A river flows north with a speed of 3 mileshr a man rows a

Question

ENGINEERING MECHANICS FINAL EXAM-

PROBLEM 1: A body moves so that the x component of acceleration is given by the equation 6 - t and the y component of acceleration is given by 6 + t. If the initial x and y components of velocity are both 2, the speed of the body at the end of 2 sec is closest to

(A) 12

(B) 14

(C) 16

(D) 18

(E) 20

PROBLEM 2: The driver of a car traveling 30 miles/hr suddenly applies the brakes and skids 60 ft before corning to a stop.

(1) If the car weighs 1600 lb and a constant rate of deceleration is assumed, the rate of deceleration is nearest to

(A) -8.0 ft/sec²

(B) -16.1 ft/sec²

(C) -24.1 ft/sec²

(D) -32.2 ft/sec²

(E) -40.2 ft/sec²

PROBLEM 3: A weight is attached to one end of a 53-ft rope passing over a small pulley 29 ft above the ground. A man whose hand is 5 ft above the ground grasps the other end of the rope and walks away at the rate of 5 ft/sec. When the man is 7 ft from a point directly under the pulley, the rate at which the weight is rising is closest to

(A) 1.0 ft/sec

(B) 1.4 ft/sec

(C) 2.5 ft/sec

(D) 3.6 ft/sec

(E) 5.0 ft/sec

 

PROBLEM 4: A river flows north with a speed of 3 miles/hr. A man rows a boat across the river. His speed relative to the water is 4 miles/hr. What is his velocity relative to the earth?

(A) 4 miles/hr

(B) 3 miles/hr

(C) 7 miles/hr

(D) 1 miles/hr

(E) 5 miles/hr

PROBLEM 5: A car jumps across a 10-ft-wide ditch with a constant velocity V. The ditch is 6 in. lower on the far side. The minimum velocity (in miles per hour) that will keep the car from falling into the ditch is nearest to

(A) 35

(B) 40

(C) 45

(D) 50

(E) 55

PROBLEM 6: A batted baseball leaves the bat at an angle of 30°.above the horizontal and is caught by an outfielder 400 ft from home plate. Assume the ball's height when hit is the same as when caught and that air resistance is negligible. The initial velocity of the ball is closest to

(A) 200 ft/sec

(B) 175 ft/sec

(C) 150 ft/sec

(D) 125 ft/sec

(E) 100 ft/sec

PROBLEM 7: A satellite travels in a perfectly circular orbit around the earth at an altitude of 1000 miles. Assume the earth is a perfect sphere with a radius of 4000 Miles and that the force of the earth's gravity g at the height of the satellite is 20.6 ft/sec². The speed of the satellite is nearest to

(A) 10,000 miles/hr

(B) 12,000 miles/hr

(C) 14,000 miles/hr

(D) 16,000 miles/hr

(E) 18,000 miles/hr

PROBLEM 8: An elevator, which with its load weighs 70,000 N (Newton's), is descending at a speed of 4.5 m/sec. If the load on the cable must not exceed 125,000 N, the shortest distance in which the elevator should be stopped is most nearly

(A) 0.6 m

(B) 1.0 m

(C) 1.3 m

(D) 2.0m

(E) 2.6 m

PROBLEM 9: The acceleration of the 8-lb weight is closest to

(A) 38.6 ft/sec²

(B) 32.2 ft/sec²

(C) 17.6 ft/sec²

(D) 9.2 ft/sec²

(E) 7.4 ft/sec²    

PROBLEM 10: This system is initially at rest. The force P that will be required to give the 100-lb block a velocity V of 10 ft/sec up the plane in a time interval of 5 sec is most nearly

(A) 360 lb

(B) 310 lb

(C) 116 lb

(D) 58 lb

(E) 45 lb

PROBLEM 11: A 16-lb weight and an 8-lb weight resting on a horizontal frictionless surface are connected by a cord A and are pulled along the surface with a uniform acceleration of 4 ft/sec² by a second cord attached to the 16-lb weight. The tension in cord A is closest to

(A) 4 lb

(B) 1 lb

(C) 2 lb

(D) 3 lb

(E) 32 lb

PROBLEM 12: A weight W is suspended by two strings, AB and AC, as shown. The ratio of the forces in AC(1) just before, to (2) just after the instant that AB is cut is most nearly

(A) 2.0

(B) 1.6

(C) 1.4

(D) 1.0  

(E) 0.5

PROBLEM 13: A 0.25-kg ball is thrown horizontally with a kinetic energy of 50 joules from a vertical cliff 20 m high.

