Physics 111/121 Vector Mini-Review Problems (See last page for answers) Contents FOP 3-11, 3-18, 3-15, 3-21 FOP 5-6, 5-7 FOP 7-6, 7-11 FOP 10-46, 12-19, 12-21, 12-25

Problem 3-11:A woman walks 250 m in the direction 30° east of north, then 175 m directly east. Find (a) the magnitude and (b) the angle of her final displacement from the starting point. (c) Find the distance she walks. (d) Which is greater, that distance or the magnitude of her displacement? Problem 3-18: Here are two vectors: What are (a) the magnitude and (b) the angle (relative to i ) of a? What are (c) the magnitude and (d) the angle of b ? What are (e) the magnitude and (f) the angle of a + b ; (g) the magnitude and (h) the angle of b - a ; and (i) the magnitude and (j) the angle of a - b ? (k) What is the angle between the directions of b - a and a - b ?

Problem 3-15E: Vector a has a magnitude of 5. 0 m and is directed east Problem 3-15E: Vector a has a magnitude of 5.0 m and is directed east. Vector b has a magnitude of 4.0 m and is directed 35° west of north. What are a) the magnitude and (b) the direction of a + b ? What are (c) the magnitude and direction of b - a ? Problem 3-21: The two vectors a and b in the figure have equal magnitudes of 10.0 m. Find (a) the x component and (b) the y component of their vector sum r , (c) the magnitude of r , and (d) the angle r makes with the positive direction of the x axis. Problem 5-6: Three astronauts, propelled by jet backpacks, push and guide a 120 kg asteroid toward a processing dock, exerting the forces shown in the figure. What is the asteroid's acceleration (a) in unit- vector notation and as (b) a magnitude and (c) a direction?

Problem 5 - 7: There are two forces on the 2 Problem 5 - 7: There are two forces on the 2.0 kg box in the sketch but only one is shown. The figure also shows the acceleration of the box. Find the second force (a) in unit-vector notation and as (b) a magnitude and (c) a direction. Problem 7-6 A floating ice block is pushed through a displacement d = (15 m)i - (12 m)j along a straight embankment by rushing water, which exerts a force F = (210 N)i - (150 N)j on the block. How much work does the force do on the block during the displacement?

Prob 7-11: The figure shows three forces applied to a trunk that moves leftward by 3.00 m over a frictionless floor. The force magnitudes are F1 = 5.00 N, F2 = 9.00 N, and F3 = 3.00 N. During the displacement, (a) what is the net work done on the trunk by the three forces and (b) does the kinetic energy of the trunk increase or decrease? By how much? Problem 10-46: Two 2.0 kg bodies, A and B, collide. The velocities before the collision VA = 15i + 30j and vB = -10i + 5.0j. After the collision, v´A = -5.0i + 20j. All speeds are given in meters per second. (a) What is the final velocity of B? (b) How much kinetic energy is gained or lost in the collision? Problem 12-19: What are the magnitude and direction of the torque about the origin on a particle located at coordinates (0, -4.0 m, 3.0 m) due to (a) force F1 with components F1x = 2.0 N and F1y = F1z = 0, and (b) force F2 with components F2x = 0, F2y = 2.0 N, and F2z = 4.0 N?

Problem 12-21: Force F = (-8. 0 N)i + (6 Problem 12-21: Force F = (-8.0 N)i + (6.0 N)j acts on a particle with position vector r = (3.0 m)i + (4.0 m)j. What are (a) the torque on the particle about the origin and (b) the angle between the directions of r and F ? Problem 12-25: At a certain time, a 0.25 kg object has a position vector r = 2.0i - 2.0k, in meters. At that instant, its velocity in meters per second is v= -5.0i + 5.0k, and the force in newtons acting on it is F= 4.0j. (a) What is the angular momentum of the object about the origin? (b) What torque acts on it?

Physics 111/106 Vector Mini-Review Problem Answers for Physics 106 Students (11/2003) 3-11: a) 370 m b) 35.8o c) 425 m d) distance 3-18: a) 5 m b) -36.9o c) 10 m d) 53.1o e) 11.2 m f) 26.6o g) 11.2 m h) 79.7o i) 11.2 m j) –100.3o k) 180o 3-15: a) 4.3 m b) 50.4o c) 8 m d) 156o 3-21: a) 1.59 m b) 12.1 m c) 122 m d) 82.5o 5-6: a) a = 0.86i – 0.167j m/s/s b) a = 0.876 m/s/s c) –10.7o 5-7: a) F2 = -32 i + 21j N b) F2 = 38 N c) 213o 7-6: 4950 J 7-11: a) 1.5 J F2 K increases by 1.5 J 10-46: a) 10i + 15j m/s b) 6.08 J lost 12-19: a) 10 N.m @ 53o b) 22 N.m along negative x-axis 12-21: a) 50k N.m b) 90o r and F are perpendicular 12-25: a) zero b) 8( i + k) N.m