Explanation Given information: The acceleration ( a E ) at a rate of 1.2 m/s 2 ( ↑ ) until it reaches a speed ( v E ) of 7.8 m/s . The initial position ( y E ) 0 of the ball is 12 m . The speed ( v B ) 0 of the ball is 20 m/s ( ↑ ) . Calculation: Show the v-t curve of the elevator and ball in Figure (1). Calculate the time ( t 2 ) using the relation: v E = ( v E ) 0 + a E t 2 Substitute 0 for ( v E ) 0 , 7.8 m/s for v E and 1.2 m/s 2 for a E . 7.8 = 0 + ( 1.2 × t ) t 2 = 7.8 1.2 t 2 = 6.5 sec Calculate the time ( t t o p ) at which the ball reaches the top of its trajectory: v B = ( v B ) 0 − g ( t t o p − t ) Here, t is time at the elevator begins to move and v B is final velocity of ball. Substitute 0 for v B , 20 m/s for ( v B ) 0 , 9.81 m/s 2 for g and 2 sec for t 2 . 0 = 20 − 9.81 ( t t o p − 2 ) t t o p = ( − 20 − 9.81 ) + 2 t t o p = 4.0387 sec Calculate the position ( y E ) of the elevator at time t top using the relation: ( y E ) t t o p = ( y E ) 0 + ( 1 2 a E t top 2 ) Substitute − 12 m for ( y E ) 0 , 1.2 m/s 2 for a E , and 4.0387 sec for t t o p . ( y E ) t t o p = − 12 + ( 1 2 × ( 1.2 ) × 4.0387 2 ) = − 12 + 9.787 = − 2.213 m Calculate the position ( y B ) of the ball when time ( t t o p ) is using the relation: ( y B ) t t o p = 1 2 ( v B ) 0 ( t top − t ) Substitute 20 m/s for ( v B ) 0 , 2 sec for t and 4.0387 sec for t t o p . ( y B ) t t o p = 1 2 × 20 × ( 4.0387 − 2 ) = 20.387 m Calculate the position ( y E ) t 2 of the elevator at time t 2 : ( y E ) t 2 = ( y E ) 0 + ( 1 2 v E t 2 ) Substitute − 12 m for ( y E ) 0 , 7

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259638091

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

Publisher: McGraw-Hill Education

See similar textbooks

Concept explainers

Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be create…

Videos

Question

Chapter 11.3, Problem 11.75P

To determine

When the ball will hit (t) the elevator.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.3, Problem 11.74P

Chapter 11.3, Problem 11.76P

Students have asked these similar questions

CORRECT AND DETAILED SOLUTION WITH FBD ONLY. I WILL UPVOTE THANK YOU. CORRECT ANSWER IS ALREADY PROVIDED. I REALLY NEED FBD. The cantilevered spandrel beam shown whose depth tapers from d1 to d2, has a constant width of 120mm. It carries a triangularly distributed end reaction.Given: d1 = 600 mm, d2 = 120 mm, L = 1 m, w = 100 kN/m1. Calculate the maximum flexural stress at the support, in kN-m.2. Determine the distance (m), from the free end, of the section with maximum flexural stress.3. Determine the maximum flexural stress in the beam, in MPa.ANSWERS: (1) 4.630 MPa; (2) 905.8688 m; (3) 4.65 MPa

CORRECT AND DETAILED SOLUTION WITH FBD ONLY. I WILL UPVOTE THANK YOU. CORRECT ANSWER IS ALREADY PROVIDED. I REALLY NEED FBD A concrete wall retains water as shown. Assume that the wall is fixed at the base. Given: H = 3 m, t = 0.5m, Concrete unit weight = 23 kN/m3Unit weight of water = 9.81 kN/m3(Hint: The pressure of water is linearly increasing from the surface to the bottom with intensity 9.81d.)1. Find the maximum compressive stress (MPa) at the base of the wall if the water reaches the top.2. If the maximum compressive stress at the base of the wall is not to exceed 0.40 MPa, what is the maximum allowable depth(m) of the water?3. If the tensile stress at the base is zero, what is the maximum allowable depth (m) of the water?ANSWERS: (1) 1.13 MPa, (2) 2.0 m, (3) 1.20 m

CORRECT AND DETAILED SOLUTION WITH FBD ONLY. I WILL UPVOTE THANK YOU. CORRECT ANSWER IS ALREADY PROVIDED. I NEED FBD A short plate is attached to the center of the shaft as shown. The bottom of the shaft is fixed to the ground.Given: a = 75 mm, h = 125 mm, D = 38 mmP1 = 24 kN, P2 = 28 kN1. Calculate the maximum torsional stress in the shaft, in MPa.2. Calculate the maximum flexural stress in the shaft, in MPa.3. Calculate the maximum horizontal shear stress in the shaft, in MPa.ANSWERS: (1) 167.07 MPa; (2) 679.77 MPa; (3) 28.22 MPa

Chapter 11 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 11.1 - A bus travels the 100 miles between A and B at 50...Ch. 11.1 - Two cars A and B race each other down a straight...Ch. 11.1 - A snowboarder starts from rest at the top of a...Ch. 11.1 - The motion of a particle is defined by the...Ch. 11.1 - The vertical motion of mass A is defined by the...Ch. 11.1 - A loaded railroad car is rolling at a constant...Ch. 11.1 - A group of hikers uses a GPS while doing a 40-mile...Ch. 11.1 - The motion of a particle is defined by the...Ch. 11.1 - A girl operates a radio-controlled model car in a...Ch. 11.1 - The motion of a particle is defined by the...

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.

When the ball will hit ( t ) the elevator.

Solution Summary: The author shows the v-t curve of the elevator and ball in Figure (1).

Concept explainers

Videos

When the ball will hit (t) the elevator.

Want to see the full answer?

Chapter 11 Solutions