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)

8th Edition

ISBN: 9781118885840

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

Publisher: WILEY

See similar textbooks

Videos

Question

Chapter 3.4, Problem 10P

To determine

The steady-state angle (α) and evaluate the expression for P=0.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 3.4, Problem 9P

Chapter 3.4, Problem 11P

Students have asked these similar questions

Q6: A turbocharged engine with a compression ratio of 8 is being designed using an air standard cycle. The ambient air is assumed to be 300K and 100 kPa. The temperature at the end of the compression in the cylinder is desired to be 1000K, assuming no combustion prior to reaching TDC. At the end of the cylinder expansion the temperature is also desired to be 1000K. If both the turbine and the compressor have mechanical efficiencies of 80%, what will be the pressure ratio of the compressor and what will be the turbine exhaust temperature?

Q5: A 5.6 litre V8 engine with a compression ratio of 9.4:1 operates on an air-standard Otto cycle at 2800 RPM, with a volumetric efficiency of 90 % and a stoichiometric air-fuel ratio using gasoline. The exhaust flow undergoes a temperature drop of 44ºC as it passes through the turbine of the supercharger. Calculate (a) mass flow rate of exhaust gas and (b) power available to drive the turbocharger compressor.

do handwritten

Chapter 3 Solutions

Engineering Mechanics: Dynamics

Ch. 3.4 - Prob. 1P Ch. 3.4 - The 50-kg crate is stationary when the force P is...Ch. 3.4 - At a certain instant, the 80-lb crate has a...Ch. 3.4 - A man pulls himself up the 15° incline by the...Ch. 3.4 - The 10-Mg truck hauls the 20-Mg trailer. If the...Ch. 3.4 - A 60-kg woman holds a 9-kg package as she stands...Ch. 3.4 - During a brake test, the rear-engine car is...Ch. 3.4 - Prob. 8P Ch. 3.4 - The inexperienced driver of an all-wheel-drive car...Ch. 3.4 - Prob. 10P

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The steady-state angle ( α ) and evaluate the expression for P = 0 .

Videos

The steady-state angle (α) and evaluate the expression for P=0.

Want to see the full answer?

Chapter 3 Solutions