crate P of mass 1.25 kg is connected to another crate, Q ,of mass 2 kg by a light inextensible string. The two crate are placed on a rough horizontal surface. A constant force F of magnitude 7.5 N, acting at angle tita to the horizontal, is applied on crate Q, as shown in the diagram below.
the crates accelerate at 0.1 m.s^-2 to the right.
Crate P experiences acontant frictional force force of 1.8 N and crate Q experiences a constant frictional force of 2.2 N.
2.1 State Newton's Second Law of motion in words?
2.2 Calculate the magnitude of the tension in string?
2.3 Calculate the magnitude of angle tita?
2.1 Newton's Second Law of motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
2.2 To calculate the tension in the string, we need to consider the forces acting on crate Q. The net force acting on crate Q in the horizontal direction can be calculated as follows:
Net Force = Force applied - Frictional force
Net Force = 7.5 cos(tita) - 2.2 N
Since the acceleration of the crates is 0.1 m/s^2, we can use Newton's Second Law to write:
Net Force = Mass x Acceleration
7.5 cos(tita) - 2.2 N = 2 kg x 0.1 m/s^2
7.5 cos(tita) - 2.2 = 0.2
7.5 cos(tita) = 2.4
cos(tita) = 2.4 / 7.5
tita = arccos(2.4 / 7.5)
2.3 Calculating the magnitude of the angle tita yields the tension in the string. We can substitute the value of tita back into the equation for the net force acting on crate Q to find the tension.