Concept explainers
Suppose that a projectile is launched upward from the earth's surface. Assume that the only force acting on the object is the downward force of gravity. Under these conditions, a force balance can be used to derive,
where
Want to see the full answer?
Check out a sample textbook solutionChapter 25 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Additional Engineering Textbook Solutions
Fundamentals of Differential Equations (9th Edition)
Basic Technical Mathematics
Advanced Engineering Mathematics
Calculus, Single Variable: Early Transcendentals (3rd Edition)
- Tp = Fq +°P/Q• (1) Here ip/Q is the "position of point P relative to point Q." Similarly the velocities of the two points are related by õp = bq + Up/Q- (2) The quantity õp/Q is the velocity of point P relative to point Q. I want you to use these ideas to solve the following problems. 1. The figure below shows a view from above of a large boat in the middle of the ocean. So that the crew on the ship can get exercise on long journeys, there is a circular walking/running track on the back deck. CA B- -D Suppose that the radius of the track is R = 6 m, and a person is running on the track at a constant speed of v = 3m/s as measured with a stopwatch by a crew-mate on board the ship. Suppose the runner is running counter-clockwise around the track when viewed from above. Write the velocity vector of the runner in terms of basis (ê1, ê2) as perceived by a crew-mate on the ship. (a) What is the velocity vector when the runner is at point A? (b) What is the velocity vector when the runner is…arrow_forwardLook at the below system. Using either the conservation of energy method or Lagrange's method, solve for the governing equation of motion for the system. Put a box around your final answer. Also, put a box around your equations for the potential and kinetic energy of the system. Assume the system's springs are initially unstretched (i.e., assume that there is no gravity until t = 0 [s]). K₁ Î E K₂ Xarrow_forwardA mass weighing 24 pounds, attached to the end of a spring, stretches it 4 inches. Initially, the mass is released from rest from a point 2 inches above the equilibrium position. Give the initial conditions. (Use g 32 ft/s? for the acceleration due to gravity.) x(0) X ft %3D x'(0) ft/s Find the equation of motion. x(t) X ft Need Help? Read It Watch Itarrow_forward
- 2- find the center of mass, the velocity of the center of mass, the momentum, and the kinetic energy of the following system: do f(xd) xaf] m₁ = 1 kg T₁=1+2j+3 k v₁ = 2î+3ĵ m₂ = 1 kg T₂ = 1-j+ k v₂ = 2) + 3karrow_forwardA particle rotates with constant speed in a circle. Let be the net torque on the particle and F the net force on the particle. Then: a. tau > 0 and F > 0 O b. tau > 0 and F = 0 . tau = 0 and F = 0 Od. tau = 0 and F > 0arrow_forwardQ6 The relationship between the velocity, u, of a construction vehicle (in km/h) and the distance, d (in metre), required to bring it to a complete stop is known to be of the form d = au² + bu + c, where a, b, and c are constants. Use the following data to determine the values of a, b, and c when: a) u 20 and d = 40 b) u = 55, and d = 206.25 c) u = 65 and d = 276.25 [Note: Use an appropriate standard engineering software such as MATLAB, CAS calculator, programmable calculator, Excel software]arrow_forward
- 2. I am planning to perform some model rocketry experiments. The payload is to be protected by a parachute as it returns to the ground. The predicted parachute drag force D can be obtained by the following equation: D = 0.5 pV²A CD Where D is the drag force in lbs., p is the density of air, V is the velocity of the falling rocket, A is the projected area of the parachute, Cp is the dimensionless coefficient of drag for the chute. My research has led me to find the following values: The density of air p is stated to be 0.074887 lbm/ft³ + 20% of the value The target falling speed is 30 ft/s + 2 ft/s The parachute is round, so the projected area is circular with a diameter of 25" + 1" The chute drag co-efficient is 0.9 ± 0.1 What is your projected drag force exerted by the chute with these parameters? What is your predicted uncertainty in this force value?arrow_forwardFor the given velocity triangle, if you know that at the inlet, alpha is -20, beta is 59, the relative velocity is 78 m/s, r= 20 cm, rotation speed is 180 rpm. At the exit, alpha is 30 and the absolute velocity is 35 m/s. Find the following: 1. the relative velocity at the exit in (m/s) 2. the work in (KJ/Kg) Vw1 U, V1 V1 V2 Uz Center of wheelarrow_forwardQ1: A100 kg man in space throws a 20kg space rock. As a result, the man accelerates to the left at 1m/s2.what is the acceleration of the rock?arrow_forward
- What is the volume of 92.4 grams of chlorine gas that is at a temperature of 46° C and a pressure of 694 mmHg? (Chlorine, R = 62.4 L- mm Hg/mole K and MW = 70.906 g/ mol) Computation: Show your Solution A lump of ice falls from an airplane as it comes into land. If the ice hits the ground with a vertical speed of 85m/s, what was the height of the plane when the ice fell off? (Assume that friction can be ignored.)arrow_forwardThe ideal gas law, discovered experimentally, is an equation of state that relates the observable state variables of the gas--pressure, temperature, and density (or quantity per volume): PV = NkBT (or pV = nRT), Figure L₂ Lx 1 of 1 Part A Find the magnitude of the average force (F) in the x direction that the particle exerts on the right-hand wall of the container as it bounces back and forth. Assume that collisions between the wall and particle are elastic and that the position of the container is fixed. Be careful of the sign of your answer. Express the magnitude of the average force in terms of m, vr, and L₂. ► View Available Hint(s) Submit Part B IVE ΑΣΦ ? Imagine that the container from the problem introduction is now filled with N identical gas particles of mass m. The particles each have different x velocities. but their average x velocity squared. denotedarrow_forwardThe small particle of mass (800 gm) spinning with angular velocity (w₁ = 2.3 rad/s, at r₁ = 400 mm), if we use force (F) to change the Angular velocity to (w₂, and r₂ = 250 mm) the value of F is: W1 Select one: A. None B. F = 5.63 N C. F = 9.47 N D. F = 3.52 N Farrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY