CURVILINEAR: Cheezy placed an order for 16 cubic meters of sand. The sand was ejected from a dump truck at a 50-degree angle, with an initial velocity of 2 feet per second. Calculate the radius of curvature of the trajectory at the direction point 1m below point A. with Illustration
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CURVILINEAR: Cheezy placed an order for 16 cubic meters of sand. The sand was ejected from a dump truck at a 50-degree angle, with an initial velocity of 2 feet per second. Calculate the radius of curvature of the trajectory at the direction point 1m below point A.
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- CURVILINEAR: Cheezy placed an order for 16 cubic meters of sand. The sand was ejected from a dump truck at a 50-degree angle, with an initial velocity of 2 feet per second. Calculate the radius of curvature of the trajectory at the direction point 1m below point A.Vince Carlo is a world renowned skateboarder who wants to try a new skateboard design. The skateboard has a length of ?AB = 1.30m. Given the figure shown, determine (a) the velocity at point ? and (b) the angular velocity of the skateboard ?? if the velocity at point ? is ?a = 3.1 m/s to the right. Neglect the diameter of the wheels. Note: Use purely RMA Method for velocity calculations. Show the complete and step-by-step solution.4. A girl tosses a ball at an initial velocity of VA = 8 ft/s at an angle of 0 = 25°. A boy catches the ball at Point B, which is at the same height as Point A. Answer the following questions. a. What is the initial velocity of the ball in A = (VA) x² + (VA) format? Show your work. Velocity in A = (VA) x + (VA)yj format C. b. Where is the ball when it reaches its maximum height? Justify your response by describing where the ball is relative to the position of Points A & B. No math is required. Units What is known about the x- and y-components of velocity and acceleration of the ball at the maximum height? No math is required. d. If we assume that Points A & B are both 3 ft above the ground, what is the maximum total height of the ball? Show your work. Magnitude rounded to 3 sig. fig. Units
- A watermelon is blown into three pieces by a large firecracker. Two pieces of equal mass m fly away perpendicular to one another, one in the x direction another in the y direction. Both of these pieces fly away with a speed of V = 22 m/s. The third piece has three times the mass of the other two pieces. What is the numeric value for the speed of the larger piece in m/s? ...and at what angle does the largest piece trave with respect to the y axis in degrees?4. 2) The hydraulic cylinder D extends, moves the rigid rod ABC, and causes the collar A to move with velocity and acceleration both to the left. If the dimensions 4 1.0 ft, and 2 = 1.7 ft, VA = 4.9 ft/s, aa = 2.6 ft/s2, and the angle 0 = 27°, determine the speed of point B. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point, and proper unit. В 12 D a Your Answer: Answer units 1,A camera on the left edge of a circular track of radius D = 4 m tracks a particle as it travels around the circle. The polar equation of the path is given above. At the moment shown, the camera angle is € = 30°, and the camera is rotating at 0 = 0.5 rad/s, which is accelerating at a rate 0 -0.1 rad/s². What is the velocity, acceleration, and rate of change of speed of the particle at that instant? = V= r = D cos(0) a = v = m/s m/s² m/s²
- OR Fig. 3 A robotic arm shown in Fig. 3 is programmed so that the 0.4-kg part A traces the radial path defined by r = 1–- 0.5 cos (2nt) meter and tranverse path of 0 = 0.5 – 0.2 sin (2nt) rad respectively. a) Calculate the velocity magnitude of part A at 1= 3 seconds. b) Determine the radial and transverse components of the force exerted on A by the robot jaws at 1= 2 seconds. Show the necessary Free-Body and Kinetic diagram to support your analysis.A bullet spins as the shot is fired from a gun. For this purpose, two helical slots as shown in the figure are cut in the barrel. Projections A and B on the bullet engage in each of the slots. Gun Barrel 0.5 m 1 A B Bullet Helical slots are such that one turn of helix is completed over distance of 0.5 m. If velocity of bullet when it exits the barrel is 20 m/s, its spinning speed in rad/s is_6.) A toy spaceship hangs by a string from a ceiling fan and as the fan rotates, the spaceship travels at v = 2. What is the angular velocity if the fan blade is 300 mm, and the string is 50 mm?
- Modern roller coasters have vertical loops like the one shown in the figure. The radius of curvature is smaller at the top than on the sides so that the downward centripetal acceleration at the top will be greater than the acceleration due to gravity, keeping the passengers pressed firmly into their seats. Part (a) What is the speed of the roller coaster, in meters per second, at the top of the loop if the radius of curvature there is 15 m and the downward acceleration of the car is 1.3g? Note that g here is the acceleration due to gravity. Part (b) The beginning of this roller coaster is at the top of a high hill. If it started from rest at the top of this hill, how high, in meters, above the top of the loop is this initial starting point? You may assume there is no friction anywhere on the track. Part (c) If it actually starts 3.5 m higher than your answer to the previous part (yet still reaches the top of the loop with the same velocity), how much energy, in joules, did it lose…3. Consider the conveyor belt shown below. As the rollers turn at a constant rate, the top portion of the belt moves to the right at speed v. D- -B Lêu E Assuming the belt does not stretch, answer the following sub-questions. Express your answers in terms of basis vectors (ê1, ê2). (a) What is the velocity vector of point A on the belt? Why? (b) What is the velocity vector of point C of the belt? Why? (c) What is the velocity vector of point B of the belt? Why? (d) What is the velocity vector of point E at the center of one of the rollers? Why? (e) What is the velocity vector ic/a? (f) What is the velocity vector Ta/c? (g) What is the velocity vector &B/A? (h) What is the velocity vector ve/c? (i) What is the velocity vector A/E?A Ferris Wheel, with radius 50 ft., turns counterclockwise one revolution every 18 seconds. Bryce stands at a point 120 ft. from the base of the wheel on the “upward motion” side and off to one side at an angle of 20°. The wind is blowing toward the Ferris Wheel, essentially into Bryce’s face, at an angle 30° to the base of the wheel. This wind results in an acceleration of 12 ft/s2 . At the instant Susan is at point A (3 o’clock on the wheel), Bryce throws a ball at the Ferris Wheel, releasing it from the same height as the bottom of the wheel. If the ball’s initial speed is 110 ft/sec and it is released at an angle of 60° with the horizontal, does Susan have a chance to catch the ball? Explain why/why not