acting on this mass.
First, we know that the two-block system accelerates at 0.5 m/s². Since the surface is frictionless, the only horizontal force acting on the system is the tension in the second string attached to the 8 kg mass.
Let's break down the forces acting on the 8 kg mass:
1. Force of gravity (weight): The weight of an object can be calculated by multiplying its mass by the acceleration due to gravity (9.8 m/s²). In this case, the weight of the 8 kg mass is (8 kg) * (9.8 m/s²).
2. Tension in the string: This is the force applied by the person pulling the blocks horizontally. We'll call this tension T.
According to Newton's second law of motion, 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 acting on the 8 kg mass is the tension force (T) acting in the positive direction.
So we have:
Net force = Force of tension (T)
Net force = (mass of the 8 kg mass) * (acceleration)
Solving for T:
T = (mass of the 8 kg mass) * (acceleration)
Now we can substitute the given values into the equation:
T = (8 kg) * (0.5 m/s²)
T = 4 N
Therefore, the tension in the second string attached to the 8 kg mass is 4 N.