A thin rod of length 2L and mass M lies flat on a frictionless plane. It is not hinged (attached) to anything. A small ball of mass m, traveling with velocity Vo, strikes the rod at a distanceh from the rod's center of mass. The collision is elastic. The ball continues to move along the original line of motion after the collision. The rod moves on the plane and rotates around its center of mass. After the collision, we want to determine the rod translational velocity, the rod angular velocity and the ball final velocity. a) Write three equations to find these three unknowns based on m, M, L, h and vo. Do not try to solve the equations. b) If the collision were inelastic and the rod was hinged at its center CM, what would be the rotational angular velocity of the system after the collision? Top view m Yo L h CM M

A thin rod of length 2L and mass M lies flat on a frictionless plane. It is not hinged (attached) to anything. A small ball of mass m, traveling with velocity Vo, strikes the rod at a distanceh from the rod's center of mass. The collision is elastic. The ball continues to move along the original line of motion after the collision. The rod moves on the plane and rotates around its center of mass. After the collision, we want to determine the rod translational velocity, the rod angular velocity and the ball final velocity. a) Write three equations to find these three unknowns based on m, M, L, h and vo. Do not try to solve the equations. b) If the collision were inelastic and the rod was hinged at its center CM, what would be the rotational angular velocity of the system after the collision? Top view m Yo L h CM M

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

Similar questions

A uniform, 0.0300 kg rod of length 0.400 m rotates in ahorizontal plane about a fixed axis through its center and perpendicularto the rod. Two small rings, each with mass 0.0200 kg, are mounted sothat they can slide without friction along the rod. They are initially heldby catches at positions 0.0500 m on each side of the center of the rod,and the system is rotating at 48.0 rev/min. With no other changes in thesystem, the catches are released, and the rings slide outward along therod and fly off at the ends. What is the angular speed (a) of the systemat the instant when the rings reach the ends of the rod; (b) of the rodafter the rings leave it?
can you aswer part b and please accept the mass on the right (2m) as 2.5kg , the one on the left (m) as 6.25 kg. and the radius as 1.9 m .
7The total sleeve movement in a Hartnell governor is 3 cm. The mass of rotating balls is 1.5 kg each. At the mid position of the sleeve arm, which is 6.5 cm long, is horizontal. The ball arm has a length of 7.5 cm. At the mid position of the sleeve, the balls rotate at a radius of 10.5 cm. Due to the mal adjustment of spring, the equilibrium speed of governor at top position is 415 rpm and In lowest position it is 430 rpm. Determine (1) Stiffness and initial compression of spring. (ii) Required initial compression in spring which gives equilibrium speed at the topmost position which is rpm more than the lowest position neglect bliquity.m = 1.5 kg
Rod OA rotates counterclockwise at a constant angular rate -4 rad/s. The double collar B is pin-connected together such that one collar slides over the rotating rod and the other collar slides over the circular rod described by the equation r= (1.6 cos ) m. Both collars have a mass of 0.7 kg. Motion is in the vertical plane. (Figure 1) Figure 1 of 1 > 7= 1.6 cos 8. 0 8=4 rad/s 0.8 m B Part A Determine the magnitude of the force which the circular rod exerts on one of the collars at the instant Express your answer to three significant figures and include the appropriate units. ▸ View Available Hint(s) HÅ F-35.8 N Submit Previous Answers X Incorrect; Try Again; 4 attempts remaining Part B Determine the magnitude of the force that OA exerts on the other collar at the instant-45 Express your answer to three significant figures and include the appropriate units. ▸ View Available Hint(s) FOA- ON Previous Answers
A ball of mass M is suspended from a vertical rod by two cables. The system rotates around this rod axis at angular velocity w. Assuming that the tensile strength of the upper cable is 2 times the tension of the lower cable. Draw a free body diagram for this ball
Zero, a hypothetical planet, has a mass of 5.7 x 1023 kg, a radius of 3.5 x 106 m, and no atmosphere. A 10 kg space probe is to be launched vertically from its surface. (a) If the probe is launched with an initial kinetic energy of 5.0 x 107 J, what will be its kinetic energy when it is 4.0 x 106 m from the center of Zero? (b) If the probe is to achieve a maximum distance of 8.0 x 106 m from the center of Zero, with what initial kinetic energy must it be launched from the surface of Zero? (a) Number: Units: (b) Number: Units:
Question 1: A sphere of mass m = 2 kg, is released from rest at point A (see Figure 1.1). Due to gravity, the sphere goes down the path AB (which is an inclined plane, at 45 degrees from the horizontal line) and then hits the ground at point D; the vertical wall BC is 2000 cm high (see Figure 1.1 for details) Assume no friction. (a) Derive the velocity of the sphere when it reaches point B. (b) Derive the distance CD and the time the sphere takes to go from point B to point D. State and justify your assumptions and comment on your working. Marks will be assigned for the quality of the presentation of the working and of the comments. (You have to assign the value of L, in centimetres, by using the last 3 digits of your student ID, and then solve the question; for example, if your student ID is 19980169, then L=169 cm; if your ID is 17680039, then L=39 cm; if your ID is 14567000, then L=1000 cm). L L C B D L = 50 cm in this Figure 1.1 case...
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?
5 ELASTIC COLLISION A puck of mass 1.0 kg is moving on frictionless ice with a speed of 9.0 m/s. It has a collision with a puck 2.0 kg that is moving a speed of 6.0 m/s; the second puck is traveling at a 90⁰ relative to the first puck. Consider the first puck to be traveling along the f-axis in the pos- itive direction, and consider the second puck to be moving along the ŷ-axis in the negative direction. The pucks collide at the origin. What are the velocity vectors of the pucks after the collision?
Do it correctly
A spring-based toy gun is used to shoot a ball of mass M straight up.The ball is not attached to the spring. The ball is pushed downward into the spring so that the spring is compressed toa distance S below its relaxation point. After the release, the ball reaches a maximum height 3S,measured from its relaxation position, see Fig. 1(b). (a) Find the constant of the spring. (b) Findthe equilibrium point of the ball when it is on the compressed spring with no forces other than gravity and thespring acting on it. Clearly indicate the point you are using as the origin of your coordinate system and which direction is positive.system and which direction is positive. (c) Now the ball is glued to the spring so that it oscillates up and downinstead of flying off the spring. The spring is again compressed to the same distance S below itsof relaxation. Write an equation for the position of the ball as a function of time after it is released. Indicateclearly which point you are using as the origin…
A thin circular disk of radius R and mass M has an axle through it close to its outer edge. The disk is rotated through 90 deg and then allowed to drop. (The figure shows the disk in its initial position before it is released, and its final position when point P passes through the lowest point). a) If the zero of height is taken to be the location of the COM when the disk is in its final position, what is the energy of the disk before it is release? b) What is the moment of inertia of the disk about the axle? c) What is the angular speed of the disk when it is in the final position? d) What is the speed of point P, on the outer edge of the disk, as it passes through the lowest point in its swing?