Two boxes of fruit on a frictionless horizontal surface are connected by a light string as in the figures below, where m1 = 15 kg and m2 = 17 kg. A force of 58 N is applied to the 17 kg box.
(a1) Determine the acceleration of the boxes (b) the tension of the string (c)
58=(m1+m2)a solve for a
Tension between=m2*a
I still don't understand how to find the tension of the string!
To solve this problem, 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) Determine the acceleration of the boxes:
First, let's calculate the net force acting on the system. The force applied to the 17 kg box is 58 N. Since the boxes are connected by a light string, the tension in the string will exert an equal force on the 15 kg box in the opposite direction.
Net force = Force applied to 17 kg box - Force exerted by tension on 15 kg box
Net force = 58 N - Tension
Since the force applied to the 17 kg box is greater than the force exerted by tension on the 15 kg box, the net force is in the same direction as the applied force.
Next, we need to determine the mass of the system. Since the boxes move together, the total mass is the sum of the individual masses: m_total = m1 + m2 = 15 kg + 17 kg = 32 kg.
Now we can apply Newton's second law:
Net force = mass * acceleration
58 N - Tension = 32 kg * acceleration
Simplify the equation:
Acceleration = (58 N - Tension) / 32 kg
(b) Determine the tension of the string:
To find the tension in the string, we need to consider the 15 kg box. The force exerted by tension on the 15 kg box is equal in magnitude but opposite in direction to the force applied to the 17 kg box.
By Newton's third law of motion, the tension in the string is equal to the force applied to the 17 kg box. Therefore, the tension = 58 N.
(c) The tension in the string is 58 N.