4. A hoop of mass M and radius R lies motionless on a frictionless surface. Aimed towards it, but off center by a distance d < R, is a smaller object of mass m<< M and radius r« R moving at speed v. The two objects undergo a totally inelastic collision. Note: For m <« M , it can be assumed that the center of mass motion of the composite object is appropriately approximated by being located at the center of mass of the hoop and that V would be parallel to v. a. Find an expression in terms of M , R , m, v and d for i. the final translational speed V , and ii. the final rotational speed, w, of the composite object. b. What are the possible range of values for both @ and V , and what values ofd correspond to each? c. Find an expression for how much energy was lost in the collision, in terms of m, M, d, R, and K,(=}mv² ). d. What is the maximum and minimum energy loss possible by varying the value of d, and e. What are the values of w and V for M = 2.0 kg, m= 25 g, R=15 cm, d = 10 cm, and v=1.0 m/s . %3D

4. A hoop of mass M and radius R lies motionless on a frictionless surface. Aimed towards it, but off center by a distance d < R, is a smaller object of mass m<< M and radius r« R moving at speed v. The two objects undergo a totally inelastic collision. Note: For m <« M , it can be assumed that the center of mass motion of the composite object is appropriately approximated by being located at the center of mass of the hoop and that V would be parallel to v. a. Find an expression in terms of M , R , m, v and d for i. the final translational speed V , and ii. the final rotational speed, w, of the composite object. b. What are the possible range of values for both @ and V , and what values ofd correspond to each? c. Find an expression for how much energy was lost in the collision, in terms of m, M, d, R, and K,(=}mv² ). d. What is the maximum and minimum energy loss possible by varying the value of d, and e. What are the values of w and V for M = 2.0 kg, m= 25 g, R=15 cm, d = 10 cm, and v=1.0 m/s . %3D

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)...

See similar textbooks

Related questions

Q: A 2.20-kg particle has a velocity (2.10 î − 5.00 ĵ) m/s, and a 3.50-kg particle has a velocity (1.00…

Q: Two objects of equal mass are moving with equal speeds. They collide and move off together…

Q: A car is stopped for a traffic signal. When the light turns green, the car accelerates, increasing…

A: (a) The magnitude of linear impulse experienced by the passenger during the car's acceleration is…

Q: A car with a mass of 1000 kg collides perpendicular to the wall at a speed of 20 m/s and then…

A: Given, Mass of car (m)= 1000kg Speed of car before collision (u)= 20m/s (right side ) Speed of…

Q: A block m starts at the bottom of a ramp of length L and angle 0 at rest. A block with mass 2m…

A: We will use conservation of momentum and conservation of energy,

Q: Two blocks of masses m₁ = 5.9kg and mp 19.1kg, resting on a frictionless table, are connected to a…

A: Asit is given that the blocks are released from rest, so initially center of mass was at rest.

Q: Ball B, moving in the positive direction of an x axis at speed v, collides with stationary ball A at…

A: Apply the momentum conservation equation along the horizontal direction.…

Q: A 1.0 kg cart travelling at 2.0 m/s [east] collides with a stationary cart, of mass 3.0 kg. The two…

A: Given: The mass is given as: m1=1 kgm2=3 kg The initial velocity is v1=2 m/s iv2=0 m/s after the…

Q: Two objects of masses m, and m, are subject to no external forces. Object 1 is traveling with…

Q: A mass of 2.80 kg is traveling in the +x direction with velocity 4.30 m/s. It strikes a stationary…

A: Let mass of first block, m1=2.8 kg Mass of second block, m2=4.33 kg Initial velocity of first block,…

Q: An asteroid with a mass of 75 kg is travelling in deep space, far away from the the gravitational…

Q: Two particles with masses in the ratio 1 : 9 are moving with equal kinetic energies. The magnitude…

A: Given data: m1/m2 = 1/9 The kinetic energies of particles are equal KE1 = KE2 Required: The ratio…

Q: An atomic nucleus at rest at the origin of an xy coordinate system transforms into three particles.…

A: Let the mass of original nucleus = M Initial velocity of original nucleus = 0 m/s m1 = 16.7×10-27 kg…

Q: A car is stopped for a traffic signal. When the light turns green, the car accelerates, increasing…

Q: The mass of a particle is 2 kg and its velocity is given by V1 = 2i-10tj m / s, with time in t s.…

Q: Two manned satellites approaching one another at a relative speed of 0.300 m/s intend to dock. The…

Q: (a) Calculate the final speed U of the less massive ball and the angle 0.

