Explanation Given: Radius of arc A B is 27 m . Radius of arc C D is 72 m . Mass of car and occupants is 250 kg . Velocity at point A is 0 m/s . Angle of Arc from A to B is 40 ° . Concept used: Write the expression for the displacement of car from A to B . h = R ( 1 − cos θ ) ...... (1) Here, h is the displacement of car from A to B , R is the radius of A B and θ is the angular displacement of car from A to B . Write the expression for kinetic energy at point A . T A = 1 2 m v A 2 Here, T A is the kinetic energy at point A , m is the mass of car and occupants and v A is the velocity of car at point A . Write the expression for kinetic energy at point B . T B = 1 2 m v B 2 Here, T B is the kinetic energy at point B and v B is the velocity of car at point B . Write the expression for the potential energy at point A . V A = m g h A Here, V A is the potential energy at point A , g is the acceleration due to gravity and h A is the elevation of point A from ground. Write the expression for the potential energy at point B . V B = m g h B Here, V B is the potential energy at point B and h B is the elevation of point B from ground. Write the expression for conservation of energy for point A to point B . T A + V A = T B + V B Substitute 1 2 m v A 2 for T A , 1 2 m v B 2 for T B , m g h A for V A and m g h B for V B in above equation. 1 2 m v A 2 + m g h A = 1 2 m v B 2 + m g h B Simplify the above expression. 1 2 m ( v B 2 − v A 2 ) = m g ( h A − h B ) Substitute 0 for v A and h for ( h A − h B ) in above expression

Vector Mechanics for Engineers: Dynamics

11th Edition

ISBN: 9780077687342

Author: Ferdinand P. Beer, E. Russell Johnston Jr., Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

See similar textbooks

Concept explainers

Forming and Shaping

Metal forming is a category of metalworking process through which the material can be given the desired shape and size by subjecting it to plastic deformation, where the component undergoes bulk deformation process upon application of loads. Unlike the s…

Videos

Question

Chapter 13.2, Problem 13.70P

To determine

The normal reaction at point B.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.2, Problem 13.69P

Chapter 13.2, Problem 13.71P

Students have asked these similar questions

A section of track for a roller coaster consists of two circular arcs ABC and CD joined by a straight portion BC. The radius of AB is 27 m and the radius of CD is 72 m. The car and its occupants, of total mass 250 kg, reach point A with practically no velocity and then drop freely along the track. Determine the normal force exerted by the track on the car as the car reaches point B . Ignore air resistance and rolling resistance.

The 50-kg package at Point A is rolling on a smooth ramp, where the ramp has two circular arcs AB and CD. Section BC is a straight path, and the radius of CD is r = 25 m. The heights of the ramp at g and b are given as a = 15 m and b = 30 m. At point 4, the package is initially at rest and then rolls freely along the ramp until it reaches point D and lands onto a cart. The air resistance and rolling resistance are ignored. a. Determine the datum line and draw Free Body Diagram (FBD) at point B, C, and D. b. Using the principle of conservation of energy, determine the normal component of acceleration at point B. c. Determine the normal force exerted by the ramp on the package at point B.

A cart has a mass of 1.5 kg. It is given some initial push toward a sensor and is slowed by a hanging mass which makes the cart turn around and speed up as it returns to its original position. This situation is illustrated in the attached image. If the acceleration towards the sensor is 0.5 m/s2 and the accaleration away from the sensor is 0.15 m/s2, a. draw the free body diagrams for the cart moving towards the sensor and away from the sensor. b. Write Newton's law for both situations and solve for the frictional force and for the force from the hanging mass.

Chapter 13 Solutions

Vector Mechanics for Engineers: Dynamics

Ch. 13.1 - Block A is traveling with a speed v0 on a smooth...Ch. 13.1 - A 400-kg satellite is placed in a circular orbit...Ch. 13.1 - A 1-Ib stone is dropped down the “bottomless pit”...Ch. 13.1 - A baseball player hits a 5.1-oz baseball with an...Ch. 13.1 - A 500-kg communications satellite is in a circular...Ch. 13.1 - Prob. 13.5P Ch. 13.1 - In an ore-mixing operation, a bucket full of ore...Ch. 13.1 - Determine the maximum theoretical speed the may be...Ch. 13.1 - A 2000-kg automobile starts from rest at point A...Ch. 13.1 - A package is projected up a 15° incline at A with...

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 normal reaction at point B .

Solution Summary: The author explains the normal reaction at point B and the expression for kinetic energy.

Concept explainers

Videos

The normal reaction at point B.

Want to see the full answer?

Chapter 13 Solutions