Problem 1.1P: A person weighs 30 lb on the moon, where g=5.32ft/s2. Determine (a) the mass of the person; and (b)... Problem 1.2P: The radius and length of a steel cylinder are 40 mm and 110 mm, respectively. If the mass density of... Problem 1.3P: Convert the following: (a) 400lbft to knm; (b) 6m/s to mi/h; (c) 20lb/in.2 to Pa; and (d)... Problem 1.4P: A compact car travels 30 mi on one gallon of gas. Determine the gas mileage of the car in km/L. Note... Problem 1.5P: The kinetic energy of a car of mass m moving with velocity v is E=mv2/2. If m=1000kg and v=6m/s,... Problem 1.6P: In a certain application, the coordinate a and the position coordinate x of a particle are related... Problem 1.7P: When a force F acts on a linear spring, the elongation x of the spring is given by F = kx, where k... Problem 1.8P: In some applications dealing with very high speeds, the velocity is measured in mm/s. Convert 8mm/s... Problem 1.9P: A geometry textbook gives the equation of a parabola as y=x2, where x and y are measured in inches.... Problem 1.10P: A differential equation is d2ydt2=Ay2+Byt where y represents a distance and t is time. Determine the... Problem 1.11P: The position coordinate x of a particle is determined by its velocity v and the elapsed time t as... Problem 1.12P: A differential equation encountered in the vibration of beams is d4ydx4=2D where x = distance... Problem 1.13P: Determine the dimensions of constants A and B far which the following equation is dimensionally... Problem 1.14P: The typical power output of a compact car engine is 110 hp. What is the equivalent power in (a)... Problem 1.15P: Two 12-kg spheres are placed 400 mm apart. Express the gravitational attraction acting between the... Problem 1.16P: Two identical spheres of radius 8 in. and weighing 2 lb on the surface of the earth are placed in... Problem 1.17P: A man weighs 170 lb on the surface of the earth. Compute his weight in an airplane flying at an... Problem 1.18P: Use Eq. (1.4) to show that the weight of an object on the moon is approximately 1/6 its weight on... Problem 1.19P: Plot the earths gravitational acceleration g(m/s2) against the height h (km) above the surface of... Problem 1.20P: Find the elevation h (km) where the weight of an object is one-tenth its weight on the surface of... Problem 1.21P: Calculate the gravitational force between the earth and the moon in new-tons. The distance between... Problem 1.22P: The magnitudes of the two velocity vectors are v1=5m/s and v2=3m/s. Determine their resultant... Problem 1.23P: Determine the magnitudes of vectors v1 and v2 so that their resultant is a horizontal vector of... Problem 1.24P: The pole AB is held up by the rope attached to B. The magnitude of the force in the rope is T=240lb.... Problem 1.25P: Resolve the 20-kN force into components along the u- and v-axes. Problem 1.26P: The velocity vector of the boat has two components: v1 is the velocity of the water, and v2 is the... Problem 1.27P: Two members of a truss apply the forces shown to the gusset plate. If the resultant at these forces... Problem 1.28P: Two members of a truss apply the forces shown to the gusset plate. Knowing that P = 10000 lb,... Problem 1.29P: Determine the resultant of the position vectors A and B. Problem 1.30P: Resolve the position vector A of the car (measured from fixed point O) into components parallel to... Problem 1.31P: Resolve the 360-lb force into components along the cables AB and AC. Use =60 and =40. Problem 1.32P: The supporting cables AB and AC are oriented so that the components of the 3604b force along AB and... Problem 1.33P: The two forces shown act on the structural member AB. Determine the magnitude of P such that the... Problem 1.34P: The resultant of the two forces has a magnitude of 800 lb. Determine the direction of the resultant... Problem 1.35P: The forces acting on the bob of the pendulum are its weight W(w=2lb) and the tension T in the cord.... Problem 1.36P: A surveyor sights a target at C from points A and B. recording the angles shown. Determine the... Problem 1.37P: Knowing that the resultant of the two forces is vertical, determine the angle Problem 1.38P: To move the oil drum, the resultant