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A brass (nonmagnetic) block A and a steel magnet B are in equilibrium in a brass tube under the magnetic repelling force of another steel magnet C located at a distance
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Vector Mechanics For Engineers
- The position of a 2 kg object is given as x(t) = 3t2 +5, where z is in meters and t is in seconds. (a) Determine the force F responsible for this motion. (b) If the force only results in a change in the kinetic energy of the object of 200J between ty =0s and ta = 5 s, determine the value of 3. (c) Without using kinematies (equations of motion), determine the displacement of the object durine these 5 seconds referred to in part (b).arrow_forwardA constant force acting on a particle can be expressed in Cartesian vector form as F = 8i - 6j + 2k lb. Determine the work done by the force on the particle if the displacement of the particle can be expressed in Cartesian vector form ass= Si + 4j + 6k ft.arrow_forwardA car weighing 500 kg moving with a speed of 10 m/s takes a turn around a circle with a radius of 25 m. Find: 1- The acceleration and the net force acting upon the car. 2- The angular velocity and angular acceleration. 3- The time period *arrow_forward
- show each step for answerarrow_forwardA spring with a spring constant k of 20 pounds per foot is loaded with a 10-pound weight and allowed to reach equilibrium. It is then displaced 1 foot downward and released. If the weight experiences a retarding force in pounds equal to four times the velocity at every point, find the equation of motion. y(t) = where t is time (in seconds) and y(t) is displacement (in feet).arrow_forwardy (m) 2 intervals. The Figure shows the result of a collision of a 10.00 kg ball with an object located at the origin. The position of the objects are shown at 1.3 s -2 06 يه ® © ® Ⓡ • 0 x (m) + 2 What is the mass of the object that was originally located at the origin? What is the change in the kinetic energy as a result of the collision?arrow_forward
- The 20-kg block is subjected to the action of the harmonic force F = (90 cos 6t) N, where t is in seconds. (Figure 1) Figure k= 400 N/m k = 400 N/m O 20 kg F= 90 cos 6t 125 N.s/m 1 of 1 Part A Write the equation which describes the steady-state motion. Express your answer in terms of t. Express your answer using three significant figures. Express the phase in radians and the final result in meters. x = Submit 17 ΑΣΦ Provide Feedback ↓↑ Request Answer vec ? m Next >arrow_forward1. An automobile of mass M=5400 kg is moving at a speed of 30 m/s.The engine is disengaged suddenly at t= 0 sec. Assume that the equation of motion after t-0 is given by 5400 v- dv = -8.276 v-2000 dx Where v= v(t) is the speed (m/sec) of the car at t. The left side represents Mv (dv/dx).The first term on the right side is the aerodynamics drag, \\\\\\\\\|\||\\\|||||| || lland the second term is the rolling resistance of the tires. Calculate how far the car travels until the speed reduces to 15 m/sec.(hint: the equation of motion may be integrated as 5400 v dv 30 = Jdx=x 8.276 v+2000 Evaluate the preceding equation using Simpson rule).arrow_forwardAn automobile P is traveling along a circular track of radius R=958.4 m. At position "A" on the track, the automobile has a speed of UA = 10.3 m/s. At this position, the driver of the automobile applies the brakes causing the speed of the automobile to change with distance s traveled along the track according to the following equation: U(S) = VA COS(0.001s) m/s (cos is in radians), where s is given in meters. Determine the magnitude of the acceleration for the driver when the automobile reaches position "B" on the track where "B" is a quarter of the distance around the track from position "A". R B O circular trackarrow_forward
- Q2. The acceleration function of an object doing curvilinear motion is a = {(-C.t) i+2j+1.5 k} m/s², where Cis a constant and t is the time in s. If the constant C is 0.4, and the initial velocity vo = 8.2 i m/s at time t = 0, and initial position is at the origin, determine the magnitude of its velocity when t = 2 s. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point, and proper Sl unit. Your Answer: Answer unitsarrow_forwardA 64 Ib object stretches a spring 4 ft in equilibrium. The object is initially displaced 18 inches above equilibrium and given a downward velocity of 4 ft/sec. Equation of motion is d(t) = A cos wnt + B sin wnt. Use 32 ft/sec2 as gravitational accelerationarrow_forwardProblem 2.23| A bicycle is moving to the right at a speed vg = 20mph on a horizontal and straight road. The radius of the bicycle's wheels is R = 1.15 ft. Let P be a point on the periphery of the front wheel. One can show that the x and y coordinates of P are described by the following functions of time: x(t) = at + R sin(uot/R) and y(t) = R[1 + cos(vor/R)]. Determine the expressions for the velocity, speed, and accelera- tion of P as functions of time. Vparrow_forward
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