State the basic physics principles, laws, or equations that students could use to graphically determine the relationship between the release height of block A and the speed at which the two-block system travels after the blocks collide and stick together
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(a) State the basic physics principles, laws, or equations that students could use to graphically determine the relationship between the release height of block A and the speed at which the two-block system travels after the blocks collide and stick together
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- In Lagrangian mechanics, the Lagrangian technique tells us that when dealing with particles or rigid bodies that can be treated as particles, the Lagrangian can be defined as: L = T-V where T is the kinetic energy of the particle, and V the potential energy of the particle. It is also advised to start with Cartesian coordinates when expressing the kinetic energy and potential energy components of the Lagrangian e.g. T = m (x² + y² + 2²). To express the kinetic energy and potential energy in some other coordinate system requires a set of transformation equations. 3.1 Taking into consideration the information given above, show that the Lagrangian for a pendulum of length 1, mass m, free to with angular displacement - i.e. angle between the string and the perpendicular is given by: 3.2 4.1 4.1.1 4.1.2 4.1.3 4.1.4 4.2 L = T-V = ²² +mg | Cos Write down the Lagrange equation for a single generalised coordinate q. State name the number of generalised coordinates in problem 3.1. Hence write…As shown in the figure, two boxes of mass and are connected by an essentially massless, non-elastic wire passing over a light, frictionless pulley. The box of mass m, is released from rest at height h above the table. Use the isolated system model to answer the following. (We assume m, > m,. Use any variable or symbol stated above along with the following as necessary: g.) (a) Determine the speed of m, just as m, hits the table. v= 5.77 Since the only force acting is the conservative force of gravity, mechanical energy is conserved. Write a statement of conservation of energy and the expressions for the change in kinetic energy and the change in gravitational potential energy. Combine these three expressions and solve for the speed in terms of known quantities. Note that you want the speed and not the velocity. (b) Find the maximum height above the table to which m, rises. hmax = 6.66 The maximum height is the distance h plus Ah the distance m, travels upward after m, lands on the…Tiny Spring: A tiny silica bead attached to a strand of DNA can be used to study the mechanical properties of DNA. The system can be approximated as a mass on a spring constrained to move in one dimension. In one such experiment, a bead of mass 7.8 × 10¬15 kg was attached to a strand of DNA with 1623 base pairs and observed for 720 seconds. (a) If the root mean square velocity of the bead is 7.56 x 10-4 m/s, at what temperature was the experiment carried out? (b) If the root mean square displacement of the particle is measured to be 1.18 × 10-7 m, what is the spring constant of the DNA molecule?
- Two masses hang next to each other from a support. Each mass has a pendulum length R = 30 cm. Object A is raised to a 66 degree angle with respect to vertical and allowed to fall as a pendulum, eventually colliding elastically with object B. Let object A have a mass ma=45g and object B have mass mb=65g. For all answers, work symbolically and then plug in numbers at the end. (a) What is the velocity of the object A before the collision? (Ignore the physical size of A and B, that is, assume y = 0 for both during the collision) (b) What quantities are conserved during the collision? (c) What are the maximum heights of each object after the collision?Two identical cars, A and B, traveling at 55 mi/h collide head-on. A third identical car, C, crashes into a brick wall going 55 mi/h. Which car has the least damage: (a) car A, (b) car B, (c) car C, or (d) all the same? Why is the answer C?In the ammonia (NH3) molecule of the figure, three hydrogen (H) atoms form an equilateral triangle, with the center of the triangle at distance d = 9.40 × 10−11 m from each hydrogen atom. The nitrogen (N) atom is at the apex of a pyramid, with the three hydrogen atoms forming the base. The nitrogen-to-hydrogen atomic mass ratio is 13.9, and the nitrogen-to-hydrogen distance is L = 10.14 × 10-11 m. What are the (a) x and (b) y coordinates of the molecule's center of mass? (a) Number Units (b) Number N L HO H d H This answer has no units Units This answer has no units
- Show all working explaining detailly each step.Pregunta 5 Sin responder aún Puntúa como 1.00 P Marcar pregunta Página anterior Tiempo restante 1:00:28 Jerome lanza una pelota de béisbol de masa 0.300 kg. La pelota llega al "home plate" con una velocidad de 40.0 m/s y es bateada directamente a Jerome con una velocidad de retorno de 52.0 m/s. ¿Cuál es la magnitud del cambio en el impulso de la pelota? O a. 12.0 kg-m/s O b. 15.6 kg-m/s. O c. 27.6 kg-m/s O d. 3.60 kg-m/s Siguiente páginaTwo marbles of the same mass perform a perfectly clastic and one-dimensional collision. If one of them is at rest, and the other has a speed of 4 m/s before the collision, determine the speeds after the collision.
- (a) Cynthia is in a boat heading due east at 15 m/s and is reading a book. She then finishes the book and throws her book off the back of the boat at a speed of 6 m/s due west. What is the boat’s speed after Cynthia throws the book if the book as a mass of 4 kg and Cynthia and the boat combined have a mass of 700 kg? (b) To demonstrate your ability to carry out deductive reasoning in the context of PC 141, determine the how the velocity of the boat after Cynthia throws the book would change if the book’s mass triples. Does your answer in question #2 above seem reasonable? Briefly explain why or why not?Please answer the question correctlyProblem 3: A force is acting on a block with a magnitude of F = 87 N. The force makes an angle of 0 = 19° with respect to the horizontal, as shown in the figure. Randomized Variables F = 87 N 0 = 19° F