PHYS 150 FINAL EXAM ; 12/07/07 ; Dr. Holmes
; NAME:
DO ALL THE PROBLEMS. THE WORTH OF EACH PART
OF EACH PROBLEM IS MARKED NEXT TO THE SLOT FOR THE ANSWER. SHOW YOUR WORK FOR
PARTIAL CREDIT. ALL ANSWERS SHOULD BE IN MKS UNITS UNLESS OTHERWISE INDICATED.
1) Add the following vectors. Express your answer in POLAR form:
vector A = (20 meters, 73 degrees)
vector B = (25 meters, 145 degrees)
vector C = (17 meters, 298 degrees)
vector A + vector B + vector C =
(19.62 meters, 109.8 degrees)
Draw a diagram showing each of the vectors A, B, and C and the resultant vector.
2) To the
right is a graph of v(t). On the graphs below it, sketch x(t) and a(t) assuming
that xo< 0.
3) An object is thrown straight up with an initial speed of 27 m/s from the ground.
a) How high will the object go (measured from ground level) before it starts to fall back down?
37.19 m .
b) How long will it take the object to reach its maximum height?
2.75 sec.
4) Below are the numerical values of velocity at specific times.
v(0 sec) = +5.0 m/s
v(1 sec) = +1.0 m/s
v(2 sec) = - 2.0 m/s
v(3 sec) = +3.0 m/s
v(4 sec) = +8.0 m/s
a) Using the numerical method, calculate the average acceleration during the time between t=3 seconds and t=4 seconds:
+5 m/s2 .
b) Calculate the position at t=3 seconds. You should assume that x = +3 m when t = 0 seconds [i.e., xo = +3 m.]:
6 m.
5) An object at the top of a building 8 meters above the ground is thrown up and out with an initial speed of 27 m/s and an initial angle of 39o with respect to the horizontal. Assume that there is negligible air resistance on the object in flight.
a) How long a time will it take the object to hit the ground?
3.89 sec.
b) How far away horizontally did the object land from the building?
81.6 m.
c) How long a time did it take the object to reach the highest point of its trajectory?
1.73 sec.
d) How high up did the object reach at its highest point (as measured from the base of the building [ground level] ?
22.66 m.
6) A weight is held up by a rope attached to the ceiling and a rigid bar attached to a side wall and pivoted so it is free to rotate. The rope is tied on the side nearer the wall. The weight is 440 Nt, qrope-ceiling = 60° and qrod-wall = 70°. (Neglect the weight of the rope and the weight of the rod).
a) Will the rod be pulling down and towards the wall of up and away from the wall?
Up and away from the wall.
b) Will the sum of the magnitudes of the tension in the rope and the pull or push of the rod be equal to, greater than, or less than the weight?
Greater than.
c) What is the tension in the rope?
420 Nt.
7) Consider an object on a scale in an elevator. At one particular instant the elevator has an acceleration of +1.2 m/s2 and a speed of –1.7 m/s. (Plus means up and minus means down.)
a) Is the elevator going slower (speed becoming less negative), going faster (negative speed getting more negative), or maintaining its speed?
Going slower (negative speed becoming less negative).
b) If the scale reads 600 Nts. at this instant, is the weight of the object: [more than 600 Nts., equal to 600 Nts., or less than 600 Nts.]?
Less than 600 Nts.
c) If the motion of the elevator changes so that the scale now reads 700 Nts., is the new acceleration of the elevator less positive than 1.2 m/s2, the same (still = 1.2 m/s2), or less positive than 1.2 m/s2 ?
More positive.
d) When the elevator has an acceleration of +1.2 m/s2 and speed of –1.7 m/s, and the scale reads 600 Nts., what is the mass of the object located on the scale?
54.54 kg.
8) INFORMATION: MASS OF EARTH = 6.0 x 1024kg; RADIUS OF EARTH =
6,390 km.
MASS OF MARS = 6.44 x 1023kg; RADIUS OF MARS = 3,400 km.
A satellite of mass 100 kg is orbiting Mars at a distance of 600 km above the surface of Mars.
a) What is the period of the circular orbit for this satellite at this height?
7,669 seconds = 127 minutes and 49 seconds.
b) What speed should this satellite have to maintain the circular orbit at this radius?
3,277 m/s = 7,340 mph.
b) What is the force of gravity on the satellite while it orbits at this height?
268.5 Nt.
d) What is the acceleration due to gravity (gMars) on the surface of Mars?
3.72 m/s2 .
9) Use the same situation as in problem 8 above: A satellite of mass 100 kg orbits Mars at a height of 600 km above the surface.
a) Using the more general form for gravity, what would be the required energy needed to lift the satellite up to this height from the surface of Mars?
1.895 x 108 Joules.
b) Using the results of part b) of question 8, what kinetic energy needs to be supplied to the satellite to have it orbit with the required orbital speed?
5.37 x 108 Joules.
c) For this height, which energy is more: the energy required to lift the satellite up, or the energy required to have the satellite orbit?
