University Physics Volume 1
18th Edition
ISBN: 9781938168277
Author: William Moebs, Samuel J. Ling, Jeff Sanny
Publisher: OpenStax - Rice University
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Chapter 9, Problem 98AP
Derive the equations giving the final speeds for two objects that collide elastically, with the mass of the objects being
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Two blocks of masses my and my approach each other on a horizontal table with the same constant speed, vo, as measured by a laboratory observer. The blocks undergo a perfectly elastic collision, and it is observed that m; stops but my moves opposite its original motion with some constant speed, v. (a) Determine the ratio of the two masses, m,/m₂. (b) What is the ratio of their speeds, v/vo?
Two blocks of masses my and my approach each other on a horizontal table with the same constant speed, vo, as measured by a laboratory observer. The blocks undergo a perfectly elastic collision, and it is observed that m; stops but my moves opposite its original motion with some constant speed, v. (a) Determine the ratio of the two masses, m,/m₂. (b) What is the ratio of their speeds, v/vo?
A perfectly elastic collision between two colliding objects of masses m₁ and m₂ is a collision that conserves
both the quantity known as the total linear momentum and the quantity known as the total kinetic energy.
For a perfectly elastic collision between mass m₁ moving at speed v₁; and mass m₂ moving at speed v2; prior
to the collision, the conservation of total linear momentum is expressed as:
m₁v₁i + m₂v₂i = m₁v₁f + m2 V2 f
and the conservation of total kinetic energy is expressed as:
1
1
1
m₁(v₁i)² + ½ m2(v2;)² = = m₁(v₁ƒ)² + 21/1m2 (v21) ²
2
where Vif and V2f are the speeds of the masses, respectively, after the collision event.
Part (a) Determine vif and V2f in terms of m₁, 22, Vli, V2i.
Part (b) If m₁ = m₂ and v₁i = 5 [m/s] and mass 2 is initially at rest (i.e., a stationary target), find the
direction and the speed of each mass after the collision.
Part (c) If m₁ = m2, v₁i = 5 [m/s] and v2i = -5 [m/s] so that the two masses are initially moving toward
each other with equal…
Chapter 9 Solutions
University Physics Volume 1
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The...Ch. 9 - Prob. 57PCh. 9 - A proton traveling at 3.0106m/s scatters...Ch. 9 - Prob. 59PCh. 9 - A family is skating. The father (75 kg) skates at...Ch. 9 - Prob. 61PCh. 9 - Two cars of the same mass approach an extremely...Ch. 9 - Three point masses are placed at the corners of a...Ch. 9 - Two particles of masses m1 and m2 separated by a...Ch. 9 - Two particles of masses m1 and m2 separated by a...Ch. 9 - Two particles of masses m1 and m2 , move uniformly...Ch. 9 - Two particles of masses m1 and m2 move uniformly...Ch. 9 - Find the center of mass of a one-meter long rod,...Ch. 9 - Find the center of mass of a rod of length L whose...Ch. 9 - Find the center of mass of a rectangular block of...Ch. 9 - Find the center of mass of a rectangular material...Ch. 9 - A cube of side a is cut out of another cube of...Ch. 9 - Find the center of mass of a cone of uniform...Ch. 9 - Find the center of mass of a thin wire of mass in...Ch. 9 - Find the center of mass of a uniform thin...Ch. 9 - Find the center of mass of a sphere of mass M and...Ch. 9 - (a) A 5.00-kg squid initially at rest ejects 0.250...Ch. 9 - A rocket takes off from Earth and reaches a speed...Ch. 9 - Repeat the preceding problem but for a rocket that...Ch. 9 - How much fuel would be needed for a 1000-kg rocket...Ch. 9 - What exhaust speed is required to accelerate a...Ch. 9 - Unreasonable Results Squids have been reported to...Ch. 9 - Two 70-kg canoers paddle in a single, 50-kg canoe....Ch. 9 - Which has a larger magnitude of momentum: a...Ch. 9 - A driver applies the brakes and reduces the speed...Ch. 9 - You friend claims that momentum is mass multiplied...Ch. 9 - Dropping a glass on a cement floor is more likely...Ch. 9 - Your 1500-kg sports car accelerates from 0 to 30...Ch. 9 - A ball of mass m is dropped. 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