Question

a block of mass 7.37 kg lies on a frictionless horizontal surface. the block is connected by a cord passing over a pulley to another block of mass 4.14 kg which hangs in the air, as shown. assume the cord to be light (massless and weightless) and unstretchable and the pulley to have no friction and no rotational inertia. 7.37 kg 4.14 kg calculate the acceleration of the first block. the acceleration of gravity is 9.8 m/s 2 . answer in units of m/s 2 .

Answer 1

To find the acceleration of the first block in the system, we can use Newton's second law and solve the equations for the tension in the rope and the acceleration.

Step-by-step explanation:

In this problem, we have two blocks connected by a massless rope over a frictionless pulley. The mass of the block on the table is 7.37 kg and the hanging mass is 4.14 kg. Since the pulley is frictionless and there is no rotational inertia, the tension in the rope is the same on either side of the pulley.

Using Newton's second law, we can write the equation for the system as:

m1 * a = m1 * g - T

m2 * a = T - m2 * g

Where m1 is the mass of the block on the table, m2 is the hanging mass, a is the acceleration, g is the acceleration due to gravity, and T is the tension in the rope.

By solving these equations simultaneously, we can find the acceleration of the first block.

Answer 2

The blocks in the given system will accelerate together at 3.526 m/s² after applying Newton's Second Law and considering the weight of the hanging block as the net force on the system.

Step-by-step explanation:

Calculating Acceleration in a Two-Block System

In the scenario described, we have two blocks of masses 7.37 kg and 4.14 kg connected by a massless cord over a frictionless pulley. To find the acceleration of the block on the horizontal surface, we apply Newton's Second Law of Motion, which states that F = ma (force equals mass times acceleration). In this system, only the weight of the hanging block (which is the force due to gravity) acts as the unbalanced force that causes acceleration.

The formula for weight is W = m*g, where W is the weight, m is the mass and g is the acceleration due to gravity. For the hanging block of mass 4.14 kg, W = 4.14 kg * 9.8 m/s2 = 40.572 N. This force is what accelerates both blocks in the system.

Since the only acceleration in the system is due to the weight of the hanging block, we can calculate the system's acceleration using the formula a = F_net / (m1 + m2), where m1 is the mass of the block on the surface and m2 is the mass of the hanging block.

The net force (F_net) here is the weight of the hanging block (only force in this frictionless and massless pulley system). Therefore, the acceleration (a) of the system is:

a = F_net / (m1 + m2)
= 40.572 N / (7.37 kg + 4.14 kg)
= 40.572 N / 11.51 kg
= 3.526 m/s2

The blocks will accelerate together at 3.526 m/s2.