Laboratory 6

A force F₁ of magnitude 6.10 units acts on an object at the origin in a direction 8 = 54.0° above the positive x-axis. (See the figure below.) A second force F₂ of magnitude 5.00 units acts on the object in the direction of the positive y-axis. Find graphically the magnitude and direction of the resultant force ₁ + ₂. units magnitude direction F₂ counterclockwise from the +x-axis

We highlighted two errors in the equation representing the motion of a body subjected to gravity: the difficulties of air resistance and the fact that the Earth is not a perfect sphere. Is this mathematical model free of extra inaccuracies? Do you believe that these additional variables should be incorporated into our falling body model? Explain why you feel they should or should not be included.

The flanged steel cantilever beam with riveted bracket is subjected to the couple and two forces shown, and their effect on the design of the attachment at A must be determined. Replace the two forces and couple by an equivalent couple M and resultant R at A. The couple is positive if counterclockwise, negative if clockwise. 1.92 KN 0.67 m 1.71 m- 68° A 6 Answers: M = i kN.m R=( i i+ i y I L 460 N.m 10.17 m 10.17 m 1.08 KN j) kN

The flight of a model rocket can be modeled as follows. During the first 0.15 s the rocket is propelled upward by the rocket engine with a force of 16 N. The rocket then flies up while slowing down under the force of gravity. After it reaches the apex, the rocket starts to fall back down. When its downward velocity reaches 20 m/s, a parachute opens (assumed to open instantly), and the rocket continues to drop at a constant speed of 20 m/s until it hits the ground. Write a program that calculates and plots the speed and altitude of the rocket as a function of time during the flight. SOLVE WITH MATLAB PLEASE

write in matlab

Problem 1 (Waypoint Navigation): Suppose the robot needs to navigate through a set of waypoints as shown in the figure below. For each step, the robot will first spin in place and then move to the specified waypoint. Suppose the robot's initial position is at the origin with a 90° orientation with respect to the positive x-axis. Compute the amount of translation and angle of rotation at each step. 4 2 0 2 -4 -6 -5 + y (m) -3 -2 -1 0 2 Complete the following table. Each Step/Maneuver O→A А→В B⇒C CO x (m) 3 4 Amount of Translation (m) Angle of rotation in degree wrapped within [−180°, 180°]

Four forces act on an object as shown in the diagram below. The total force acting on the object is directed 3 N 2N 2N 4 N

A 3T MRI scanner used is tuned for proton imaging. For a given imaging sequence applied to image a patient's leg the gradient strength is 1 G/cm, FOV is 25 cm, and matrix is 250x250. The patient has a titanium screw in their leg that causes a magnetic susceptibility change to the main magnetic field of 0.5 Gauss. How much shift is image position ( in pixels) will be seen in this part of the leg?

Given the table: Initial d Left Turn Right Turn -1 -i i 1 i -i i -1 1 -i 1 -1 d di -di ...write an expression that will tell you the direction the robot is going if, in the course of its journey, it turns left 21 times and turns right 22 times. Does the order the robot makes the turns in matter for the purpose of knowing the direction it is finally facing?

4. Consider the building from the figure below. a) If it is 200 feet tall and you are 20 feet away, at what angle from the ground will you have to tilt your head to see the top of the building? (For simplicity assume that your head is even with the ground.) How far is it from your head to the top of the building? Repeat parts (a) and (b) assuming your head is NOT even with the ground, but is 6 feet above ground level. b) c) angle distance d height h

Show all working and steps please. First picture is the question and second picture is a graph which is for Question 1 (b)

Code requirements: A robot is positioned on an integral point in a two-dimensional coordinate grid (xr, yr). There is a treasure that has been placed at a point in the same grid at (xt, yt). All x’s and y’s will be integral values. The robot can move up (North), down (South), left (West), or right (East). Commands can be given to the robot to move one position in one of the four direction. That is, “E” moves a robot one slot East (to the right) so if the robot was on position (3, 4), it would now be on (4, 4). The command N would move the robot one position north so a robot at position (4, 4) would be at (4, 5). Because the robot cannot move diagonally, the shortest distance between a robot at (xr, yr) and a treasure at (xt, yt) is | xr – xt | + | yr - yt | = ShortestPossibleDistance Write a recursive program which determines all the unique shortest possible paths from the robot to the treasure with the following stipulation: The robot may never move in the same direction more than…

Please show the graph.

