Explanation Given information: The rock A falls a distance ( y ) is 20 m . The coefficient of restitution between the ball and wall ( e ) is 0.2. The inclined slope ( α ) is 40 ° . The acceleration due to gravity ( g ) is 9.81 m/s 2 . Calculation: Show the free body diagram of the rock falling with the velocity acting as in Figure (1). Consider the position (1). The initial kinetic energy of the rock falling ( T 1 ) is zero as it rest initially. The expression for the gravitational potential energy of the rock falling ( V g 1 ) as follows: V g 1 = m g y The elastic potential energy of the rock ( V e 1 ) is zero. The work done ( U 1 − 3 N C ) for non-conservative force of the rock is zero. Consider the position 2. The expression for the final kinetic energy of the rock ( T 2 ) as follows: T 2 = 1 2 m v B 2 The final gravitational potential energy and elastic potential energy of the rock ( V g 2 ) and ( V e 2 ) is zero respectively. The expression for the work energy on the rock falling as follows: T 1 + V g 1 + V e 1 + U 1 − 3 N C = T 2 + V g 2 + V e 2 Substitute 0 for T 1 , m g y for V g 1 , 0 for V e 1 , 0 for U 1 − 3 N C , 1 2 m v B 2 for T 2 , 0 for V g 2 and 0 for V e 2 . 0 + m g y + 0 + 0 = 1 2 m v B 2 + 0 + 0 g y = v B 2 2 v B = 2 g y Substitute 9.81 m/s 2 for g and 20 m for y . v B = 2 × 9.81 × 20 = 19.8091 m Calculate the velocity of the rock in n direction using the relation: ( v B ) n = − v B cos α Substitute 19.8091 m for v B and 40 ° for α . ( v B ) n = − 19.8091 cos 40 ° = − 15.17 m/s Calculate the velocity of the rock in t direction using the relation: ( v B ) t = v B sin α Substitute 19.8091 m for v B and 40 ° for α . ( v B ) t = 19.8091 sin 40 ° = 12.733 m/s Calculate the velocity of the rock in tangent t -direction after impact using the relation: ( v ′ B ) t = ( v B ) t = − v B sin α Substitute 19.8091 m for v B and 40 ° for α . ( v ′ B ) t = ( v B ) t = − 19

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259977251

Author: BEER

Publisher: MCG

See similar textbooks

Concept explainers

Types of loading

In mechanical terminology, the term load indicates that external force/weight, either constant or variable, acts on a mechanical member/structure. The weight of an object of a specific material is also an external load, and the external force that works …

Videos

Question

Chapter 13.4, Problem 13.172P

To determine

Find the velocity of the rock (v′B) after the impact.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.4, Problem 13.171P

Chapter 13.4, Problem 13.173P

Students have asked these similar questions

Rock falls can cause major damage to roads and infrastructure. To design mitigation bridges and barriers, engineers use the coefficient of restitution to model the behavior of the rocks. Rock A falls a distance of 20 m before striking an incline with a slope of α = 40o. Knowing that the coefficient of restitution between rock A and the incline is 0.2, determine the velocity of the rock right after the impact, both magnitude and angle with respect to the horizontal.

A vehicle of mass 45 tonnes is moving at 85kmph. It collides with a second vehicle of mass 30 tonnes moving in the opposite direction at 50 kmph. After the collision the second vehicle has changed its speed to 2400 cm/s in the opposite direction as before the collision. Find: (i) the velocity of the first vehicle after the collision (ii) the coefficient of restitution. 1.The velocity of the first vehicle after the collision in (m/s) is 2.The Coefficient of Restitution is

The 3 kg object A and the 5 kg object B undergo oblique impact as shown in Figure P5. The coefficient of restitution between the objects is 0.6. The magnitude of the velocity of A is 10 m/s, while the magnitude of the velocity of B is 5 m/s just before impact. The angle theta =36.9?. What is the magnitude of the velocity of each particle after impact?

Chapter 13 Solutions

Vector Mechanics for Engineers: Statics and 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 0.5-lb 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 that may...Ch. 13.1 - A 2000-kg automobile starts from rest at point A...Ch. 13.1 - An athlete is holding 30 lb of weights at a height...

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.

Find the velocity of the rock ( v ′ B ) after the impact.

Solution Summary: The author shows the free body diagram of the rock falling with the velocity acting as in Figure (1).

Concept explainers

Videos

Find the velocity of the rock (v′B) after the impact.

Want to see the full answer?

Chapter 13 Solutions