(6) Use the scalar components approach to determine the moment of the 5 kN force applied at A about point B. Ans: MB=75.0 kN·m CW y, m F=5 kN B (16, 0) 60° | A (12,-15) x, m
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- A basket of flowers of mass 3 kg is placed on a flat grassy slope that makes an angle θ with the horizontal. The coefficient of static friction between the basket and the slope is 0.45 and the basket is on the point of slipping down the slope. Model the basket of flowers as a particle and the grassy slope as a plane. Take the magnitude of the acceleration due to gravity, g, to be 9.8 m s−2 Express the forces in component form, in terms of θ and unknown magnitudes where appropriate. Write down the equilibrium condition for the basket and hence show that tan θ = 0.45. Determine the angle, in degrees, that the slope makes with the horizontal.Find a unit vector parallel to the tangent line of y = x at (2,8). What angle does this vector make with a horizontal line in the positive direction?(7) The effect of a slam dunk can be simulated by a force F = 47 lb acting at the front edge of the rim at point A shown. Use the scalar components approach to determine the moments of the force F about point O Mo and point B MB. Ans: Mo=81.5 lb-ft CCW, MB = 115.9 lb-ft CW -36"- B 12" 28" 10' F
- A sodium ion (Na+) moves in the xy-plane with a speed of 2.90 ✕ 103 m/s. If a constant magnetic field is directed along the z-axis with a magnitude of 3.25 ✕ 10−5 T, find the magnitude of the magnetic force acting on the ion and the magnitude of the ion's acceleration. HINT (a) the magnitude (in N) of the magnetic force acting on the ion N (b) the magnitude (in m/s2) of the ion's acceleration m/s24. Your upper arm exerts 60N and lower arm exerts 40N anteriorly and superiorly. When your upper and lower arms are bent at 90°, describe the magnitude and direction of the resultant force exerted on your arm. nff a long jumper has a forward (horizontal) velocity of 15m/sec and a vertical ntall and the magnitude of theWrite Newton’s Second Law of Motion for three-dimensionalmotion with only the gravitational force (acting in the z-direction).
- A sheet of water of uniform thickness (h = 0.03 m) flows from the device shown in the figure below. The water enters vertically through the inlet pipe and exits horizontally with a speed that varies linearly from 0 to 11 m/s along the 0.2-m length of the slit. Determine the y component of anchoring force necessary to hold this device stationary. FAY = 0 m/s- i 0.2m 0.03m N 11m/sA particle is moving along the curve having the vector equation R(t) = 4 cos ti + 4 sin tj + 6tk. Find the magnitude of velocity and acceleration vectors when t = 2A seasoned parachutist went for a skydiving trip where he performed freefall before deploying the parachute. According to Newton's Second Law of Motion, there are two forcës acting on the body of the parachutist, the forces of gravity (F,) and drag force due to air resistance (Fa) as shown in Figure 1. Fa = -cv ITM EUTM FUTM * UTM TM Fg= -mg x(t) UTM UT UTM /IM LTM UTM UTM TUIM UTM F UT GROUND Figure 1: Force acting on body of free-fall where x(t) is the position of the parachutist from the ground at given time, t is the time of fall calculated from the start of jump, m is the parachutist's mass, g is the gravitational acceleration, v is the velocity of the fall and c is the drag coefficient. The equation for the velocity and the position is given by the equations below: EUTM PUT v(t) = mg -et/m – 1) (Eq. 1.1) x(t) = x(0) – Where x(0) = 3200 m, m = 79.8 kg, g = 9.81m/s² and c = 6.6 kg/s. It was established that the critical position to deploy the parachutes is at 762 m from the ground…