standard science experiment is to drop a ball and see how high it bounces. Once the “bounciness” of the ball has been determined, the ratio gives a bounciness index. For example, if a ball dropped from a height of 10 feet bounces 6 feet high, the index is 0.6, and the total distance traveled by the ball is 16 feet after one bounce. If the ball were to continue bouncing, the distance after two bounces would be 10 ft + 6 ft +6 ft + 3.6 ft = 25.6 ft. Note that the distance traveled for each successive bounce is the distance to the floor plus 0.6 of that distance as the ball comes back up. Write a program that lets the user enter the initial height from which the ball is dropped, the bounciness index, and the number of times the ball is allowed to continue bouncing. Output should be the total distance traveled by the ball.

Even the tiniest activities may be made easier using the Spiral Model.

Computer Science Write a code (in Python) for a simulated (or actual) bipedal robot, that will allow it to maintain its balance, while withstanding external perturbations.

3. The equations of motion of the airplane in a straight line steady symmetrical climb are: V md- dt =T-D L-W=0 OT W siny - D= 0 L W cosy 0 V md- = T L - dt = W siny - D W cos y = 0

Please work out question 28 and show work for explanation of how you came up with your answer.

R-2000 2 An electrical capacitor with an unknown capacitance is connected to the circuit shown. The switch is first connected to B and the capacitor is charged. Then, the switch is connected to A and the capacitor discharges through the resistor. As the capacitor is discharging, the voltage across the capacitor is measured for 10 s in intervals of 1 s. The recorded measurements are given in the table below. Vo | 3| 4 | 5 | 3.55 2.81 6 7 1.26 | 2 8 10 V(V) | 9.4. 7.31 | 5.15 2.04 0.97 0.74 | 0.58 You recall from PHYS2102 that the voltage of the capacitor, during a discharge, as function of time is given by V = V, e*t/(RC) This exponential equation can be written as a linear equation of In(V) and t in the form : In(V) = t + In(V6) Use Matlah to do the following: "In all graphs add title, sgend and axis labels 1. Estimate the time at which the voltage V = 6.5 V. 2. Estimate, using spline interpolation, the voltage V1 corresponding to 30 times varying from 1 to RC 10s. 3. In the same…

Opload answer sheets A single link robot with a rotary joint is motionless at theta = -5 degree. It is desired to move the joint in a smooth manner to theta = 80 degree in 4 seconds. Find the coefficients of a cubic which accomplishes this motion and brings the arm to rest at the goal. Plot the position, velocity and acceleration of the joint as a function of time.

Consider X is the independent variable and Y is the dependent one, plot the function Y in terms of X such that: graph title is “Y Scores” and the curve color is blue. (Matlab Statement)

When purifying drinking water you can use a so-called membrane filtration. In an experiment one wishes to examine the relationship between the drop across a membrane and the flux (flow per area) through the membrane. We observe the following 10 related values of pressure (x) and flux (y): pressure 2 3 4 5 6 7 8 9. 10 Pressure (x) 1.02 2.08 2.89 4.01 5.32 5.83 7.26 7.96 9.11 9.99 Flux (y) 1.15 0.85 1.56 1.72 4.32 5.07 5.00 5.31 6.17 7.04 Copy this into R to avoid typing in the data: D <- data.frame( pressure=c(1.02,2.08,2.89,4.01,5.32,5.83,7.26,7.96,9.11,9.99), flux=c(1.15,0.85,1.56,1.72,4.32,5.07,5.00,5.31,6.17,7.04)

Please help me answer these questions related to simulation in detail.

Use MATLAB to solve the question in the image attached

A standard science experiment is to drop a ball and see how high it bounces. Once the “bounciness” of the ball has been determined, the ratio gives a bounciness index. For example, if a ball dropped from a height of 10 feet bounces 6 feet high, the index is 0.6 and the total distance traveled by the ball is 16 feet after one bounce. If the ball were to continue bouncing, the distance after two bounces would be 10 ft + 6 ft + 6 ft + 3.6 ft = 25.6 ft. Note that distance traveled for each successive bounce is the distance to the floor plus 0.6 of that distance as the ball comes back up. Write a program that lets the user enter the initial height of the ball and the number of times the ball is allowed to continue bouncing. Output should be the total distance traveled by the ball. Please name your function "bounce" that has three arguments (initial height, index, number of bounce) and return the total distance traveled by the ball. (float) Skip the part where users can enter the inputs of…