An Atwood machine is constructed using two wheels (with the masses concentrated at the rims). The left wheel has a mass of 2.4 kg and radius 24.26 cm. The right wheel has a mass of 2 kg and radius 33.62 cm. The hanging mass on the left is 1.62 kg and on the right 1.09 kg. m3 m1 m4 m2 What is the acceleration of the system

The acceleration of the system is 0.7305 m/s²

Explanation:

Given that:

m₁ = 2.4 kg , m₂ = 2 kg, m₃ = 1.62 kg, m₄ = 1.09 kg

Torque (τ) = mra

For left pulley:

T₁r₁ - T₂r₁ = m₁r₁a

Dividing through by r₁

T₁ - T₂ = m₁a  1)

For right pulley:

T₂r₂ - T₃r₂ = m₂r₂a

Dividing through by r₂

T₂ - T₃ = m₂a  2)

Also

m₃g - T₁ = m₃a ... 3)

T₃ - m₄g = m₄a  ... 4)

adding equations 1, 2, 3 and 4 to get:

(m₁ + m₂ + m₃ + m₄)a = (m₃ - m₄)g

(2.4 + 2 + 1.62 + 1.09)a = (1.62 - 1.09)9.8

7.11a = 5.194

a = 5.194 / 7.11 = 0.7305

a = 0.7305 m/s²

The acceleration of the system is 0.7305 m/s²

1 - wave length

2 - amplitude

3 - crest

4 - trough

explanation:

duh.

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.