A: There are two spheres, one has a mass of m and the other has a mass of 2m. They collide. The initial…

Q: a 2kg ball is moving horizontally with a speed of 1.2m/s. it strikes an 8kg triangular block…

Q: Two manned satellites approaching one another at a relative speed of 0.400 m/s intend to dock. The…

A: Given values - u1=0.400 msm1=2.50×103u2=0ms (second satellite is initially at rest)m2=7.50×103 kg…

Q: Object A of mass 10 kg moving at 10 m/s [E] collides with Object B of mass 8 kg moving at 10 m/s…

A: The problem statement mentions that Object B is moving at 10 m/s [E N], which means it is moving at…

Q: 1. A spaceship at rest relative to a nearby star in interplanetary space has a total mass of 2.50 x…

Q: A 2.30-kg particle has a velocity (2.20 î − 4.50 ĵ) m/s, and a 3.50-kg particle has a velocity (1.00…

A: Given,

Q: The mass of a particle is 2 kg and its velocity is given by V1 = 2i-10tj m/s, with time in t and s.…

A: The velocity of the center of mass of a given system of particles is given by- vCM=m1v1+m2v2m1+m2…

Q: Particle P has a mass of 3 kg and Particle Q has a mass of 'm' kg. The particles are moving in…

A: Mass of particle Q. given, Initial speed of P, viP=4 m·s-1Initial speed of Q, viQ=2 m·s-1Final speed…

Q: If the total momentum of a system is changing: O Particles of the system must be exerting forces on…

A: By Newton’s second law: “ the net external force is equal to the rate of change of momentum”If the…

Q: A block of mass m = 2.40 kg starts from the rest and slides down a 30.0∘ incline which is 3.60 m…

Q: A particle of mass m, = 1.50 kg and initial velocity U1, i = (9.30 i + 8.00 j) m/s collides with the…

Q: A projectile with a mass m = 200 kg and a velocity v = 100 m s−1 is fired at an angle of ϕ = 60 ◦ .…

Q: A bullet of mass m= 0.500 [g] fired horizontally with a speed v=10.0 [m/s] into a bob of a…

A: Given, mass of the bullet, m = 0.500 g = 0.5×10-3 kginitial velocity, v = 10.0 m/smass of the…

Q: A marksman standing on a motionless railroad car fires a gun into the air at an angle of 30.00 °from…

Q: 10. An object (A) of mass mA = 17.5 kg is moving due west with a speed VA = 8.10 m/s, while object…

Q: Two manned satellites approaching one another at a relative speed of 0.450 m/s intend to dock. The…

A: Assume that, the reference frame in which the second satellite is initially at rest, and the…

Q: Two manned satellites approaching one another at a relative speed of 0.300 m/s intend to dock. The…

Q: H) If m, Skg, m, = 25kg,u, 4Sm/s and 8 30°, find the final speeds v and vy of the two objects. #)…

A: Mass, m1 = 5 kg Mass, m2= 2.5 kg Speed of m1 before collision, u1 = 4.5 m/s Angle made with the…

Q: A rigid ball of mass m and velocity u undergoes an inelastic collision with another rigid ball of…

A: Given: The mass of the rigid ball is m1=m, The initial velocity of the rigid ball is u1=u, The mass…

Q: Two manned satellites approaching one another at a relative speed of 0.300 m/s intend to dock. The…

Question

4. A hoop of mass M and radius R lies motionless on a frictionless surface. Aimed towards
it, but off center by a distance d < R, is a smaller object of mass m<< M and radius
r« R moving at speed v. The two objects undergo a totally inelastic collision.
Note: For m <« M , it can be assumed that the center of mass motion of the composite
object is appropriately approximated by being located at the center of mass of the hoop
and that V would be parallel to v.
a. Find an expression in terms of M , R , m, v and d for
i. the final translational speed V , and
ii. the final rotational speed, w, of the composite object.
b. What are the possible range of values for both @ and V , and what values ofd
correspond to each?
c. Find an expression for how much energy was lost in the collision, in terms of m,
M, d, R, and K,(=}mv² ).
d. What is the maximum and minimum energy loss possible by varying the value of
d, and
e. What are the values of w and V for M = 2.0 kg, m= 25 g, R=15 cm,
d = 10 cm, and v=1.0 m/s .
%3D

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Step 8

Trending now

This is a popular solution!

