block a in figure 1 has a mass of 10kg, and block b and the horizontal surface is 0.3. a) what is the mass of block c if block b is moving with an acceleration of 3m/s/s b) what is the tension in each cord when b is moving with a constant velocity?
To answer these questions, we need to apply Newton's laws of motion and solve for the desired variables. Let's break down each question step by step:
a) What is the mass of block c if block b is moving with an acceleration of 3 m/s²?
To find the mass of block c, we need to analyze the forces acting on the system. We know that block b is experiencing an acceleration of 3 m/s². From this, we can conclude that the net force acting on block b is equal to its mass (let's call it mb) multiplied by its acceleration.
The net force on block b is provided by the tension in the cord connecting it to block c. Additionally, we have the force of friction acting in the opposite direction. The force of friction is given by the equation:
friction force = coefficient of friction * normal force
where the normal force is equal to the weight of block b. The weight is calculated by multiplying the mass of block b (mb) by the acceleration due to gravity (9.8 m/s²).
Now, let's denote the mass of block c as mc. The force of tension exerted by block b on block c will be the same as the force pulling in block c, which is given by mc * acceleration.
Therefore, we can set up the following equation for the net force on block b:
Tension - (coefficient of friction * mb * 9.8 m/s²) = mb * 3 m/s²
Simplifying the equation, we have:
Tension = (mb * 3 m/s²) + (coefficient of friction * mb * 9.8 m/s²)
Given that mb = 10 kg and the coefficient of friction is 0.3, we can substitute these values into the equation to find the tension:
Tension = (10 kg * 3 m/s²) + (0.3 * 10 kg * 9.8 m/s²)
Now, we can calculate the value for tension.
b) What is the tension in each cord when b is moving with a constant velocity?
When block b is moving with a constant velocity, we know that the net force acting on it is zero. This means that the force of tension in the cord is equal to the force of friction.
Using the equation for the force of friction:
friction force = coefficient of friction * normal force
we can substitute in the values for the coefficient of friction and the normal force (which, as mentioned earlier, is equal to the weight of block b).
The equation for the tension in this scenario will be:
Tension = coefficient of friction * mb * 9.8 m/s²
Given that mb = 10 kg and the coefficient of friction is 0.3, we can substitute these values into the equation to find the tension.