A 4.40kg bucket of water is accelerated upward by a cord of negligible mass whose breaking strength is 74.0N
To determine the maximum acceleration that the bucket of water can have without breaking the cord, we can use Newton's second law of motion.
1. Start by converting the mass of the bucket of water to kilograms (kg). We are given that the mass is 4.40 kg, so no conversion is needed in this case.
2. Determine the force acting on the bucket of water due to gravity. The force due to gravity can be calculated using the equation F = m * g, where F is the force in Newtons (N), m is the mass in kilograms (kg), and g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth). Therefore, the force due to gravity acting on the bucket of water is F = 4.40 kg * 9.8 m/s^2 = 43.12 N.
3. Since the cord's breaking strength is given as 74.0 N, the maximum force that the cord can withstand before breaking is 74.0 N.
4. To determine the maximum acceleration that the bucket of water can have without breaking the cord, we need to consider the net force acting on the bucket. The net force can be calculated using the equation F_net = F_applied - F_gravity, where F_net is the net force, F_applied is the force applied on the bucket, and F_gravity is the force due to gravity. In this case, the net force is equal to the tension in the cord, which is limited by its breaking strength.
5. Since the cord's breaking strength is the maximum tension it can withstand, we can set the net force equal to the breaking strength: F_net = 74.0 N.
6. Substitute the values we know into the equation: 74.0 N = F_applied - 43.12 N.
7. Solve for F_applied: F_applied = F_net + F_gravity = 74.0 N + 43.12 N = 117.12 N.
8. Finally, we can determine the maximum acceleration using Newton's second law of motion: F_net = m * a, where m is the mass of the bucket and a is the acceleration. Rearranging the equation, we find that a = F_net / m.
9. Plug in the values we know: a = 117.12 N / 4.40 kg = 26.62 m/s^2.
Therefore, the maximum acceleration that the bucket of water can have without breaking the cord is 26.62 m/s^2.