A 5.0 kg object (m1) is connected to a 10.0 kg object (m2) by a string. If a pulling force F of 20 N is applied to the 5.0 kg object as shown,
A) what is the acceleration of the system?
B) what is the tension in the string connecting the objects?
(Assume a frictionless surface.)
To find the acceleration of the system, we can use 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.
A) To find the acceleration, we need to determine the net force acting on the system. The net force is equal to the force applied minus the force of gravity acting on the objects.
The force applied (F) is 20 N.
The force of gravity acting on the 5.0 kg object (m1) is given by the equation:
F1 = m1 * g, where g is the acceleration due to gravity (approximately 9.8 m/s^2).
F1 = 5.0 kg * 9.8 m/s^2 = 49 N.
The force of gravity acting on the 10.0 kg object (m2) is given by:
F2 = m2 * g.
F2 = 10.0 kg * 9.8 m/s^2 = 98 N.
Therefore, the net force acting on the system is:
Net force = Force applied - Force of gravity on m1 - Force of gravity on m2
Net force = 20 N - 49 N - 98 N
Net force = -127 N
Since the net force is negative, it means that the system will be accelerating in the opposite direction of the pulling force.
Now, we can find the acceleration by dividing the net force by the total mass of the system.
Acceleration = Net force / (m1 + m2)
Acceleration = -127 N / (5.0 kg + 10.0 kg)
Acceleration = -127 N / 15 kg
Acceleration ≈ -8.47 m/s^2
The acceleration of the system is approximately -8.47 m/s^2.
B) To find the tension in the string connecting the objects, we can use Newton's third law of motion, which states that for every action, there is an equal and opposite reaction. The tension force in the string for m1 is equal to the force applied (F), and the tension force in the string for m2 is equal to the force of gravity acting on m2.
Therefore, the tension in the string connecting the objects is equal to the force applied (F) = 20 N.
The tension in the string is 20 N.