o1.3 points I Previous Answers SerCP10 4 PO38 Notes Ask Yo Two objects with mass

Question

o1.3 points I Previous Answers SerCP10 4 PO38 Notes Ask Yo Two objects with masses of m- 3.10 kg and m2-5.60 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. Due to the nature of this problem, do not use rounded intermediate values in your calculations including answers submitted in WebAssign.) 1.79 (b) Determine the acceleration of each object. (Enter the magnitude only.) 9.23 m/s2 (c) Determine the distance each object will move in the first second of motion if both objects start from rest

Explanation / Answer

let a be the accelration of the masses

for mass m2

along vertical

Fnet = m2*a

m2*g - T = m2*a

T = m2*g - m2*a .........(1)

for mass m1

T - m1*g = m1*a .............(2)

using 1 in 2

m2*g - m2*a - m1*g = m1*a

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

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

from (1)

tension T = m2*g - m2*(m2 - m1)*g/(m1+m2)

T = 2*m1*m2*g/(m1+m2)

part(a)

T = 2*3.1*5.6*9.8/(3.1 + 5.6) = 39.1 N

=======================

part (b)

acceleration = (5.6-3.1)*9.8/(3.1+5.6) = 2.82 m/s^2

=================

part(c)

along vertical

distance y = (1/2)*a*t^2

y = 0.5*2.83*1^2 = 1.415 m

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