A filled treasure chest of mass m with a long rope tied around its center lies i

Question

A filled treasure chest of mass m with a long rope tied around its center lies in the middle of a room. Dirk wishes to drag the chest, but there is friction between the chest and the floor with a coefficient of static friction mu_s. If the angle between the rope and the floor is theta, what is the magnitude of the tension required to just get the chest moving? Express your answer in terms of m, mu_s, theta, and g. A filled treasure chest (m = 375 kg) with a long rope tied around its center lies in the middle of a room. Dirk wishes to drag the chest, but there is friction between the chest and the floor with mu_s = 0.52. If the angle between the rope and the floor is 30.0 degree, what is the magnitude of the tension required to just get the chest moving?

Explanation / Answer

(16)
Equating Horizontal and vertical Forces,
Normal Force, Fn = m*g - T*sin()
Friction Force, Fr = us*Fn = us * (m*g - T*sin())

To just get the chest moving,
T*cos() =  us * (m*g - T*sin())
T*cos() + us*T*sin() = us*m*g
T = (us*m*g) / (cos() + us*sin())

17)
Substituing the values in above eq,
T = (us*m*g) / (cos() + us*sin())
T = (0.52 * 375 * 9.8 ) / ( cos(30) + 0.52 * sin(30) )
T = 1697 N

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