The system of blocks shown in the diagram below is being accelerated to the right at 4.4 m/s2
What is the applied force
Small box mass- 0.10 kg
Big box mass - 0.20 kg
Acceleration - 4.4 m/s2
Coefficient kinetic - 0.35
To find the applied force, we can start by using 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 equation form, this is represented as:
F_net = m * a
In this case, we are given the mass of the small box (0.10 kg) and the acceleration (4.4 m/s^2). We can calculate the net force acting on the small box by substituting these values into the equation:
F_net = 0.10 kg * 4.4 m/s^2
= 0.44 N
However, this is not the applied force. The net force is the vector sum of all the forces acting on an object. In this system, there are multiple forces at play, including the gravitational force and the force of friction.
The gravitational force is given by the equation:
F_gravity = m * g
where m is the mass of the object and g is the acceleration due to gravity (approximated as 9.8 m/s^2).
The force of friction can be calculated using the equation:
F_friction = μ * N
where μ is the coefficient of kinetic friction and N is the normal force. The normal force, in this case, is equal to the weight of the object, which can be calculated as:
N = m * g
Given that the coefficient of kinetic friction (μ) is 0.35, we can calculate the force of friction:
F_friction = 0.35 * N
= 0.35 * (0.10 kg * 9.8 m/s^2)
= 0.35 * 0.98 N
= 0.343 N
Now, to find the applied force, we need to consider that the net force is equal to the applied force minus the force of friction:
F_net = F_applied - F_friction
Rearranging the equation, we can solve for the applied force:
F_applied = F_net + F_friction
Substituting the given values, we get:
F_applied = 0.44 N + 0.343 N
= 0.783 N
Therefore, the applied force is 0.783 N.