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
- A ball is thrown vertically up from the top of a building with height h= 30m with an initial speed of v0=20 m/s A. Ignoring effects of air resistance find the maximum height reached by the ball above the top of the building. B. The total time the ball is in the air before it hits the horizontal ground at the foot of the building. C. The total displacement. D. The total distance traveled by the ball. E. The average velocity of the ball. F. The average speed of the ball. G. The velocity of the ball just before it hits the ground.arrow_forwardPART OF MECHANICAL VIBRATIONS A viscously damped single degree of freedom mass–spring system hasm = 0.5 kg, k = 1000 N/m, and c = 10 N ·s/m. The mass is set in motion withinitial conditions x0 = 0.05 m and x˙0 = 0.5 m/s. Determine the displacement,velocity, and acceleration of the mass after 0.3 sarrow_forwardThe figure shown below is released from rest with the spring unstretched. Use the datum shown for zero gravitational potential energy. For the values given below answer the following questions:Position 1 is Ha1 μk=0.14 k=32.5 Nm hA1=0.6 m mA=4.6 kg mB=1.3 kg What is the Gravitational Potential Energy for mass mA at position 1 (remember your signs)? What is the Gravitational Potential at position 1 for mB? What is the Potential Energy of the spring at position 1? What is the Kinetic Energy at position 1 for mA? What is the Kinetic Energy at position 1 for mB? Again we have the figure shown below that was released from rest with the spring unstretched. Use the datum shown for zero gravitational potential energy. At position 2 the spring is at its max stretch. Remember we have the values below; answer the following questions: μk=0.14 k=32.5 Nm hA1=0.6 m mA=4.6 kg mB=1.3 kg What is the max stretch in the spring?arrow_forward
- 1) A 100-V shunt motor is developing 6 hp while operating at an overall efficiency of 86%. The armature and shunt field resistances are 0.06 and 50 ohms respectively. Determine the stray power losses. 2) The field and armature resistance of a 400 V shunt motor are 200 ohms and 0.1 ohms, respectively. The motor takes 30 A of current while running at 1000 rpm. If the frictional losses are 400 W, determine the motor efficiency. 3) In a brake test of an elevator door, the ammeter and voltmeter measuring the input read 34 A at 220 V. The speed of the motor is found to be 910 rpm and the balance on the 0.61 m brake arm reads 11.9 kg. The dead weight of the arm is found to be 1.09 kg. What is the hp output of the motor?arrow_forwardDetermine the time required to stop a Car weighing 1000 kg, moving at a velocity of 120 km/hr, provided with a braking system, develops a pressure of 10 bar in the brake cylinder, with a diameter of 25 cm.arrow_forwardThe figure below shows a conducting rod sliding along a pair of conducting rails. The conducting rails have an angle of inclination of θ = 32.0 degrees. There is a resistor at the top of the ramp that connects the two conducting rails (R = 1.5 ohms). The mass of the rod is 0.43 kg. The rod starts from rest at the top of the ramp at time t = 0. The rails have negligible resistance and friction, and are separated by a distance L = 15.3 m. There is a constant, vertically directed magnetic field of magnitude B = 1.40 T. What is the rod's terminal speed?arrow_forward
- Consider a mass-and -spring system containing two masses m1=1 and m2=1 whose displacement functions x(t) and y(t) satisfy the differential equations : x'' = -10x + 2y y'' = 3x -15y Assume that the two masses start in motion with the initial conditions x(0) =32, x'(0)=6, and y(0)=36, y'(0)=3 and are acted on by the same force F1(t)=F2(t)=-1320cos(7t). Describe the resulting motion as a superposition of oscillations at the three different frequencies. The three frequencies consist of lower, higher, and the forcing frequency. For each one please compare the magnitude of m2 to m1.arrow_forwardBallistic Pendulum To apply conservation of energy and momentum. As shown, an object of mass m is fired with an initial speed v0 at a ballistic pendulum’s bob. The bob has mass M and is suspended by a massless rod of length L. After the collision, the pendulum’s bob and object stick together and swing to a maximum angular displacement θ. Find an expression for v0, the initial speed of the object fired. Express your answer in terms of some or all of the variables m, M, L, and θ and g, the acceleration due to gravity.arrow_forwardA lightweight drone (1.00 kg) is launched at 800 m high and moves upward at a constant velocity (while ignoring the effects of gravity only on the drone). The balloon, when measured at a horizontal distance from you, is about 1600 m away from you. At the moment when the drone moves, you shoot a bullet (weight =180 g) with an initial velocity of 1009 m/s at a fixed angle α, where sin α=3/5 and cos α= 4/5. (g = 9.8 m/s2) c. What is the upward velocity of the drone?arrow_forward
- The displacement of a machine is expressed as x(t) = A sin(6t + Φ), where x is in meters and t is in seconds. If the displacement and the velocity of the machine at t = 0 are known to be 0.05 m and 0.005 m/s, determine by how much the response of the system leads the reference wave.arrow_forwardTwo types of motorcycle, Type A has two identical and independent tires, and the failure rate of each tire is 0.0006 failures per hour. Type B has three identical and independent tires, and the failure rate of each tire is 0.0006 failures per hour. Obviously, when any one of the tires for both types is punctured, the motorcycle cannot be driven. Calculate the following for both types A and B: (a) Motorcycle failure rate with respect to tires. (b) Motorcycle reliability for a 20-h mission with respect to tires. (c) Motorcycle mean time to failure with respect to tires. (d) Which motorcycle type would you recommend buying and why?arrow_forwardHailstorms such as the one that broke the tiles on this roof cause billions of dollars of damage every year in North America alone. Which would do the greater amount of damage? (i) A 0.2 kg hailstone that hits at speed 15 m/s; (ii) a 0.1 kg hailstone that hits at speed 30 m/s; (iii) both would do the same amount of damage.arrow_forward
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