Question

. A mass m1 is connected by a light string that passes over a pulley of mass M to a mass m2 sliding on a frictionless incline. There is no slippage between the string and the pulley. The moment of inertia of the pulley is Mr2 . If m1 is 4.0 kg, m2 is 4.0 kg, and M is 4.0 kg, and the angle is 20°, then what is the acceleration of the masses?

Answer 1

The acceleration of the masses in this system is approximately 1.48 m/s^2.

Step-by-step explanation:

To find the acceleration of the masses in this system, we can start by calculating the net force acting on the system. The net force is equal to the force of gravity pulling mass m2 down the incline minus the force of friction opposing its motion. The force of friction can be calculated by multiplying the coefficient of friction (0.4) by the normal force, which is equal to the weight of m1. Once we have the net force, we can use Newton's second law (F = ma) to find the acceleration.

Let's break down the forces:

• The force of gravity on m2 is equal to m2 * g * sin(angle).
• The normal force on m1 is equal to m1 * g * cos(angle).
• The force of friction is equal to the coefficient of friction times the normal force.

Now we can calculate the net force and acceleration:

• The net force is equal to the force of gravity minus the force of friction: F_net = m2 * g * sin(angle) - (m1 * g * cos(angle) * Mk).
• The acceleration is given by Newton's second law: a = F_net / (m1 + m2).

Plugging in the values, we get:

• F_net = 4.0 kg * 9.8 m/s^2 * sin(20°) - (4.0 kg * 9.8 m/s^2 * cos(20°) * 0.4) ≈ 19.64 N - 7.81 N ≈ 11.83 N
• a = 11.83 N / (4.0 kg + 4.0 kg) = 1.48 m/s^2

Therefore, the acceleration of the masses is approximately 1.48 m/s^2.