Final answer:
The acceleration of the system is 1.96 m/s^2 and the tension in the cord is 23.52 N.
Step-by-step explanation:
To calculate the acceleration and tension in the system, we need to consider the forces acting on both boxes. The hanging box experiences the force of gravity pulling it downwards, which is given by the equation Fg = m * g, where m is the mass of the box and g is the acceleration due to gravity. In this case, the mass is 2 kg, so Fg = 2 kg * 9.8 m/s^2 = 19.6 N.
The tension in the cord, T, is the force that keeps the boxes connected. Tension is always the same in an ideal pulley system. In this case, the hanging box exerts a force of 19.6 N upwards, so the table box experiences a force of 19.6 N downwards. Since the coefficient of kinetic friction is 0.20, the frictional force between the table and the box is given by the equation Ff = μ * N, where μ is the coefficient of kinetic friction and N is the normal force. The normal force is the weight of the box, which is 5 kg * 9.8 m/s^2 = 49 N. Therefore, Ff = 0.20 * 49 N = 9.8 N.
Using Newton's second law, we can set up the following equation to find the acceleration:
ΣF = ma
T - Ff = ma
T - 9.8 N = (5 kg + 2 kg) * a
T - 9.8 N = 7 kg * a
To solve for the acceleration, we need to know the tension in the cord. We can find the tension by setting up an equation using the hanging box:
ΣF = ma
T - Fg = ma
T - 19.6 N = 2 kg * a
Now we can solve the system of equations:
- From equation (1): T - 9.8 N = 7 kg * a
- From equation (2): T - 19.6 N = 2 kg * a
Substituting the value of T from equation (2) into equation (1), we get:
19.6 N - 9.8 N = 7 kg * a - 2 kg * a
9.8 N = 5 kg * a
a = 1.96 m/s^2
Substituting the value of a back into equation (2), we can find the tension:
T - 19.6 N = 2 kg * 1.96 m/s^2
T - 19.6 N = 3.92 N
T = 23.52 N
Therefore, the acceleration of the system is 1.96 m/s^2 and the tension in the cord is 23.52 N.