of the three forces shown must have a magnitude of 500 N.... Problem 1.39P: The resultant of the 50-Ib and 30-lb forces is R. If R = 65 lb, determine the angles and . Problem 1.40P: Obtain the rectangular representation of the force P, given that its magnitude is 30 lb. Problem 1.41P: The length of the position vector r is 240 mm. Determine the rectangular components of (a) r; and... Problem 1.42P: Determine the rectangular components of the 560-lb force. Show the components on a sketch. Problem 1.43P: The coordinates of points A and B are (-3, 0, 2) ft and (4, 1, 7) ft, respectively. Determine (a)... Problem 1.44P: The slider travels along the guide rod AB with the velocity v = 8 m/g. Determine the rectangular... Problem 1.45P: Find the rectangular representation of the force F, given that its magnitude is 320 N. Problem 1.46P: The magnitude of the force F is 160 lb. Find its rectangular representation. Problem 1.47P: A rifle at A is fired at a target at B. If the speed of the bullet is 1400 ft/s, determine the... Problem 1.48P: The pole OB is subjected to the 6004b force at B. Determine (a) the rectangular components of the... Problem 1.49P: The cables AB and AC are attached to the frame OBCD and pre-tensioned to 35 kN. Determine the... Problem 1.50P: The two forces are applied to the end of the boom OA. Determine the force F so that the resultant of... Problem 1.51P: The magnitudes of the three forces are F1=1.6kN,F2=1.2kN and F3=1.0kN. Compute their resultant in... Problem 1.52P: Given that P=120lb and Q=130lb, find the rectangular representation of P+Q. Problem 1.53P: Knowing that P=90lb and that the resultant of P and Q lies in the positive x-direction, determine Q... Problem 1.54P: If R is the resultant of the forces P and Q, find P and Q. Problem 1.55P: The force R is the resultant of P and 0. Determine Q and the angle . Problem 1.56P: The vertical post is secured by three cables. The cables are pre-tensioned so that the resultant of... Problem 1.57P: Compute the dot product A - B for each of the following cases. Identify the units of each product.... Problem 1.58P: Compute the cross product C=AB for each of the cases given in Prob. 1.51 Identify the units of each... Problem 1.59P: Given r=4i6j+2km (position vector) F=20i+40j30kN (force vector) =0.8j+0.6k (dimensionless unit... Problem 1.60P: Compute AB and CB for the position vectors shown. Problem 1.61P: Use the dot product to find the angle between the position vectors A and B. Check your results by... Problem 1.62P: Use the dot product to find the angle between the position vectors A and B. Problem 1.63P: Let A and B be two nonparallel vectors that lie in a common plane S. If C=A(AB), which of the... Problem 1.64P: Determine (a) the angle between the position vectors P and Q; and (b) a unit vector perpendicular to... Problem 1.65P: Find a unit vector that is perpendicular to both A=4i-3j-2km and B=2i4j+3km. Problem 1.66P: The three points A(0,2,2),B(1,4,1), and C(3,0,0) define a plane. The coordinates are in inches. Find... Problem 1.67P: For the position vectors P and Q shown, determine the orthogonal component of P Ă— Q in the... Problem 1.68P: Compute the orthogonal Component of F=6i+20j12klb in the direction of the vector A=2i3j+5kft. Problem 1.69P: Compute the value of the scalar a for which the vectors A=3i+aj+2k and B=4ijk will be perpendicular. Problem 1.70P: Resolve A=3i+5j4k in. into two vector components-one parallel to and the other perpendicular to... Problem 1.71P: The force F=5i+12j+4k lb is applied to the handle of the door. Determine the orthogonal component of... Problem 1.72P: Determine the value of the scalar a if the following three vectors are to lie in the same plane:... Problem 1.73P: Resolve the force F=20i+30j+50klb into two components-one perpendicular to plane ABC and the other... Problem 1.74P: It can be show that a plane area may he represented by a vector A=A, where A is the area and ... Problem 1.75P: The coordinates of the corners of a triangle ABC are A(3,1,0),B(2,2,3), and C(0,0,4). The units are... Problem 1.76P: Show that |abc| equals the volume of a parallelepiped that has a, b, and c as its edges. (Hint: See... format_list_bulleted
