Question

A bale of hay (400 kg) is raised from the ground to the second story of a barn (9 m). A rope is tied to the hay to lift it. The rope extends up from the bale and maintains a tension of 9000 N. (Use g = 10 N/kg) a. What are the forces acting on the bale of hay? b.. What is the magnitude of the net force on the bale of hay? c. What is the acceleration of the bale of hay? d.How fast is the bale traveling when it reaches the second story of the barn 9.00 m above the ground?

Answer 1

The forces acting on the bale are gravity and the rope tension, with a net force of 5000 N upwards. This results in an acceleration of 12.5 m/s². When it reaches the second floor 9 meters high, its velocity is 15 m/s.

Step-by-step explanation:

a. The forces acting on the bale of hay are the gravitational force, also known as the weight of the bale, and the tension in the rope.
The weight is calculated by the product of mass (400 kg) and the acceleration due to gravity (10 N/kg), giving a result of 4000 N downwards. The tension in the rope is given as 9000 N upwards.

b. The net force is obtained by subtracting the weight from the tension, giving 9000 N - 4000 N = 5000 N upwards.

c. The acceleration of the bale is calculated by using Newton's second law, which states that Force = mass x acceleration. So, acceleration = Force / mass = 5000 N / 400 kg = 12.5 m/s² upwards.

d. The final velocity of the bale of hay when it reaches the second story of the barn is found by using the kinematic equation, v² = u² + 2as, where u is the initial velocity (0 m/s since it starts from rest), s is the distance, and a is the acceleration. Therefore, v = sqrt(2 * 12.5 m/s² * 9 m) = 15 m/s

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