A 9.5-kg watermelon and a 7.2-kg pumpkin are attached to each other via a cord that wraps over a pulley, as shown. Friction is negligible everywhere in this system.

(a) Find the accelerations of the pumpkin and the watermelon. Specify magnitude and direction.
magnitude direction

Pumpkin?m/s^2
Watemelon? m/s^2

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To find the accelerations of the pumpkin and watermelon, we need to apply the principles of Newton's second law of motion.

Newton's second law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

First, let's identify the forces acting on each object:
1. Gravity force (weight) pulling downwards: Fg = mass * acceleration due to gravity (g = 9.8 m/s^2)
2. Tension force in the cord pulling upwards (the same for both objects)

For the pumpkin (7.2 kg):
The net force acting on the pumpkin is the tension force minus the weight force (since it is moving upwards):
Net force on pumpkin = Tension - Weight[pumpkin]

For the watermelon (9.5 kg):
The net force acting on the watermelon is only the tension force (since it is moving downward):
Net force on watermelon = Tension

Now, we can calculate the tensions in the cord for both objects.
Since the weight of the pumpkin and watermelon are proportional to their masses, their ratio remains the same:
Weight[pumpkin] / Weight[watermelon] = 7.2 kg / 9.5 kg = 0.758

The tension force in the cord is the same (due to the pulley being massless and frictionless), so we can equate the tension for both objects:
Tension - Weight[pumpkin] = Tension
Tension = Weight[pumpkin] = mass[pumpkin] * g

Now, let's calculate the values:

For the pumpkin:
Weight[pumpkin] = 7.2 kg * 9.8 m/s^2 = 70.56 N

For the watermelon:
Weight[watermelon] = 9.5 kg * 9.8 m/s^2 = 93.1 N

Since the tension force is the same for both objects, it is equal to the weight of the pumpkin:
Tension = 70.56 N

Now, let's calculate the accelerations:

For the pumpkin:
Net force on pumpkin = Tension - Weight[pumpkin] = Tension - Tension = 0 N
Since the net force on the pumpkin is zero, its acceleration is zero. Therefore, the magnitude of the pumpkin's acceleration is 0 m/s^2.

For the watermelon:
Net force on watermelon = Tension = 70.56 N
Using Newton's second law (F = m * a), we can find the acceleration of the watermelon:
70.56 N = 9.5 kg * a
a = 70.56 N / 9.5 kg = 7.43 m/s^2
The magnitude of the watermelon's acceleration is 7.43 m/s^2.

Direction:
The direction of the pumpkin's acceleration is upwards (opposite to the direction of gravity).
The direction of the watermelon's acceleration is downwards (in the same direction as gravity).