Step by step

Solved in 8 steps with 7 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

A 2.09-kg particle has a velocity (1.90 î – 2.90 j) m/s, and a 2.95-kg particle has a velocity (0.92 î + 6.01 j) m/s. (a) Find the velocity of the center of mass. |î + i) m/s (b) Find the total momentum of the system. i) kg · m/s
A particle is moving along the x-axis with 4.00 [m/s]. It collides with a second 17. an initial speed vo = particle of identical mass that is at rest, and is deflected with a speed of v = 2.00 [m/s], ø = 30.0° above the x- %3| axis. The second particle deflects at an angle 0 below the x-axis. What is the angle 0? BEFORE AFTER А. 23.8° С. 53.8° В. 36.2° D. 66.2°
Two manned satellites approaching one another at a relative speed of 0.300 m/s intend to dock. The first has a mass of 2.50 ✕ 103 kg, and the second a mass of 7.50 ✕ 103 kg. If the two satellites collide elastically rather than dock, what is their final relative velocity? Adopt the reference frame in which the second satellite is initially at rest and assume that the positive direction is directed from the second satellite towards the first satellite.
Pls asap
A particle with mass mA = 3.00 kg is located at rA = (2.50 i + 3.50 j) m, and a second particle of mass m2B = 5.00 kg is located at rB = (1.50 i – 3.00 j) m. Find the location of the center of mass of the system relative to the point (1,1).
Two smooth disks A and B, having a mass of 6 kg and 9 kg rolling with velocities ua = 2 m/s and ug = 5 m/s respectively, collide as shown in Figure. If the coefficient of restitution for the disks is 0.35. Determine the x and y components of the final velocity of each disk just after collision (consider e =40° and ф%3D 50%). y UB MA UA
A firework with mass M is launched from the origin with initial speed v0 and angle θ0 and travels along the usual parabolic path above flat ground. At the peak of its path, it explodes into two pieces. Piece one has mass .5M and speed v1 in an angle of 30◦ below the horizontal direction and the other piece has mass .5M and speed v2 in an unknown direction. (a) Do the two pieces land at the same time? (Justify your answer) (b) Sketch the motion of the COM and of both pieces. Note any external forces, and describe if p is conserved in x, y or both for the duration of the flight. Also note if the two pieces land at the same distance from the target or describe which one lands closer/further.
A 1.95-kg particle has a velocity (1.95 î – 3.07 ĵ) m/s, and a 2.91-kg particle has a velocity (1.06 î + 5.99 ĵ) m/s. (a) Find the velocity of the center of mass. i) m/s (b) Find the total momentum of the system. |î) kg · m/s
Problem 3: A particle with mass ma = 3.00 kg is located at ra = (2.50 i + 3.50 j) m, and a second particle of mass m2B = 5.00 kg is located at rB = (1.50 i - 3.00 j) m. Find the location of the center of mass of the system relative to the point (1,1).
A system of three particles with masses m1 = 3.0 kg, m2 = 4.0 kg and m3 = 8.0 kg is placed on a two dimensional xy plane. The scales on the axes are set by x, = 2.0 m and y, = 2.0 m. y (m) mg m1 * (m) Figure 2 (a) Find out the x coordinate of the system's center of mass. (b) Find out the y coordinate of the system's center of mass. (c) Find out the acceleration of the system if an external force of 5 N acts on it.
A bullet of mass 0.018 kg traveling horizontally at a high speed of 200 m/s embeds itself in a block of mass 4 kg that is sitting at rest on a nearly frictionless surface. (a) What is the speed of the block after the bullet embeds itself in the block? Vf = 7 X m/s (b) Calculate the total translational kinetic energy before and after the collision. Ktrans,/ = 180 X J Ktrans,f = 260 X J (c) Compare the two results and explain why there is a difference. O The Energy Principle isn't valid for an inelastic collision. The internal energy of the block-bullet system has increased. O Some of the momentum is lost in an inelastic collision.
41. A smooth sphere S, of mass 3m, moving with speed u collides directly with an identical smooth sphere Q, of mass 2m, moving in the opposite direction with speed u. Given that the coefficient of restitution between the spheres is, the speed of Q after impact is и в Зи с и D u