Question

Two objects with masses of m₁ = 2.70 kg and m₂ = 5.70 kg are connected by a light string that passes over a frictionless pulley, as in the figure below.

Two objects with masses of m1 = 2.70 kg and m2 = 5.70 kg are connected by a light string that passes over a frictionless pulley, as in the figure below. (a) Determine the tension in the string. (Enter the magnitude only.) N (b) Determine the acceleration of each object. (Enter the magnitude only.) m/s2 (c) Determine the distance each object will move in the first second of motion if both objects start from rest. m

(a) Determine the tension in the string. (Enter the magnitude only.)

N

(b) Determine the acceleration of each object. (Enter the magnitude only.)

m/s²

(c) Determine the distance each object will move in the first second of motion if both objects start from rest.
m

Answer 1

AT T

From above FBD:

For 1st block

m1*a = T - m1*g

For 2nd block

m2*a = m2*g - T

From above two equations:

add both equation:

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

a = (m2 - m1)*g/(m1 + m2)

a = (5.70 - 2.70)*9.81/(5.70 + 2.70)

a = 3.50 m/sec^2 = acceleration of each object (Part B)

So,

T = m2*g - m2*a

T = m2*(g - a) = 5.70*(9.81 - 3.50)

T = 35.967 N = 36.0 N (Part A)

Part C.

distance traveled in 1st second will be:

Using 2nd kinematic equation

d = U*t + (1/2)*a*t^2

d = 0*1 + (1/2)*3.50*1^2

d = 1.75 m

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