2 masses are connected through a non-stretchable string that passes over a frictionless pulley. The masses of the objects are 12 kg and 5.5 kg respectively. The obj with larger mass is hanging 2.5 m fr the surface of a table. Suppose that the two objs are initially at rest. (a) Calculate the resulting acceleration magnitude when the 2 are released fr rest. (b) How long will the larger mass travel before hitting the table surface? (c) At what speed willit hit the table surface?
To solve this problem, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
(a) To find the resulting acceleration when the two objects are released from rest, we need to calculate the net force acting on the system. Since there is no friction in the system and the pulley is frictionless, the tension in the string is the same throughout.
Step 1: Determine the weight of each object.
The weight of an object can be calculated using the formula: weight = mass * acceleration due to gravity (g).
The acceleration due to gravity is approximately 9.8 m/s^2.
For the 12 kg mass:
Weight1 = 12 kg * 9.8 m/s^2
For the 5.5 kg mass:
Weight2 = 5.5 kg * 9.8 m/s^2
Step 2: Calculate the net force.
The net force acting on the system is equal to the difference in the weights of the two masses.
Net force = Weight1 - Weight2
Step 3: Calculate the resulting acceleration.
The resulting acceleration can be calculated using Newton's second law of motion:
Resulting acceleration = Net force / total mass
Total mass = mass1 + mass2
(b) To find how long the larger mass will travel before hitting the table surface, we can use the equations of motion. Since the acceleration is constant, we can use the SUVAT equation:
s = ut + (1/2)at^2
Here, s represents the displacement, u represents the initial velocity, a represents the acceleration, and t represents the time.
Since the objects start from rest (u = 0) and are released at the same time, we can calculate the displacement of the larger mass using the equation:
s = (1/2)at^2
(c) To find the speed at which the larger mass will hit the table surface, we can use the equation:
v = u + at
Since the object starts from rest (u = 0), the equation simplifies to:
v = at
Now that we've discussed the steps involved, let's calculate the answers to the three questions.
(a) Calculate the resulting acceleration magnitude when the two objects are released from rest:
1. Calculate the weight of each mass:
Weight1 = 12 kg * 9.8 m/s^2
Weight2 = 5.5 kg * 9.8 m/s^2
2. Calculate the net force:
Net force = Weight1 - Weight2
3. Calculate the resulting acceleration:
Resulting acceleration = Net force / (mass1 + mass2)
(b) How long will the larger mass travel before hitting the table surface:
1. Calculate the displacement of the larger mass:
Displacement = (1/2) * acceleration * time^2
2. Rearrange the equation to solve for time:
time^2 = (2 * Displacement) / acceleration
(c) At what speed will the larger mass hit the table surface:
1. Calculate the speed of the larger mass:
Speed = acceleration * time
Now you have the steps to calculate the answers to the three questions. Plug in the given values into the appropriate equations to find the final answers.