Which is a correct equation of motion for a the diagram shown? Assume the motion

Question

Which is a correct equation of motion for a the diagram shown? Assume the motion is in the indicated direction, and the system was released from rest. There is a friction coefficient of mu_k between m_2, and the ramp. -m_2g cos(theta) - mu_km_2g sin(theta) + m_1(g) = (m_1 +m_2)alpha -m_2g sin(theta) + mu_km_2g cos(theta) + m_1(g) = (m_1 +m_2)alpha +m_2g sin(theta) + mu_km_2g cos(theta)_m_1(g) = (m_1 +m_2)alpha +m_2g cos(theta) + mu_km_2g sin(theta) - m_1(g) = (m_1 +m_2)alpha -m_2g sin(theta) - mu_km_2g cos(theta) + m_1(g) = (m_1 +m_2)alpha A small .shelf bracket is designed to hold 80 N as shown. It is supported by a screw is .attached to the wall. Take the pivot point to be the bottom point of the bracket, and assume the bracket is slightly loose, so that it only touches the wall at the bottom. How much torque about is exerted by the 80 N load? 80 N-cm 400 N-cm 480 N-cm 720 N -cm 823 N-cm What is the minimum horizontal force exerted by the screw to hold the bracket on the wall? 67N 80 N 96 N 144 N 137 N If a 20 kg mass is hung from the cable configuration shown, what is the tension T_2 in the horizontal string? 113N 196 N 226 N 339 N 392 N If a ladder is leaning against a frictionless wall, and the floor has a coefficient of friction of only 0.2, what angle must the ladder make with the floor to keep from slipping? 0degree 51degree 68degree 78degree 84degree.

Explanation / Answer

24) e) -m2*g*sin(theta) - mue_k*m2*g*cos(theta) + m1*g = a*(m1+m2)

Let T is the tension in the string.

Apply, net force acting on m1, Fnet1 = m1*g - T

m1*a = m1*g - T

T = m1*g - m1*a ---(1)

net force acting on m2, Fnet2 = T - m2*g

m2*a = T - m2*g*sin(theta) - m2*g*cos(theta)*mue_k

T = m2*g*sin(theta) + m2*g*cos(theta)*mue_k + m2*a ---(2)

from equations 1 and 2

we get

m1*g - m1*a = m2*g*sin(theta) + m2*g*cos(theta)*mue_k + m2*a

m1*g - m2*g*sin(theta) - m2*g*cos(theta)*mue_k = a(m1+m2)

-m2*g*sin(theta) - mue_k*m2*g*cos(theta) + m1*g = a*(m1+m2)

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