SOLUTION(A) Find the final speed after collision.Let m₁ and V₁¡ represent the massand initial velocity of the pickup truck,while m₂ and V2; pertain to thecompact. Apply conservation ofmomentum.Substitute the values and solve for thefinal velocity, Vf.m₁v₁i + m₂V₂iVf(B) Find the change in velocity for each vehicle.Change in velocity of the pickup truck.Change in velocity of the compact car.Calculate the final kinetic energy of thesystem and the change in kineticenergy, AKE.==Pi Pf(1.80 × 10³ kg)(15.0 m/s) + (9.00 × 10² kg)(-15.0 m/s)(1.80 x 10³ kg + 9.00 × 10² kg)vf+5.00 m/s(C) Find the change in kinetic energy of the system.Calculate the initial kinetic energy ofthe system.=(m₁ + m₂) vfAV₁ = VfV₁₁ = 5.00 m/s 15.0 m/s = = -10.0 m/sAV₂ = VfV₂i == 5.00 m/s - (-15.0 m/s) = 20.0 m/sKE₁ = 1/3m₁v₁/² + 1/{m₂v₂/²=−(1.80 × 10³ kg)(15.0 m/s)²+ (9.00 x 10² kg)(-15.0 m/s)²= 3.04 x 105 J1KE₁ = =— (m₁ + m₂)v₁²2(1.80 × 10³ kg + 9.00 × 10² kg)(5.00 m/s)²= 3.38 x 104 JAKE = KE - KE; = -2.70 × 105 J EXERCISEHINTS: GETTING STARTED | I'M STUCK!Use the values from PRACTICE IT to help you work this exercise. Suppose the same two vehicles are bothtraveling eastward, the compact car leading the pickup truck. The driver of the compact car slams on thebrakes suddenly, slowing the vehicle to 6.09 m/s. If the pickup truck traveling at 17.7 m/s crashes intothe compact car, find the following.(a) the speed of the system right after the collision, assuming the two vehicles become entangledm/s(b) the change in velocity for both vehiclesm/sAv truckm/sAv car==(c) the change in kinetic energy of the system, from the instant before impact (when the compactcar is traveling at 6.09 m/s) to the instant right after the collisionΔΚΕ =J

Introduction: Law of conservation of momentum between object 1 & 2 in an isolated system, where no external force is acting, then the total momentum of the two objects before and after collision are same. Pi = Pf (Initial momentum of system= Final momentum of the system).Solution: Diagram of the vehicles before collision as given: Given data: Shown as per diagram. 1) To find the speed of system (Pick up truck + compact car) right after collision: Solution: Applying conservation of momentum, Pi = Pf . (m1 x v1i) + (m2 x v2i) = (m1+m2) Vf (where, Vf is the final velocity of system right after collision in m/s) Vf = (1800 x 17.7) + (900 x 6.09)(1800 + 900)= 373412700= 13.8 m/s. Hence, Final speed of the system right after the collision= 13.8 m/s 2) To find the change in velocities: (a) Change in velocity of pick up truck (∆V1)= Vf - V1i = (13.8 - 17.7)= -3.9 m/s. (b) Change in velocity of compact car (∆V2)= Vf - V2i = (13.8 - 6.09)= 7.71 m/s. 3) To find the change in K.E of the system: Initial K.E. of the system= 12m1(v1i)2 + 12m2(v2i)2 = 12 x 1800 x (17.7)2 + 12 x 900 x 6.092 = 2,81,961 + 16,689.645= 2,98,650.645= 2.98 x 105 J. Final K.E of the system=12 (m1 + m2). Vf2= 12 (1800 + 900) x (13.8)2 = 1350 x 190.44 = 2,57,094= 2.57 x 105 J. Hence, Change in K.E (∆K.E)= Final K.E of the system - Initial K.E of the system= (2.57 - 2.98) X 105 J. = -0.41 x 105 J = -4.1 x 104 J (∆K.E)= -4.1 x 104 J.

