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.
Pumpkin is at left of angle n is 53 degrees and watermelon is on right and at 30 degrees calculate acceleration of each??? i got 7.8 m/s^2 for pumkin n 4.9 for watermelon but its wrong :/ Please helppp
To calculate the acceleration of each object, we can use Newton's second law of motion, which states that the net force on an object is equal to the product of its mass and acceleration.
In this system, we have two objects – the watermelon and the pumpkin – connected by a cord that wraps over a pulley. The acceleration of the objects will be the same since they are connected by the cord and will move together.
To begin, let's resolve the forces acting on each object:
For the watermelon:
1. Identify the weight of the watermelon, which is given by the formula: weight = mass × gravitational acceleration.
Given that the mass of the watermelon is 9.5 kg, and the gravitational acceleration is approximately 9.8 m/s^2, the weight of the watermelon is approximately 93.1 N.
2. Resolve the weight of the watermelon into its vertical and horizontal components.
The vertical component is given by: vertical component = weight × sin(theta).
Substituting the values, we get: vertical component = 93.1 N × sin(30°) ≈ 46.55 N.
The horizontal component is given by: horizontal component = weight × cos(theta).
Substituting the values, we get: horizontal component = 93.1 N × cos(30°) ≈ 80.56 N.
For the pumpkin:
1. Identify the weight of the pumpkin, which is given by the formula: weight = mass × gravitational acceleration.
Given that the mass of the pumpkin is 7.2 kg, and the gravitational acceleration is approximately 9.8 m/s^2, the weight of the pumpkin is approximately 70.56 N.
2. Resolve the weight of the pumpkin into its vertical and horizontal components.
The vertical component is given by: vertical component = weight × sin(theta).
Substituting the values, we get: vertical component = 70.56 N × sin(53°) ≈ 54.08 N.
The horizontal component is given by: horizontal component = weight × cos(theta).
Substituting the values, we get: horizontal component = 70.56 N × cos(53°) ≈ 39.9 N.
Next, let's calculate the net force acting on each object:
For the watermelon:
1. The only horizontal force acting on the watermelon is the horizontal component of the weight. Therefore, the net force in the horizontal direction is equal to the horizontal component: net force = 80.56 N.
2. Calculate the acceleration of the watermelon using Newton's second law: acceleration = net force / mass.
Substituting the values, we get: acceleration = 80.56 N / 9.5 kg ≈ 8.49 m/s^2.
For the pumpkin:
1. The only horizontal force acting on the pumpkin is the horizontal component of the weight. Therefore, the net force in the horizontal direction is equal to the horizontal component: net force = 39.9 N.
2. Calculate the acceleration of the pumpkin using Newton's second law: acceleration = net force / mass.
Substituting the values, we get: acceleration = 39.9 N / 7.2 kg ≈ 5.54 m/s^2.
Therefore, the correct acceleration values are approximately 8.49 m/s^2 for the watermelon and 5.54 m/s^2 for the pumpkin.