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)
To determine the acceleration of the boxes (a1), the tension in the string (b), and the force experienced by the 15 kg box (c), we can use Newton's second law of motion.
(a1) Acceleration of the boxes:
The force applied to the 17 kg box will cause both boxes to accelerate. We can set up the equation using Newton's second law: F = m * a, where F is the net force and a is the acceleration of the system.
First, determine the net force acting on the system. The force applied to the 17 kg box is given as 58 N. Since the boxes are connected by a string, the tension in the string also exerts a force on the 17 kg box. The force on the 15 kg box is simply the tension in the string. Since the boxes are connected, the tension in the string will be the same for both boxes.
To find the net force, subtract the force applied to the 17 kg box from the force on the 15 kg box (which is the tension in the string): Net Force = Tension - Applied Force.
Since the two boxes are connected and do not experience any friction, the tension in the string is the same as the force on the 15 kg box. Therefore, the equation becomes: Net Force = Tension - Applied Force = Tension - 58 N.
Next, we can express the net force in terms of the mass and acceleration of the system: Net Force = (m1 + m2) * a, where m1 is the mass of the 15 kg box, m2 is the mass of the 17 kg box, and a is the acceleration.
Setting up the equation for the net force: Tension - 58 N = (m1 + m2) * a.
(b) Tension of the string:
Since the tension in the string is the same for both boxes, we can solve for it using the equation from part (a1): Tension - 58 N = (m1 + m2) * a.
(c) Force experienced by the 15 kg box:
The force experienced by the 15 kg box is equal to the tension in the string. Therefore, we can use the equation from part (b) to find the force experienced by the 15 kg box.
To solve these equations, we need to know the masses of the boxes and the applied force. In this case, m1 = 15 kg, m2 = 17 kg, and the applied force is 58 N. Plug in these values and solve the equations to find the acceleration, tension, and force experienced by the 15 kg box.