Two objects with masses of 2.90 kg and 8.00 kg are connected by a light string t

Question

Two objects with masses of 2.90 kg and 8.00 kg are connected by a light string that passes over a frictionless pulley, as in the figure below.

Two objects with masses of 2.90 kg and 8.00 kg are connected by a light string that passes over a frictionless pulley, as in the figure below. Determine the tension in the string. (Enter the magnitude only.) N Determine the acceleration of each object. (Enter the magnitude only.) m/s2 Determine the distance each object will move in the first second of motion if both objects start from rest. m

Explanation / Answer

1)

mass m1 = 2.90 kg

m2 = 8 kg

apply newtons second law to mass m2

T - m2 g = - m2 a

a = (m2g - T)/m2 ------------->(1)

and apply for m1

T - m1 g = m1 a

T - m1g = m1 ((m2g - T)/m2)

m2 T - m1m2 g = m1m2 g - m1 T

T = 2 m1m2g/(m1+m2) = (2*2.9 * 8 *9.8)/{{2.9+8} = 41.71 N

2)

from eq(1)

a = (8*9.8- 41.71) / 8 = 4.58 m/s^2

3)

intial velocity u = 0

time t= 1 sec

a = 4.58 m/s^2

distance travelled   s = ut + 0.5 at^2 = 0+0.5 *4.58 *1^2 = 2.293 m

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