Two masses m1 500 g and m2 1.5 kg on a frictionless, horizontal surface are connected by a light string. A force Fì with magnitude 5 N is exerted on m2 to the right. Assume the tension has
the same magnitude at every point in the string, and neglect air resistance.
(a) Since the masses are connected by a string, they are constrained to move together. Express this constraint as an equation relating the accelerations of the two masses.
(b) Draw free-body diagrams for the two masses and write down the horizontal component of the net force on each mass.
(c) Use Newton’s 2nd law and the constraint from part (a) to find the acceleration of both masses and the magnitude T of the tension in the string.

Two masses m1 500 g and m2 15 kg on a frictionless horizontal surface are connected by a light string A force Fì with magnitude 5 N is exerted on m2 to the righ class=

Respuesta :

(a) The equation relating to the acceleration of the two masses is a = F/(m₁ + m₂).

(b) The acceleration of both masses is 2.5 m/s².

(c) The magnitude  of the tension in the string is 1.25 N.

Equation relating the accelerations of the two masses

The equation relating to the acceleration of the two masses is given as;

F - T = m₂a  ---- (1)

T = m₁a      ---- (2)

F - m₁a  = m₂a

F = m₁a  + m₂a

F = a(m₁ + m₂)

a = F/(m₁ + m₂)

Free body diagram (FBD)

→       ←      →

T       T      F

Acceleration of both masses

The acceleration is calcuated as follows;

a = F/(m₁ + m₂)

a = 5/(0.5 + 1.5)

a = 5/(2)

a = 2.5 m/s²

Tension in the string

T = m₁a

T = 0.5 x 2.5

T = 1.25 N

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