Physics, 14.11.2019 21:31, sonnyboi2305

Two gliders with different masses (m1 and m2) are placed on a frictionless air track and given initial velocities v1i and v2i. they elastically collide, bouncing off each other. (a) determine the equations for the final velocity of each glider. (b) for m1 = 0.51 kg, m2 = 0.98 kg, v1i=1.5 im/s, and v2i=-2.2 im/s, find v1f and v2f.

Answers: 2

Show answers

Answers

answered: steven983

(a)

vf₁ = (m₁*v₀₁+2m₂v₀₂- m₂v₀₁) / ( m₁+ m₂)

vf₂ = (v₀₁ - v₀₂ ) + ((m₁*v₀₁+2m₂v₀₂- m₂v₀₁) / ( m₁+ m₂))

(b)

vf₁ = - 3.367 m/s

vf₂ = 0.333 m/s

Explanation:

Theory of collisions

Linear momentum is a vector magnitude (same direction of the velocity) and its magnitude is calculated like this:

p=m*v

where

p:Linear momentum

m: mass

v:velocity

There are 3 cases of collisions : elastic, inelastic and plastic.

For the three cases the total linear momentum quantity is conserved:

P₀ = Pf Formula (1)

P₀ :Initial linear momentum quantity

Pf : initial linear momentum quantity

Nomenclature

m₁ : mass of the first glider

m₂ : mass of the second glider

v₀₁:initial velocity of m₁

v₀₂ :initial velocity of m₂

vf₁: final velocity of m₁

vf₂: final velocity of m₂

Data

m₁,m₂,v₀₁i,v₀₂i

Problem development

(a) We appy the formula (1):

Because the initial and final velocities are in the same direction (i), (i) is canceled in the equation:

P₀ = Pf

m₁*v₀₁ + m₂*v₀₂ = m₁*vf₁ + m₂*vf₂ Equation( 1)

Because the shock is elastic, the coefficient of elastic restitution (e) is equal to 1.

$e=\frac{v_{f2} -v_{f1}}{v_{o1} -v_{o2}}$

(equation 1)

vf₂ = (v₀₁ - v₀₂ ) + vf₁ Equation( 2)

We replace Equation( 2) in Equation( 1)

m₁*v₀₁ + m₂*v₀₂ = m₁*vf₁ + m₂* ((v₀₁ - v₀₂ ) + vf₁ )

m₁*v₀₁ + m₂*v₀₂ = m₁*vf₁ + m₂*v₀₁ - m₂ v₀₂ + m₂vf₁

m₁*v₀₁ + m₂*v₀₂ + m₂ v₀₂ - m₂*v₀₁= m₁*vf₁ + m₂vf₁

m₁*v₀₁+2m₂v₀₂- m₂v₀₁ = vf₁( m₁+ m₂)

vf₁ = (m₁*v₀₁+2m₂v₀₂- m₂v₀₁) / ( m₁+ m₂) Equation (3)

vf₂ = (v₀₁ - v₀₂ ) + vf₁

vf₂ = (v₀₁ - v₀₂ ) + ((m₁*v₀₁+2m₂v₀₂- m₂v₀₁) / ( m₁+ m₂)) Equation (4)

(b) Data

m₁, = 0.51 kg

m₂ = 0.98 kg

v₀₁,= 1.5 im/s

v₀₂ = -2.2 im/s

We replace data in the Equation (3) to calculate vf₁

vf₁ = (m₁*v₀₁+2m₂v₀₂- m₂v₀₁) / ( m₁+ m₂)

vf₁ = ( 0.51)* ( 1.5)+2 ( 0.98) ( -2.2) -(0.98) ( 1.5) / ( 0.51+ 0.98)

vf₁ = -3.367 m/s

We replace data in the Equation (2) to calculate vf₂

vf₂ = (v₀₁ - v₀₂ ) + vf₁

vf₂ = (1.5 -(-2.2 ) +(-3.367)

vf₂ = (1.5+2.2 ) -3.367

vf₂ = 0.333 m/s

answered: Guest

$efficiency \: = \frac{useful \: energy \: output}{total \: energy \: input} \ \times$ $100$ therefore, the efficiency is: $\frac{222}{222} \times 100$ $= 100\%$

answered: Guest

You get 6 for mechanical

Other questions on the subject: Physics

Physics, 22.06.2019 13:00, maiahfogel1351

Which of the following are appropriate acceleration units?

Answers: 1

continue

Physics, 22.06.2019 14:30, lizzie3545

Aweight lifter raises a 1600 n barbell to a height of 2.0 meters. how much work was done? w = fd a) 30 joules b) 3000 joules c) 320 joules d) 3200 joules

Answers: 2

continue

Physics, 22.06.2019 15:20, mjwaple57

Acarpenter builds an exterior house wall with a layer of wood 2.9 cm thick on the outside and a layer of styrofoam insulation 2.3 cm thick on the inside wall surface. the wood has k=0.080w/(m⋅k), and the styrofoam has k= 0.010 w/(m⋅k). the interior surface temperature is 19.0 ∘c , and the exterior surface temperature is -15.0 ∘c . a.)what is the temperature at the plane where the wood meets the styrofoam? celsius b.)what is the rate of heat flow per square meter through this wall? /m^2

Answers: 2

continue

Physics, 22.06.2019 19:50, nadiareese

Aleaky 10-kg bucket is lifted from the ground to a height of 15 m at a constant speed with a rope that weighs 0.7 kg/m. initially the bucket contains 45 kg of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 15-m level. find the work done. (use 9.8 m/s2 for g.) show how to approximate the required work by a riemann sum. (let x be the height in meters above the ground. enter xi* as xi.) lim n → ∞ n (9.8)(45−3 xi) i = 1 δx express the work as an integral. 0 dx evaluate the integral. (round your answer to the nearest integer.) j

Answers: 3

continue

Do you know the correct answer?

Two gliders with different masses (m1 and m2) are placed on a frictionless air track and given initi...