A particle P of mass m = 4 kg arrives at point O with a horizontal velocity vo and startsrolling down a circle with radius R = 3.5 m. The particle is attached to the point O bymeans of a linear spring of stiffness k = 60 N/m that is unstretched when the particle is atO. Assume that during the motion of P along the circle, the spring follows the circle. Let= {În, ŵy} be a fixed reference frame as shown in the figure and let B = {bx, by} bea reference frame attached to P so that ĥ is tangent to the circular path and by isperpendicular to the circular path. For convenience, take g =N=10 m/s² in this question.nynxIPa)Determine the Direction Cosine Matrices N[C]B and BCN.b)Determine for P in the frame N the position vector NrP, velocity vector NP, andacceleration vector NaP.e)For each value ofleaves the circular path at 0 = 00.Draw a Free Body Diagram of the particle, clearly indicating all forces acting on theparticle, and use the Free Body Diagram to determine the equation(s) of motion of theparticle.d)What relationship between 0 and needs to be satisfied at the point where the particleleaves the circle?between 0 and, determine the value of åå for which the particle

Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

A particle P of mass m = 4 kg arrives at point O with a horizontal velocity vo and starts rolling down a circle with radius R = 3.5 m. The particle is attached to the point O by means of a linear spring of stiffness k = 60 N/m that is unstretched when the particle is at O. Assume that during the motion of P along the circle, the spring follows the circle. Let N = {â, ŵy} be a fixed reference frame as shown in the figure and let B = {bæ, by } be a reference frame attached to P so that ĥ is tangent to the circular path and ɓy is perpendicular to the circular path. For convenience, take g = 10 m/s² in this question. nx a) Determine the Direction Cosine Matrices [C]B and BCN. b) Determine for P in the frame N the position vector NTP, velocity vector NVP, and acceleration vector NaP. c) Draw a Free Body Diagram of the particle, clearly indicating all forces acting on the particle, and use the Free Body Diagram to determine the equation(s) of motion of the particle.

A particle P of mass m = 4 kg arrives at point O with a horizontal velocity vo and starts rolling down a circle with radius R = 3.5 m. The particle is attached to the point O by means of a linear spring of stiffness k = 60 N/m that is unstretched when the particle is at O. Assume that during the motion of P along the circle, the spring follows the circle. Let N = {â, ŵy} be a fixed reference frame as shown in the figure and let B = {bæ, by } be a reference frame attached to P so that ĥ is tangent to the circular path and ɓy is perpendicular to the circular path. For convenience, take g = 10 m/s² in this question. nx a) Determine the Direction Cosine Matrices [C]B and BCN. b) Determine for P in the frame N the position vector NTP, velocity vector NVP, and acceleration vector NaP. c) Draw a Free Body Diagram of the particle, clearly indicating all forces acting on the particle, and use the Free Body Diagram to determine the equation(s) of motion of the particle.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Related questions

Q: Refers to Figure 3, the conveyor belt delivers each 17-kg crate to the ramp at A such %3D that the…

Q: The sphere of mass m1 = 5 kg falls from a height H = 1.4 m onto the homogeneous board of negligible…

A: The block will reach a height of 0.575 m after the collision. See attachment for detailed…

Q: Draw a Free Body Diagram of the particle, clearly indicating all forces acting on the particle, anc…

A: Given: m=1 kgR=1.5 mk=65 N/m

Q: k Force Cart I Cart 2 Sensor Mass = M Mass = 3.5M The figure above shows second experimental setup.…

A: After releasing from spring the cart 1 is free to move with some velocity and when it collides with…

Q: 4. A 3-kg ball is attached to a rope connected to the center of a table and initially travelling in…

A: Given: The mass of the ball: →m=3 Kg Initial radius→R1=4 m final radius→R2=2 m Initial speed→V1=3m/s…

Q: Object A, mass 12 kg, is attached to a pulley with mass 15 kg and a radius of 0.25 m. The pulley is…

A: To solve this problem, we need to consider the conservation of energy and torque equilibrium. First,…

Q: Situation 10. A vehicle starts from rest at t = 0 and travels along a horizontal. circular track…

Q: block with some mass m is connected to a string that is attached to the ceiling. The block on the…

Q: A truck with mass of M is going to tow the car with mass m. For values of M and m please follow the…

A: Mass of the truck→M=150000g Mass of the car→m=800g Initially the truck is moving with 130 Km/h speed…

Q: The sphere of mass m1 = 5 kg falls from a height H = 1.4 m onto the homogeneous board of negligible…

A: The objective of the question is to find out how high the body of mass m2 rises after the collision.…

Q: Determine for P in the frame N the position vector, velocity vectory, and acceleration vector NaP.

