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 in this system, we can use Newton's second law of motion. The formula for this law is:
F = m * a
Where F represents the net force acting on an object, m represents the mass of the object, and a represents the acceleration of the object.
In this case, we need to consider the forces acting on each object separately:
1. Pumpkin:
The forces acting on the pumpkin are its weight (mg) and the tension in the cord (T). The weight can be calculated using the formula w = m * g, where g is the acceleration due to gravity (approximately 9.8 m/s^2). Since the cord wraps over a pulley, the tension in the cord is the same on both sides. So we have the equation:
T = m_pumpkin * g
Since the object is accelerating, there is also a net force acting on the pumpkin. This force is equal to the difference between the tension (T) and the weight (mg):
F_pumpkin = T - m_pumpkin * g
Now we can set up the equation using Newton's second law:
F_pumpkin = m_pumpkin * a_pumpkin
Since the weight acts in the opposite direction to the acceleration, we can rewrite the equation as:
T - m_pumpkin * g = m_pumpkin * a_pumpkin
Plug in the given values for the mass of the pumpkin (7.2 kg) and the angle (53 degrees):
T - (7.2 kg) * (9.8 m/s^2) = (7.2 kg) * a_pumpkin
Now you need to solve for the tension (T) using the equations:
T = (7.2 kg) * (9.8 m/s^2)
With the calculated tension value, you can solve for the acceleration of the pumpkin (a_pumpkin).
2. Watermelon:
The forces acting on the watermelon are also its weight (mg) and the tension in the cord (T). However, the angle is different (30 degrees). Using the same steps as above, you can set up the following equation:
T - m_watermelon * g = m_watermelon * a_watermelon
Plug in the given values for the mass of the watermelon (9.5 kg) and the angle (30 degrees):
T - (9.5 kg) * (9.8 m/s^2) = (9.5 kg) * a_watermelon
Solve for the tension (T) using the equation:
T = (9.5 kg) * (9.8 m/s^2)
With the calculated tension value, you can solve for the acceleration of the watermelon (a_watermelon).
Following these steps and plugging in the given values, you should be able to calculate the correct accelerations for both the pumpkin and the watermelon.