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

gpe = mass x gravity constant x height or… gpe = mgh

where… mass: measured in kilograms (kg)

gravity: gravity constant on earth = 10.00 m/s2

height: measured in meters (m)

gpe: measured in joules (j) or kilojoules (kj)

how do you solve gpe?

gravitational potential energy (gpe) is the energy an object has because of its position above the. ground.

gpe = mass x gravity constant x height or… gpe = mgh.

mass:

note: to earn full marks when solving science word problems, you must show your work:

formula.

example:

given values:

mass = 0.3 kg.