Question

In an open belt drive, the diameters of the larger and smaller pulley are 1.2 m and 0.8 m respectively. the smaller pulley rotates at 320 rpm. the center distance between the shaft is 4 m. when stationary, the initial tension on the belt is 2.8 kn. the mass of belt is 1.8 kg/m and the coefficient of friction between the belt and pulley is 0.25.

a. determine the power transmitted.

Answer 1

To determine the power transmitted by an open belt drive, one must calculate the belt's linear velocity, the frictional force at the pulley interface, and use these values to compute the power.

Step-by-step explanation:

The question provided involves an open belt drive which is a common mechanical system. The key parameters given include the diameter of large and small pulleys, the rotational speed of the smaller pulley, the tension on the belt, the mass of the belt per unit length, and the coefficient of friction between the belt and the pulleys. To determine the power transmitted by the belt, we must calculate the velocity of the belt, the frictional force acting at the pulley interface, and then use these values to compute the power.

Since the smaller pulley has a diameter of 0.8 meters and rotates at 320 rpm (revolutions per minute), its linear velocity (v) can be calculated by the formula v = (π * d * n) / 60, where d is the diameter and n is the rpm. With the linear velocity and the frictional force (calculated by the product of tension, mass per unit length, and the coefficient of friction), we can then calculate the transmitted power using the formula Power = Frictional Force * velocity.

Answer 2

To calculate the power transmitted by an open belt drive, one must find the belt's velocity using the rotational speed and diameter of the smaller pulley, then calculate the effective tension with the initial tension and the coefficient of friction, and finally use these to estimate the power transmitted.

Step-by-step explanation:

Power Transmitted by an Open Belt Drive

To determine the power transmitted by an open belt drive, several factors related to the system's mechanics must be considered, including the velocity of the belt, the tension in the belt, and the coefficient of friction between the belt and the pulleys. The velocity of the belt can be calculated using the rotational speed of the smaller pulley and its radius. Following that, the difference in tension on either side of the belt due to the frictional force provides insight into the effective tension that is used to calculate the power transmitted.

The velocity (v) of the belt is given by the linear speed of the smaller pulley, which can be calculated using the formula:
v = π x D_small x RPM_small / 60, where D_small is the diameter of the smaller pulley and RPM_small is the rotational speed of the smaller pulley. The power (P) transmitted can be estimated with the formula P = (T_1 - T_2) x v, where T_1 and T_2 are the tensions on the tight and slack side, respectively, which are influenced by the initial tension and the coefficient of friction (μ). The tensions can be further refined by using the belt’s mass and friction considerations.

Calculation Procedure

1. Calculate the velocity (v) of the belt using the given rotational speed and diameter of the smaller pulley.
2. Find the tensions (T_1 and T_2) on the belt using the coefficient of friction, the mass of the belt, and the initial tension when stationary.
3. Calculate the power transmitted (P) using the effective tension and the belt velocity.