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Use the values from PRACTICE IT to help you work this exercise. Suppose the same two vehicles are both traveling eastward, the compact car leading the pickup truck. The driver of the compact car slams on the brakes suddenly, slowing the vehicle to 6.09 m/s. If the pickup truck traveling at 17.7 m/s crashes into the compact car, find the following. (a) the speed of the system right after the collision, assuming the two vehicles become entangled m/s (b) the change in velocity for both vehicles Avtruck m/s Av car m/s = (c) the change in kinetic energy of the system, from the instant before impact (when the compact car is traveling at 6.09 m/s) to the instant right after the collision ΔΚΕ = J

Use the values from PRACTICE IT to help you work this exercise. Suppose the same two vehicles are both traveling eastward, the compact car leading the pickup truck. The driver of the compact car slams on the brakes suddenly, slowing the vehicle to 6.09 m/s. If the pickup truck traveling at 17.7 m/s crashes into the compact car, find the following. (a) the speed of the system right after the collision, assuming the two vehicles become entangled m/s (b) the change in velocity for both vehicles Avtruck m/s Av car m/s = (c) the change in kinetic energy of the system, from the instant before impact (when the compact car is traveling at 6.09 m/s) to the instant right after the collision ΔΚΕ = J

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Centripetal Force

A particle, body, object or certain mass while travelling in a rotational path or semicircular path, experiences an inertia force. If that inertia force pulls the towards the inward of the imaginary circle in the rotation, it is termed as centripetal force.

Question

SOLUTION
(A) Find the final speed after collision.
Let m₁ and V₁¡ represent the mass
and initial velocity of the pickup truck,
while m₂ and V2; pertain to the
compact. Apply conservation of
momentum.
Substitute the values and solve for the
final velocity, Vf.
m₁v₁i + m₂V₂i
Vf
(B) Find the change in velocity for each vehicle.
Change in velocity of the pickup truck.
Change in velocity of the compact car.
Calculate the final kinetic energy of the
system and the change in kinetic
energy, AKE.
=
=
Pi Pf
(1.80 × 10³ kg)(15.0 m/s) + (9.00 × 10² kg)(-15.0 m/s)
(1.80 x 10³ kg + 9.00 × 10² kg)vf
+5.00 m/s
(C) Find the change in kinetic energy of the system.
Calculate the initial kinetic energy of
the system.
=
(m₁ + m₂) vf
AV₁ = VfV₁₁ = 5.00 m/s 15.0 m/s = = -10.0 m/s
AV₂ = VfV₂i =
= 5.00 m/s - (-15.0 m/s) = 20.0 m/s
KE₁ = 1/3m₁v₁/² + 1/{m₂v₂/²
=
−(1.80 × 10³ kg)(15.0 m/s)²
+ (9.00 x 10² kg)(-15.0 m/s)²
= 3.04 x 105 J
1
KE₁ = =— (m₁ + m₂)v₁²
2
(1.80 × 10³ kg + 9.00 × 10² kg)(5.00 m/s)²
= 3.38 x 104 J
AKE = KE - KE; = -2.70 × 105 J

EXERCISE
HINTS: GETTING STARTED | I'M STUCK!
Use the values from PRACTICE IT to help you work this exercise. Suppose the same two vehicles are both
traveling eastward, the compact car leading the pickup truck. The driver of the compact car slams on the
brakes suddenly, slowing the vehicle to 6.09 m/s. If the pickup truck traveling at 17.7 m/s crashes into
the compact car, find the following.
(a) the speed of the system right after the collision, assuming the two vehicles become entangled
m/s
(b) the change in velocity for both vehicles
m/s
Av truck
m/s
Av car
=
=
(c) the change in kinetic energy of the system, from the instant before impact (when the compact
car is traveling at 6.09 m/s) to the instant right after the collision
ΔΚΕ =
J

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