Orbit.
10) A car of mass 1850 kg has an engine that delivers an average power of 160 horse power for a time of 8 seconds. Neglect the energy lost to friction and air resistance in your answers below.
a) What is the average power provided the car during the 8 seconds in Watts?
119,360 Watts.
b) If the car started from rest, what is the car’s final kinetic energy?
954,880 Joules.
c) What is the car’s final speed after 8 seconds if it started from rest?
In meters/sec: 32.13 m/s; in
miles/hour: 72 mph.
d) If the power was constant, was the force applied to the car [constant, decreasing with increasing speed, increasing with increasing speed] ?
Decreasing with increasing speed.
d) If the power was constant, did the car accelerate [at a constant acceleration, at a decreasing acceleration with increasing speed, or at an increasing acceleration with increasing speed]?
At a decreasing acceleration with increasing speed.
11) An object of mass, m1 = 7.0 grams, is moving to the right with a speed, v1i = 280 m/s, and hits another object of mass, m2 = 5,000 grams that is moving to the leftt with a much slower speed of v2i = 2 m/s.
a) Which object (#1 or #2) has the bigger initial kinetic energy?
#1.
b) Which object (#1 or #2) has the bigger initial momentum (magnitude) ?
#2.
c) If the two masses stick together after the collision, and if all the external forces can be neglected, then what will the speed of the combined masses after the collision, vf, be? {Be careful of signs: a + sign means moving to the right, a - sign means moving to the left.}
-1.61 m/s.
12) For the following use the information in the plot of potential energy (PE) versus distance (x) shown below and the fact that the total energy of the object is +10 Joules, its mass is 0.120 kg, and there is no air resistance or friction.
a)
What is the particle's potential energy at x = 2.5 m?
-5 Joules.
b) What is the particle's kinetic energy at x = 2.5 m?
15 Joules.
c) What is the particle's speed at x = 2.5 m?
15.81 m/s.
d) Which direction is the force n the particle at x = 2.5 m? [left, right, none-zero, undeterminable with info given]
Left.
e) If the particle moves from the 2.5 m position towards the 3.0 m position, will its speed: [increase, stay the same, decrease, undeterminable with info given] ?
Decrease.
13) A car of mass 1850 kg accelerates from 0 m/s to 24 m/s at a constant rate in 8 seconds on wheels of radius 33 cm.
a) What is the acceleration of the car during the 8 seconds?
3.0 m/s2.
b) What is the angular acceleration of the wheels during the 8 seconds?
9.09 rad/sec2.
c) What is the final angular speed (in rad/sec) of the wheels?
72.73 rad/sec.
d) If each of the four wheels can be considered a solid disk of mass 20 kg and radius 33 cm, what is the total moment of inertia of all four wheels?
4.36 kg*m2.
e) What is the kinetic energy of the car moving at a speed of 24 m/s?
532,800 Joules.
f) What is the rotational kinetic energy of the four wheels when rotating at the angular speed of part c?
11,531 Joues.
14) Consider a board of weight 250 Nt. and length 2.4 meters. A person lifts this board by applying a downward force at the left end by the left hand and an upward force by the right hand at a point 20 cm from the left end.
a) How much force must the person exert with the right hand?
1,500 Nt.
b) Will the person have to exert more, the same, or less force with the left hand than with the right?
Less.
c) If the right hand were moved further to the right (e.g., to 40 cm instead of 20 cm from the left end), would your answer to part a above (force of the right hand) be more, the same, or less?
Less.
d) If the board were 2.0 meters long (instead of 2.4 meters) but still had the same 250 Nt weight and the right hand was still 20 cm from the left end as in part a, would the answer to part a be more, the same, or less?
Less.
15) Two balls (solid spheres) are to be rolled down an incline which has a constant slope and makes an angle, q , with the horizontal. Assume that q is greater than zero degrees but less than 90 degrees, and assume that there is enough friction to cause the ball to roll without slipping. Also assume that the ball will be going slow enough so that we can neglect air resistance.
a) If the balls have the same mass but r1 > r2 , which one will win a race down the ramp? (#1, #2, it will be a tie, can’t tell because it depends on the angle of the ramp)
A tie.
b) If the balls have the same radius but m1 > m2 , which one will win a race down the ramp? (#1, #2, it will be a tie, can’t tell because it depends on the angle of the ramp)
A tie.
c) If ball #2 is replaced by a ring with the same mass and radius as the ball, which object will win the race down the ramp? (fall, ring, it will be a tie, can’t tell because it depends on the angle of the ramp)
Ball.
d) If ball #2 is replaced by a cylinder with the same mass and radius as the ball, which object will win the race down the ramp? (fall, ring, it will be a tie, can’t tell because it depends on the angle of the ramp)
Ball.
e) If h = 75 cm, m1 = 280 grams, r1 = 6 cm, and q = 35o, what will be the speed of ball #1 as it reaches the floor if it is released from rest at the top of the ramp?
3.24 m/s.