(1) The ball's kinetic energy when it strikes the ground, level with the base of the cliff, is most nearly

(A) 50 J

(B) 55 J

(C) 100 J

(D) 250 J

(E) 5000 J

(2) The distance from the foot of the cliff to the point where the ball strikes the ground is most nearly

(A) 20m

(B) 25 m

(C) 30 m

(D) 35 m

(E) 40 m

PROBLEM 14: A 150-lb man stands at the rear of a 250-lb boat. The distance from the man to the pier is 30 ft, and the length of the boat is 16 ft. Assume no friction between the boat and the water. The distance of the man from the pier after he walks to the front of the boat at a velocity of 3 miles/hr is most nearly

(A) 14 ft

(B) 16 ft

(C) 20 ft

(D) 24 ft

(E) 30 ft

PROBLEM 15: A projectile weighing 100 lb strikes the concrete wall of a fort with an impact velocity of 1200 ft/sec. The projectile comes to rest in 0.01 sec, having penetrated the 8-ft thick wall to a distance of 6 ft. The average force exerted on the wall by the projectile is closest to

(A) 2 x 10⁵ lb

(B) 3 x 10⁵ lb

(C) 1 x 10⁷ lb

(D) 2 x 10⁸ lb

(E) 1 x 10¹⁰ lb

PROBLEM 16: A 10-lb block which is suspended by a long cord is at rest when a 0.05-lb bullet traveling horizontally to the left strikes and is embedded in it. The impact causes the block to swing upward 0.5 ft measured vertically from its lowest position.

(1) The velocity of the bullet just before it strikes the block is most nearly

(A) 80 ft/sec

(B) 200 ft/sec

(C) 1135 ft/sec

(D) 1140 ft/sec

(E) 1600 ft/sec

(2) The loss of kinetic energy of the system during impact is most nearly

(A) 5 ft-lb

(B) 30 ft-lb

(C) 1005 ft-lb

(D) 1010 ft-lb

(E) 1980 ft-lb

PROBLEM 17: A static weight W produces a static deflection of 2 in. in a spring having a spring constant k. The mass of the spring is neglected.

1) The maximum deflection x when the weight W is dropped on the spring from a point 6 in. above the free position of the spring is most nearly

(A) 2.0 in.

(B) 4.6 in.            

(C) 5.3 in.

(D) 6.6 in.

(E) 7.3 in.            

2) The maximum velocity of the falling weight is most nearly

(A) 5.5 ft/sec

(8) 5.7 ft/sec

(C) 5.9 ft/sec

(D) 6.1 ft/sec

(E) 6.3 ft/sec

PROBLEM 18: An unbalanced flywheel has its center of mass 4.00 in. from the axis of rotation. The radius of gyration of the flywheel with respect to an axis through the center of mass parallel to the axis of rotation is 16.00 in. The flywheel, which weighs 145.0 lb, is rotating clockwise about its axis at an angular speed of 3600 rpm when a counterclockwise torque T 18.0t² is applied, where T is in pound-feet and t is in seconds. Neglecting friction, the angular speed in revolutions per minute of the flywheel when t is 10.00 sec is closest to

(A) 1500 rpm clockwise

(B) 2900 rpm clockwise

(C) 3600 rpm counterclockwise

(D) 3100 rpm counterclockwise

(E) 16,600 rpm counterclockwise

PROBLEM 19: A homogeneous solid cylinder of mass m and radius R has a string wound around it. One end of the string is fastened to a fixed point, and the cylinder is allowed to fall as shown.

The moment of inertia of a cylinder about its axis is ½mR². The tension in the string is

(A) 1/3mg

(B) 1/2mg

(C) 3/5mg

(D) 2/3mg

(E) mg  

PROBLEM 20: If the system shown in figure is released from rest, the angular acceleration of the circular drum is most nearly.

(A) 4.4 rad/sec²

(B) 1.3 rad/sec²

(C) 8.3 rad/sec²

(D) 1.7 rad/sec²

(E) 24.2 rad/sec²