Concept explainers
The differential equation for the velocity of a bungee jumper is different depending on whether the jumper has fallen to a distance where the cord is fully extended and begins to stretch. Thus, if the distance fallen is less than the cord length, the jumper is only subject to gravitational and drag forces. Once the cord begins to stretch, the spring and dampening forces of the cord must also be included. These two conditions can be expressed by the following equations:
where
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Chapter 28 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
- Q1: The rubber mallet is used to drive a cylindrical plug into the wood member. If the impact force varies with time as shown in the plot, determine the magnitude of the linear impulse delivered by the mallet to the plug. [ Ans: Impulse (1) = 1.7 N.m ] 200 70.010 0.009 0 0.002 F,Narrow_forwardDamian’s car weighs 2000kg. The spring has a natural unstretched length of 2m and a spring constant of k = 80000N/m. Hooke's law can be written as T = kd. Where T is the tension force in newtons, k is the spring constant and d is the length in metres. Let x(t) be the position of the front of Damian’s car and let y(t) be the position of the back of Eva’s 4WD. We will assume that the position of Eva’s car is a known function of time. Q1 a) Create a sketch of the positions of the vehicles similar to the one given and add the positions x and y. b) What is the extension of the spring in terms of x(t) and y(t)? Be careful to take into account that the unstretched length of the spring is 2m.arrow_forwardA force of F = 50 N is applied to the rope that causes the angle 0₁ = 60 degrees to keep the system at equilibrium. The N spring constant is k = 100 m B a 0₁ с a b с Variable Value 2 m 2 m 2 m F b Values for the figure are given in the following table. Note the figure may not be to scale. cc i❀O BY NC SA 2013 Michael Swanbomarrow_forward
- 5. An experiment has a data set that fits the function T = a x³ + 4 where T is the temperature, t is time in seconds and a is a constant to be determined. Using the least square method, derive an expression for 'a' that minimizes the error for the data set. Hint: Start with S = Σ(T; - a x₁³ — 4)² = 0 and take the partial derivative of S with respect to a.arrow_forward4. A spring with stiffness constant k = 2000 N/m attached to a platform launched a mass of 2kg vertically in the air to some maximum height (measured from the equilibrium point of the spring). The spring was compressed by 0.3 meters before launch. Due to internal friction of the spring, 10 Joules of energy was lost as the spring expanded. How fast was the mass travelling when it was at half of its maximum height? You must use g= 10m/s? for this problem or you will actually find it much more difficult to calculate. Hint: First solve the problem of finding what the maximum height is and then solve the problem of finding the speed at half of that height.arrow_forwardNewton's Law of Cooling as a Differential Equation dT k(м-т) dt where Tis the temperature of the object at a given time t, M is the temperature of the surrounding medium, and k is a positive constant. From this we note that if M>T, we have heating, since M – T > 0 thus dT/dt > 0, which means an increasing T, heating up! If Marrow_forwardEach time your heart beats, your blood pres- sure first increases and then decreases as the heart rests between beats. The maximum and minimum blood pressures are called the systolic and diastolic pressures, respectively. Your blood pressure reading is written as systolic/diastolic. A reading of 120/80 is considered normal. A certain person's blood pressure is modeled by the function p(1) = 115 + 25 sin(16071) where p(t) is the pressure in mmHg (millimeters of mer- cury), at time t measured in minutes. Find the blood pressure reading. How does this compare to normal blood pressure?arrow_forward1. For your science fair project, you decided to design a model rocket ship. The fuel burns exerting a time-varying force on the small 2.00 kg rocket model during its vertical launch. This force obeys the equation F= A + Bt2. Measurements show that at t=0, the force is 25.0 N, and at the end of the first 2.00 s, it is 45.0 N. Assume that air resistance is negligible. a. What are the forces acting on the rocket? b. Draw its free-body diagram. c. Find the constants A and B, including their SI units using this equation F= A + Bt². d. Find the net force on this rocket and its acceleration the instant after the fuel ignites. e. Find the net force on this rocket and its acceleration 3.00 s after fuel ignition. f. Suppose you were using this rocket in outer space, far from all gravity. What would its acceleration be 3.00 s after fuel ignition? g. What is the rocket's mass in outer space? What is its weight?arrow_forwardThe equivalent spring stiffness of an inclined spring whose k = 5 N/m and angle of inclination θ = 35° 3.355 N/m 4.095 N/m 5.867 N/m 4.511 N/marrow_forward4. For a particular thermocouple, if one junction is maintained at 0°C (cold junction) and the other junction is used as a probe to measure the desired Celsius temperature t, the voltage V generated in the circuit related to the temperature t as V = t (a + bt) Further, for this thermocouple, when V is in millivolts, the two constants are a = 0.25 and b = -5.5 x10+. Determine the value of V if the measured temperature is 100°C.arrow_forwardA vehicle moving horizontally gets a load of wind resistance acting in the opposite direction to the vehicle's motion F M cv? v is the horizontal speed of the vehicle. F is the thrust that comes from the vehicle engine c damping coefficient for wind resistance force (c =0.20 N.sec2/m2) M is the mass of the vehicle (M = 1000 kg) Using Newton's 2nd law, we get the equation of motion dv 1000- + 0,2 v² = F dt At steady state the speed of the car is vo = 30 m/s and thrust F, = 0.2 v3 = 180 N. If the car is moving at a speed around steady state v = vo + dv = 180 and F = F, + 8F, derive a linear differential equation connecting d(dv) ,8v and SF. dtarrow_forwardInitially, the temperature of an object is 70 degrees celsius, it is taken outside. The temperature of the surrounding is 20 degrees celsius at 3:03 Pm, the temperature of the body becomes 42 degrees celsius. Later, the object is then taken back inside where the temperature is 80 degrees celsius. At 3:10 PM, the temoerature of the object is 71 degrees celsius. Determine the time when the object is brought inside.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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