Explanation Draw the free body diagram of the cart and bob as shown in Figure 1. Refer Figure 1, Consider the Bob only: Resolve the forces along x − axis (motion along x − axis ). ∑ F x = m a x m g ( sin θ ) + T sin α = m a x (I) Here, the mass of the bob is m , tension acting on the rigid bar is T , the gravitational acceleration is g , and the acceleration along x − axis is a x . Resolve the force along y − axis (no motion along y − axis ). ∑ F y = m a y − m g ( cos θ ) + T cos α = m ( 0 ) T cos α − m g ( cos θ ) = 0 (II) Consider both bob and cart: Resolve the forces along x − axis (motion along x − axis ). ∑ F x = m a x P + ( M + m ) g ( sin θ ) = ( M + m ) a x a x = P + ( M + m ) g sin θ M + m (II) Here, the mass of the cart is M , force acting on the cart is P . Conclusion: Substitute P + ( M + m ) g sin θ M + m for a x in Equation (I) and obtain T . m g ( sin θ ) + T sin α = m [ P + ( M + m ) g sin θ M + m ] T sin α = m [ P + ( M + m ) g sin θ M + m ] − m g sin θ T = m [ P + ( M + m ) g sin θ ( M + m ) sin α ] − m g sin θ sin α Substitute m [ P + ( M + m ) g sin θ ( M + m ) sin α ] − m g sin θ sin α for T in Equation (III)

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ISBN: 9781118885840

Author: James L. Meriam, L. G. Kraige, J. N. Bolton

Publisher: WILEY

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Chapter 3.4, Problem 10P

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