Two blocks with different mass are attached to either end of a light rope that passes over a light, frictionless pulley that is suspended from the ceiling. the masses are released from rest, and the more massive one starts to descend. after this block has descended a distance 1.30 m, its speed is 3.50m/s . if the total mass of the two blocks is 14.0 kg, what is the mass of the more massive block?

m₁ = 10.36 Kg

Explanation:

Newton's second law:

∑F = m*a Formula (1)

∑F : algebraic sum of the forces in Newton (N)

m : mass in kilograms (kg)

a : acceleration in meters over second square (m/s²)

Calculating of the acceleration (a)

Because the masses moves with uniformly accelerated movement we apply the following formula:

vf²=v₀²+2*a*d  Formula (2)

Where:  

d:displacement in meters (m)  

vi: initial speed in m/s  

vf: final speed in m/s  

a: acceleration in m/s²

Data:

vi = 0

vf = 3.5 m/s

d = 1.3 m

We replace data in the formula (2) to calculate the acceleration of the masses:

vf²=vi²+2*a*d

a= 4.7 m/s²

Problem development

m₁+m₂= 14.0 kg

g=9.81 m/s² acceleration due to gravity

W= m*g: Weight

We take m₁>  m₂We identify a direction as positive and observe that m₁ will accelerate downwards and  m₂ will accelerate upwards, since m₁>  m₂.

Newton's second law for m₁:

We apply the formula (1)

We take + in the direction of the downward movement:

∑F = m*a

W₁ -T = m₁ *a

W₁- m₁ *a=T  Equation (1)

Newton's second law for m₂:

We take + in the direction of the upward movement:

∑F = m*a

T-W₂ = m₂*a

T = W₂+m₂*a  Equation (2)

Equation (1)=Equation (2) =T

W₁- m₁ *a = W₂+m₂*a

W₁- W₂ = m₁ *a + m₂*a

(m₁-m₂ )*g =a*( m₁ + m₂ )       m₁+ m₂ =14  ,   m₂ =14-m₁

(m₁-(14-m₁ )*9.8 = 4.7(14)

(m₁-14+m₁ )= ( 4.7((14) / (9.8)

2m₁ = 6.71 + 14

2m₁ = 20.71

m₁ = 10.36 Kg

m₂= 14 kg-10.36 kg

m₂= 3.64 kg

The answer is d) by requesting advice on science internet sites

Is a  vector quantity  that refers to "the rate at which an object changes its position." imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. while this might result in a frenzy of activity, it would result in a zero velocity. because the person always returns to the original position, the motion would never result in a change in position. since velocity is defined as the rate at which the position changes, this motion results in zero velocity. if a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. every step must go into moving that person further from where he or she started. for certain, the person should never change directions and begin to return to the starting position.