Q: m R

Q: A particle P of mass m = 3 kg arrives at point O with a horizontal velocity vo and starts rolling…

A: Given: m=3 kgR=3.5 mk=60 N/m

Q: A particle of mass m moves along the x-axis such that its acceleration is d²x dt² = 8x³. - -X. (a)…

A: Expression of acceleration,d2xdt2=8x3-xBoundary condition, at x=0, U=0

Q: Consider a slider, modeled as a particle P of mass m, moving along a frictionless shaft. The slider…

A: Given data:No radial acceleration, No angular acceleration,

Q: M= 2,500 kg m= 800 kg

Q: A box is released from rest at the top of a ramp at timet = 0. It slides down the ramp and collides…

A: Consider the time interval 0<t<tA. Let W be the weight of box so calculate the weight in the…

Q: |Q.1. A block of mass m = 0.5 kg is pushed against a horizontal spring of spring constant k 450 N/m…

A: Given, m = 0.5 kg k = 450 N/m vB = 12 m/s

Q: Determine for P in the frame N the position vector NP, velocity vector NP, and acceleration vector…

A: Given: m=3.5 kgR=2 mk=70 N/m

Q: A particle P of mass m = 3 kg arrives at point O with a horizontal velocity Up and starts rolling…

A: Given:

Question

A particle P of mass m = 4 kg arrives at point O with a horizontal velocity vo and starts
rolling down a circle with radius R = 3.5 m. The particle is attached to the point O by
means of a linear spring of stiffness k = 60 N/m that is unstretched when the particle is at
O. Assume that during the motion of P along the circle, the spring follows the circle. Let
= {În, ŵy} be a fixed reference frame as shown in the figure and let B = {bx, by} be
a reference frame attached to P so that ĥ is tangent to the circular path and by is
perpendicular to the circular path. For convenience, take g =
N
=
10 m/s² in this question.
ny
nx
IP
a)
Determine the Direction Cosine Matrices N[C]B and BCN.
b)
Determine for P in the frame N the position vector NrP, velocity vector NP, and
acceleration vector NaP.
e)
For each value of
leaves the circular path at 0 = 00.
Draw a Free Body Diagram of the particle, clearly indicating all forces acting on the
particle, and use the Free Body Diagram to determine the equation(s) of motion of the
particle.
d)
What relationship between 0 and needs to be satisfied at the point where the particle
leaves the circle?
between 0 and, determine the value of åå for which the particle

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1: Determine the given details

VIEW

Step 2: Solve for Part a and b

VIEW

Step 3: Draw the Free body diagram

VIEW

Solution

VIEW

Step by step

Solved in 4 steps with 8 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

Please do all parts. Thank you!
The sphere of mass m1 = 5 kg falls from a height H = 1.4 m onto the homogeneous board of negligible mass. The board can rotate around a horizontal axis passing through point O, and a body of mass m2 = 3.9 kg is placed on it at a distance b = 1 m from the axis of rotation. The collision is perfectly inelastic. How high does the body of mass m2 rise after the collision (in m) if a = 0.5 m?
3/170 The system is at rest with the spring unstretched when 0 = 0. The 3-kg particle is then given a slight nudge to the right. (a) If the system comes to mo- mentary rest at 0 = 40°, determine the spring con- stant k. (b) For the value k = 100 N/m, find the speed of the particle when 0 = 25°. Use the value b = 0.40 m throughout and neglect friction. C B b m Problem 3/170 A 1.256
Q5
Q1 [Type B]: The 20-lb crate A rests on a smooth surface. If the crate starts from rest and P = (t² + 1.5t) lb where t is in seconds, determine the speed of the crate A at t = 2 s using the method of linear impulse and momentum. Not using the required method would result in a 0 for this question. A Shaobo Huang P 30⁰
Dynamics
I need help please
Am = 12 kg particle is moving along a horizontal path defined by the equations r= (4.5.t+13) m and = = (4.5-t2-3) rad, where t is in seconds. Using equations of motion in cylindrical coordinates, a. Determine the radial force component at the instant t = 5 s, Fr. b. Determine the transverve force component at the instant t = 5 s, F. c. Determine the magnitude of the resultant force at the instant t = 5 s, FR Round your final answers to 3 significant digits/figures. Fr= Fe= FR = N N N
A particle P of mass m = 3 kg arrives at point O with a horizontal velocity and starts rolling down a circle with radius R = 1.5 m. The particle is attached to the point O by means of a linear spring of stiffness k = 50 N/m that is unstretched when the particle is at O. Assume that during the motion of P along the circle, the spring follows the circle. Let N = {x, ây} be a fixed reference frame as shown in the figure and let B = {bx, by} be a reference frame attached to P so that b is tangent to the circular path and by is perpendicular to the circular path. For convenience, take g = 10 m/s² in this question. ny ĤT IP
If you have a material that is initially hard and strong, would you expect it to cyclically harden or soften? What would be a way of characterizing how strong it must be initially to make your answer a bit more quantitative?
4. A loading car is at rest on a track forming an angle of 25° with the vertical when a force is applied to the cable attached at C. The gross weight of the car and its load is 5465 lb WG, and it acts at point G. Know the tension in the cable connected at C is 5000 Ib Tc. Neglect friction between the car and the track. Determine how far the car travels in 15 seconds. Model this as a particle at G. 24 in. B 25 in. 30 in. 25 in.
The sphere of mass m1 = 5 kg falls from a height H = 1.4 m onto the homogeneous board of negligible mass. The board can rotate around a horizontal axis passing through point O, and a body of mass m2 = 3.9 kg is placed on it at a distance b = 1 m from the axis of rotation. The collision is perfectly inelastic. How high does the body of mass m2 rise after the collision (in m) if a = 0.5 m?