Engineers are examining how shock absorber designs affect the displacement of a mountain biker's hip after she lands from a jump. Immediately after the jump, the x and y locations of her hip can be described by
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Vector Mechanics For Engineers
- 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_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_forward100 10 Circular disk Sphere 0.1 0.01 1 10 100 1,000 10,000 100,000 1,000,000 10,000,000 Reynolds number Re = U d/v A spherical weather balloon of 2 m diameter is filled with hydrogen. The total mass of the balloon skin and the instruments it carries is 3.7 kg. At a certain altitude the density of air is 1.0 kg/m3 and is 10 times the density of hydrogen in the balloon; the viscosity of air is 1.8x10-5 Ns/m3. Determine the steady upward velocity of the balloon. m/s Drag coefficlent Caarrow_forward
- According to the Stefan-Boltzmann Law, the thermal radiation energy emitted (per unit time) by a hot object is proportional to the fourth power of the absolute temperature: E = kT, where k is a proportionality constant and T is measured in kelvin. Find the relationship between the measured error in temperature T and the resulting error in energy E.arrow_forwardThe displacement of a particle is given by s = 4t3 - 54t2 + 105t - 49 where s is in feet and t is in seconds. Plot the displacement, velocity, and acceleration as functions of time for the first 10 seconds of motion. After you have made the plots, answer the questions. Questions: Att- 2 sec, ft. v= ft/sec, a = ft/sec? %3D Att = 4.1 i ft. v= i ft/sec, a = i ft/sec? sec, Att = 8.7 i ft, v= i ft/sec, a = i ft/sec? sec, The velocity is zero when t = i sec and whent%3D i secarrow_forwardA weight is attached to a spring and reaches its equilibrium position (x = 0). It is then set in motion resulting in a displacement of x = 6 cos t, where x is measured in centimeters and t is measured in seconds. See the figure shown to the right. Answer parts (a) and (b). (b) What is the spring's velocity when t = 0? cm/sec (Type an integer or decimal rounded to one decimal place as needed.) ī www winn - 6 0 6 Equilibrium position at x = 0arrow_forward
- Newton'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_forwardFrom the curves shown in Animated Figure and using the following Equation, determine the rate of recrystallization for pure copper at the several temperatures. Make a plot of In(rate) versus the reciprocal of temperature (in K-1). (a) Determine the activation energy for this recrystallization process. (See Section FACTORS THAT INFLUENCE DIFFUSION.) (b) By extrapolation, estimate the length of time required for 50% recrystallization at room temperature, 20°C (293 K). (a) i kJ/mol (b) i daysarrow_forwardTo be able to solve rectilinear problems with variable functions. Let A=1/V feet per second per second; V0= 5fps. Find A, V and t when s = 25 ft.arrow_forwarda=2, b=1 A bullet is to be tested in the laboratory to determine the drag force on it. Dependent parameter the drag force D (Newton) depends on the velocity of the bullet V(m/s), the length of the bullet L(m), sound velocity c(m/s), density of fluid ρ (kg/m3) and dynamic viscosity µ(kg/ms). Solve the problem by making the necessary assumptions and drawing the schematic figure I-Determine the nondimensional p parameters using repeating variables ii-a bullet with a speed of 9a,b m/s in air may be modelled in a water tunnel with a test section velocity of 2ab cm/s. Determine the length of the model, if the length of the bullet is 5a,b mm. The air and water temperature is 20 oC degree at 1 atm. iii- if the drag force on the model is measured to be 2,ab N, then determine the expected drag force on the bullet. Comment on dynamic similarity equivalence?arrow_forwardHenri Darcy, a French engineer, proposed that the pressuredrop ∆ p for fl ow at velocity V through a tube of length Lcould be correlated in the form ∆p ___________ = α LV2 ρ If Darcy’s formulation is consistent, what are the dimensionsof the coefficient α ?arrow_forwardQI: A shaft carries four masses in parallel planes A, B, C and D in this order along its length. The masses at B and C are 18 kg and 12.5 kg respectively, and each has an eccentricity of 60 mm. The masses at A and D have an eccentricity of 80 mm. The angle between the masses at B and C is 100° and that between the masses at B and A is 190°, both being measured in the same direction. The axial distance between the planes A and B is 100 mm and that between B and C is 200 mm. If the shaft is in complete dynamic balance, determine: 1. The magnitude of the masses at A and D; 2. the distance between planes A and D ; and 3. the angular position of the mass at D.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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