a 2 kg mass and a 3 kg mass are attached to a lightweight cord that passes over a frictionless pully. the hanging masses are left free to move.
a. in what direction will the smaller masses move?
b.what will be its acceleration
*smaller mass move?
a. The smaller mass will move upwards.
b. To find the acceleration, we can use Newton's second law of motion, which states that the acceleration of an object is equal to the net force acting on it divided by its mass. In this case, the net force acting on the smaller mass is the weight of the larger mass pulling it downwards. The weight (W) is equal to the mass (m) multiplied by the acceleration due to gravity (g), which is approximately 9.8 m/s^2.
So, the net force (F_net) acting on the smaller mass is F_net = m * g, where m is the mass of the larger mass (3 kg).
Since the smaller mass is being pulled upwards, the net force acting on it is in the opposite direction, so we have F_net = -m * g.
Substituting the values, we get F_net = - (3 kg) * (9.8 m/s^2) = -29.4 N.
Using Newton's second law, we know that F_net = m * a, where m is the mass of the smaller mass (2 kg) and a is the acceleration.
Therefore, -29.4 N = (2 kg) * a.
Solving for a, we find that the acceleration of the smaller mass is a = -14.7 m/s^2.
Since the acceleration is negative, it means that the smaller mass will move upwards with an acceleration of 14.7 m/s^2.
To determine the direction in which the smaller mass will move and its acceleration, we need to analyze the forces acting on the system.
a. Direction of movement:
Since the mass on the left side (2 kg) is smaller than the mass on the right side (3 kg), the force due to gravity acting on the left side is smaller. As a result, the left side will have a net downward force, causing it to move downward. So, the smaller mass will move downward.
b. Acceleration:
To find the acceleration, we need to consider the net force acting on the system. In this case, the only force present is the force of gravity:
- For the 2 kg mass on the left side:
The force of gravity acting on it is given by F = m * g, where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s^2). Therefore, the force of gravity on the 2 kg mass is F_2kg = 2 kg * 9.8 m/s^2 = 19.6 N (downward).
- For the 3 kg mass on the right side:
The force of gravity acting on it is F_3kg = 3 kg * 9.8 m/s^2 = 29.4 N (downward).
Since the 3 kg mass experiences a greater force due to gravity, it will create a net downward force on the system. The acceleration can be calculated using Newton's second law:
F_net = (m_3kg - m_2kg) * a
where F_net is the net force, m_3kg and m_2kg are the masses, and a is the acceleration.
Substituting the values:
F_net = (3 kg - 2 kg) * a
29.4 N - 19.6 N = (3 kg - 2 kg) * a
9.8 N = 1 kg * a
Therefore, the acceleration (a) of the system is 9.8 m/s^2. Since the smaller mass (2 kg) is moving downward, its acceleration will also be 9.8 m/s^2.