Explanation Refer Figure 1. Write an expression to calculate the distance between points A and B . d A B = ( x 2 − x 1 ) 2 + ( y 2 − y 1 ) 2 (I) Here, d A B is the distance between points A and B , ( x 1 , y 1 ) is the coordinates of point A , ( x 2 , y 2 ) is the coordinates of point B . Write an expression to calculate the force acting at point A which is directed from point A to B . F = F λ A B (II) Here, F is the force vector acting at point A , F is the magnitude of the force and λ A B is the unit vector directing along A B . Write an expression to calculate the unit vector along A B . λ A B = r B − r A d A B (III) Here, r A is the point vector of point A directing from the origin and r B is the point vector of point B directing from origin. Write an expression to calculate the moment of the force at the origin O due to the force acting at point A . M O = | r A × F | (IV) Here M O is the magnitude of the moment of the force at the origin O due to the force acting at point A . Write an expression to calculate the moment of force at origin O . M O = | − F d k | (V) Here, d is the perpendicular distance from the line to the origin O of the system of the coordinates. Conclusion: Substitute 2 m for x 2 , − 4 m for x 1 , 7 m for y 2 , and − 3 for y 1 m in equation (I) to find d A B . d A B = ( 2 m − ( − 4 m ) ) 2 + ( 7 m − ( − 3 m ) ) 2 = 136 m Substitute ( 2 m ) i + ( 7 m ) j for r B , ( − 4 m ) i + ( − 3 m ) j for r A , and 136 for d A B in equation (III) to find λ A B

12th Edition

ISBN: 8220106797068

Author: BEER

Publisher: YUZU

See similar textbooks

Videos

Question

Chapter 3.1, Problem 3.18P

To determine

The perpendicular distance d from the line to the origin O of the system of the coordinates.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 3.1, Problem 3.17P

Chapter 3.1, Problem 3.19P

Students have asked these similar questions

An office building is planned with a lateral-force-resisting system designed for earthquake resistance in aseismic zone. The seismic capacity of the proposed system, expressed as a force factor, is assumed tofollow a lognormal distribution with a median of 6.5 and a standard deviation of 1.5. The ground motionfrom the largest expected earthquake at the site is estimated to correspond to an equivalent force factor of 5.5.(a) What is the estimated probability that the building will experience damage when subjected to the largest expected earthquake? (b) If the building survives (i.e., experiences no damage) during a previous moderate earthquake with aforce factor of 4.0, what is the updated probability of failure of the building under the largest expectedearthquake?(c) Suppose future occurrences of the largest expected earthquake follow a Poisson process with a mean return period of 500 years. Assuming that damage events from different earthquakes are statisticallyindependent,…

During a plant visit, it was noticed that a 12-m-long section of a 10-cm-diameter steam pipe is completely exposed to the ambient air. The temperature measurements indicate that the average temperature of the outer surface of the steam pipe is 75°C when the ambient temperature is 5°C. There are also light winds in the area at 10 km/h. The emissivity of the outer surface of the pipe is 0.8, and the average temperature of the surfaces surrounding the pipe, including the sky, is estimated to be 0°C. Determine the amount of heat lost from the steam during a 10-h-long work day. Steam is supplied by a gas-fired steam generator that has an efficiency of 80 percent, and the plant pays $1.05/therm of natural gas. If the pipe is insulated and 90 percent of the heat loss is saved, determine the amount of money this facility will save a year as a result of insulating the steam pipes. Assume the plant operates every day of the year for 10 h. State your assumptions.

An old fashioned ice cream kit consists of two concentric cylinders of radii Ra and Rb. The inner cylinder is filled with milk and ice cream ingredients while the space between the two cylinders is filled with an ice-brine mixture. Ice cream begins to form on the inner surface of the inner cylinder. To expedite the process, would you recommend rotating the inner cylinder? Justify your recommendation. icecream/ ice-brine Ra Rb

Chapter 3 Solutions

EBK VECTOR MECHANICS FOR ENGINEERS: STA

Ch. 3.1 - A foot valve for a pneumatic system is hinged at...Ch. 3.1 - 3.2A foot valve for a pneumatic system is hinged...Ch. 3.1 - It is known that a vertical force of 200 lb is...Ch. 3.1 - A 300-N force is applied at A as shown. Determine...Ch. 3.1 - A 300-N force is applied at A as shown. Determine...Ch. 3.1 - An 8-lb force P is applied to a shift lever....Ch. 3.1 - Prob. 3.7P Ch. 3.1 - An 11-lb force P is applied to a shift lever. The...Ch. 3.1 - Rod AB is held in place by the cord AC. Knowing...Ch. 3.1 - Rod AB is held in place by the cord AC. Knowing...

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 perpendicular distance d from the line to the origin O of the system of the coordinates.

Solution Summary: The author calculates the perpendicular distance d from the line to the origin O of the system of coordinates.

Videos

The perpendicular distance d from the line to the origin O of the system of the coordinates.

Want to see the full answer?

Chapter 3 Solutions