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. The acceleration of the boxes is 1.8.
Find the tension in the string.
you take the mass of the object that the force is acted upon, in your case, 15kg and multiply that by you acceleration
so:
T = (15)kg x 1.8 m/s^2 = 27N
To find the tension in the string, we need to apply Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration (F = ma).
Let's analyze the given information:
- Mass of the first box (m1) = 15 kg
- Mass of the second box (m2) = 17 kg
- Applied force (F) = 58 N
- Acceleration (a) = 1.8 m/s²
First, let's calculate the net force acting on the system by considering the force applied to the second box. Since the force is applied only to the second box, it will be responsible for accelerating both boxes.
Net force = Force applied to the second box (F) = 58 N
Now, using Newton's second law, we can equate the net force to the total mass of both boxes multiplied by the acceleration:
Net force = (m1 + m2) * a
58 N = (15 kg + 17 kg) * 1.8 m/s²
Simplifying the equation:
58 N = 32 kg * 1.8 m/s²
58 N = 57.6 kg·m/s²
Finally, to find the tension in the string, we need to consider the force acting on the first box (Tension) and apply Newton's second law in the opposite direction:
Net force on the first box = Tension = m1 * a
Tension = 15 kg * 1.8 m/s²
Tension = 27 N
Therefore, the tension in the string is 27 N.