A meterstick of negligible mass is placed on a fulcrum at the 0.4 m mark, with a 1 kg mass hung at the zero mark and a 0.5 kg mass hung at the 1.0 m mark. The meterstick is held horizontal and released. Immediately after release, the magnitude of the net torque on the meterstick about the fulcrum is most nearly (A) 1 N middot m (B) 2 N middot m. (C) 2.5 N middot m. (D) 7 N middot m (E) 7.5 N squareroot m

Respuesta :

To develop the problem it is necessary to solve the exercise through the equations of balance of force, specifically with those of Torque.

The torque is given by the function

[tex]\tau = F*d[/tex]

Where,

F= Force

d= Distance

Force is defined by second Newton's law as

F = mg

By balance the total torque would be given by

[tex]\tau = m_1g*d_1-m_2g*d_2[/tex]

[tex]\tau = (1kg)(9.8m/s^2)(0.4m)-(0.5)(9.8)(0.6)[/tex]

[tex]\tau = 1Nm[/tex]

Therefore the correct answer is 1Nm.

The magnitude of the net torque on the meterstick about the fulcrum is most nearly 1 N middot  m. hence, option (A) is correct.

Given data:

The distance between the fulcrum and mark is, d = 0.4 m/

The mass hung with fulcrum is, m = 1 kg.

Value of another mass is, m' = 0.5 kg.

The distance kept is, d' = 1.0 m.

The problem is  solved through the equations of balance of force, specifically with those of Torque. By balance the total torque would be given by,

[tex]\tau = Fd-F'(d'-d)\\\\\tau = mgd-m'g(d'-d)[/tex]

Here, g is the gravitational acceleration.

Solving as,

[tex]\tau = (1 \times 9.8 \times 0.4)-0.5 \times 9.8 (1-0.4)\\\\\tau = 1 \;\rm N[/tex]

Thus, we can conclude that the magnitude of the net torque on the meterstick about the fulcrum is most nearly 1 N middot  m. hence, option (A) is correct.

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