   Chapter 6, Problem 62AP

Chapter
Section
Textbook Problem

Consider a frictionless track as shown in Figure P6.62. A block of mass m1 = 5.00 kg is released from . It makes a head-on elastic collision at with a block of mass m2= 10.0 kg that is initially at rest. Calculate the maximum height to which m1 rises after the collision. Figure P6.62

To determine
The height to which m1 rises after collision.

Explanation

Given Info:

Mass of the block at position A is 5.00kg , the mass of the block at B is 10.0kg , initial speed of mass at position B is zero.

According to conservation of energy , kinetic energy will be equal to the potential energy of the mass.

Formula to calculate the kinetic energy of the mass 1 is at position A is ,

KE=12m1v12 (I)

• m1 is the block released from top.
• v1 is the speed of the mass 1 at position A before collision

Formula to calculate the potential energy of the mass 1 at position A is,

PE=m1gh (II)

• g is the acceleration due to gravity
• h is the height of the mass m1

According to the principle of conservation of energy, Potential energy of mass 1 at position A is converted into its equivalent the kinetic energy at position B.

Equate (I) and (II) to calculate v1 .

12m1v12=m1ghv12=2ghv1=2gh

Substitute 9.80ms2 for g and 5.00m for h in the above equation to calculate v1 .

v1=2(9.80ms2)(5.00m)=98.0m2s2=9.899ms19.90ms1

Collisions conserve momentum.

Apply conservation of momentum before and after collision for the masses m1 and m2

m1v1+m2v2=m1v1+m2v2 (III)

• v2 is the speed of the mass m2 at position B
• v1 is the speed of mass m1 after collision
• v2 is the speed of mass m2 after collision
• m2 is the mass of the mass of the block at rest at bottom

Initial speed of mass2 is zero.

Substitute 0m/s for v2 in the above equation and rewrite in terms of v2 .

m1v1+m2(0m/s)=m1v1+m2v2m2v2=m1v1m1v1=m1(v1v1)v2=m1m2(v1v1)

But for elastic collision

v1v2=(v1v2)

Since initial speed of m2 is zero,

Substitute 0m/s for v2 in the above equation and rewrite in terms of v2 .

v2=v1+v1 (IV)

Substitute the above equation (IV) in (III) to calculate v1

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Vitamin C deficiency symptoms include: red spots. loose teeth. anemia. all of the above.

Nutrition: Concepts and Controversies - Standalone book (MindTap Course List)

What does the word apparent mean in apparent visual magnitude?

Horizons: Exploring the Universe (MindTap Course List)

What is hereditarianism, and what is the invalid assumption it makes?

Human Heredity: Principles and Issues (MindTap Course List)

Lignin is not found in stems of_____. a. mosses b. ferns c. monocots d. a and b

Biology: The Unity and Diversity of Life (MindTap Course List) 