Two objects with masses of 2.20 kg and 5.05 kg are connected by a light string t

Question

Two objects with masses of 2.20 kg and 5.05 kg are connected by a light string that passes over a light frictionless pulley to form an Atwood machine.

(a) Determine the tension in the string.

(b) Determine the acceleration of each object.

__________ m/s2 upwards (2.20 kg mass)

__________ m/s2 downwards (5.05 kg mass)

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

__________ m (2.20 kg mass)

__________ m (5.05 kg mass)

Two objects with masses of 2.20 kg and 5.05 kg are connected by a light string that passes over a light frictionless pulley to form an Atwood machine. (a) Determine the tension in the string. (b) Determine the acceleration of each object. __________ m/s^2 upwards (2.20 kg mass) __________ m/s^2 downwards (5.05 kg mass) (c) Determine the distance each object will move in the first second of motion if they start from rest. __________ m (2.20 kg mass) __________ m (5.05 kg mass)

Explanation / Answer

A.
m1a1=T-m1g and m2a2=T-m2g are your two equations, substitute and add and you get this -->
T= (2xm1xm2)/(m1+m2) all multiplied by 9.8 (g).

T= (2(2.2)(5.05))/(2.2+5.05) = 3.064(9.8) = 30.035 N

B.

Then just plug it in to one of your original equations.

m1a1 = T-m1g
(2.2)a = (30.035N)-(2.2)(9.8)
a= 3.852 m/s squared.

C.

First use equation Vf = Vi + at
Vf = (0) + (3.852)(1)
Vf= 3.852 m/s

Then plug that into V(squared) = Vi(squared) + 2aX

(3.852)squared = 0(squared) + 2 (3.852)X
X= 1.926m

both objects moves same distance but in opposite direction

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