a person attaches a 25kg hay bale to one end of a rope passing over a frictionless pulley connected to a beam in the hay barn. another person then pulls down on the opposite end of the rope with a force of 277-N Ignoring the mass of the rope what will be the magnitude and direction of the bale's acceleration?
1.3 m/s^2 upward
To find the magnitude and direction of the bale's acceleration in this scenario, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
In this case, the net force acting on the bale is the difference between the force of gravity acting on it and the pulling force applied by the person.
1. The force of gravity acting on the bale can be calculated using the formula F_gravity = m * g, where m is the mass of the bale and g is the acceleration due to gravity (approximately 9.8 m/s^2). So, F_gravity = 25 kg * 9.8 m/s^2 = 245 N.
2. The pulling force applied by the person is given as 277 N.
Now we can find the net force and the acceleration:
Net force = force applied - force of gravity
Net force = 277 N - 245 N
Net force = 32 N (upward)
The net force is upward because the pulling force is greater than the force of gravity.
Now we can use Newton's second law:
Net force = mass * acceleration
32 N = 25 kg * acceleration
Dividing both sides of the equation by 25 kg:
acceleration = 32 N / 25 kg
acceleration = 1.28 m/s^2
Therefore, the magnitude of the bale's acceleration is 1.28 m/s^2, and the direction is upward.