05 practice ALIBHAI, ZAHID Latest unpenalized work: Feb 18 2007 Sunday 04:00 (after this date you can not make a perfect score). Work cutoff: Feb 18 2007, 4:00 am. Question 1 part 1 of 1 10 points A copper block rests 46.9 cm from the center of a steel turntable. The coefficient of static friction between block and surface is 0.49. The turntable starts from rest and rotates with a constant angular acceleration of 0.616 rad/s2 . The acceleration of gravity is 9.8 m/s2 . After what interval will the block start to slip on the turntable? Answer in units of s. Question 2 part 1 of 2 10 points The coefficient of static friction between the person and the wall is 0.77 . The radius of the cylinder is 5.22 m . The acceleration of gravity is 9.8 m/s2 . An amusement park ride consists of a large vertical cylinder that spins about its axis fast enough that any person inside is held up against the wall when the floor drops away.
1
being held up against the wall with an angular velocity of = 2 min . The magnitude of the frictional force between the person and the wall is 1. F = 1 mg. 2
2. F = 3 m g . 3. F = 2 m g . 4. F = m g . 5. F = 5 m g . 1 mg. 5 1 7. F = m g . 4 6. F = 8. F = 4 m g . 9. F = 1 mg. 3 Question 4 part 1 of 2 10 points An ant of mass m clings to the rim of a flywheel of radius r, as shown. The flywheel rotates clockwise on a horizontal shaft S with constant angular velocity . As the wheel rotates, the ant revolves past the stationary points I, II, III, and IV . The ant can adhere to the wheel with a force much greater than its own weight. I Ant
r
5.22 m
IV What is the minimum angular velocity min needed to keep the person from slipping downward? Answer in units of rad/s. Question 3 part 2 of 2 10 points Suppose the person, whose mass is m, is
II
S
III
It will be most difficult for the ant to adhere to the wheel as it revolves past which of the four points?
practice 05 ALIBHAI, ZAHID 1. II 2. IV 3. It will be equally difficult for the ant to adhere to the wheel at all points. 4. III 5. I Question 5 part 2 of 2 10 points What is the magnitude of the minimum adhesion force necessary for the ant to stay on the flywheel at point III? 1. F = m 2 r - m g 2. F = m r + m g 3. F = m 2 r 2 4. F = m 2 r 2 + m g 5. F = m g Question 6 part 1 of 1 10 points A highway curves to the left with radius of curvature R = 41 m. The highway's surface is banked at = 29 so that the cars can take this curve at higher speeds. Consider a car of mass 892 kg whose tires have static friction coefficient = 0.61 against the pavement. The acceleration of gravity is 9.8 m/s2 .
2
2
top view R = 41 m
=
0. 6
1
29
rear view
How fast can the car take this curve without skidding to the outside of the curve? Answer in units of m/s. Question 7 part 1 of 1 10 points A ball rolls around a circular wall, as shown in the figure below. The wall ends at point X. D E C B A X
When the ball gets to X, which path does the ball follow? 1. Path C 2. Path A 3. Path D 4. Path B 5. Path E Question 8
practice 05 ALIBHAI, ZAHID part 1 of 2 10 points 1. Tperiod = 2 2. Tperiod = 2 3. Tperiod = 2 4. Tperiod = 2 5. Tperiod = 2
3 sin2 g cos2 g tan g g sin g cos g g cos 2 tan g tan g
A small metal ball is suspended from the ceiling by a thread of negligible mass. The ball is then set in motion in a horizontal circle so that the thread's trajectory describes a cone. The acceleration of gravity is 9.8 m/s2 .
g
6. Tperiod = 2 r v
m What is the speed of the ball when it is in circular motion? Answer in terms of g, and .
1. v = 2. v = 3. v = 4. v = g cos g tan g sin g tan
7. Tperiod = 8. Tperiod = 9. Tperiod = 2 10. Tperiod =
cos g
Question 10 part 1 of 1 10 points You and a friend are riding on a ferris wheel which is moving with constant velocity. You, as a seeker of deep understanding, are sitting on a bathroom scale, wondering what will happen. Your friend observes 3 bathroom scale readings, on at the top, Rt , one at the middle, Rm , and one at the bottom, Rb . Which of the following is the correct relationship between Rb , Rt , Rm ?
5. v = g tan 6. v = tan 7. v = 8. v = 9. v = 10. v = g sin g tan sin g sin g cos Question 9 part 2 of 2 10 points How long does it take Tperiod for the ball to rotate once around the axis?
practice 05 ALIBHAI, ZAHID
top
4
3. T + m g cos = + 4. T 5. T 6. T 7. T
middle
bottom
m v2 r m v2 + m g sin = + r m v2 - m g sin = - r m v2 - m g sin = + tan r m v2 - m g cos = + r
8. None of these 1. Rt = Rb > Rm 2. not enough information 3. Rt = Rb < Rm 4. Rt > Rm > Rb 5. Rt < Rm < Rb 6. Rt = Rb = Rm Question 11 part 1 of 2 10 points A small sphere of mass m is connected to the end of a cord of length r and rotates in a vertical circle about a fixed point O. The tension force exerted by the cord on the sphere is denoted by T . 9. T - m g sin = + m v2 r
Question 12 part 2 of 2 10 points Hint: To solve this part, first find both the radial and the tangential component of the acceleration. The magnitude of a, the total acceleration, is 1. |a| = T m
2
- g2 .
2. None of these 3. |a| = 4. |a| = T m T m T m T m T m T m T m
2
cos2 + g 2 sin2 .
2
- 2 g cos
2
T + g2 . m
O
5. |a| = 6. |a| = 7. |a| = 8. |a| = 9. |a| =
+ g 2 cos2 .
2
r
+ g 2 sin2 .
2
What is the correct equation for the forces in the radial direction when the cord makes an angle with the vertical? m v2 tan 1. T - m g sin = - r m v2 2. T - m g sin = + cos r
+ 2 g cos
2
T + g2 . m
+ g2 .
2
sin2 + g 2 cos2 .
practice 05 ALIBHAI, ZAHID Question 13 part 1 of 1 10 points Given: g = 9.8 m/s . Consider a boxcar accelerating up a 13.1 slope. Inside the boxcar, an object of unknown mass m hangs on a string attached to the boxcar's ceiling. When the car accelerates uphill at a steady rate a, the string hangs at a constant angle = 27.1 from the perpendicular to the boxcar's ceiling and floor.
2
5
1. v = 2. v = 3. v = 4. v = 5. v = 6. v =
a
2 (F cos + m g sin ) D m 2 (F sin + k N ) D m 2 (F cos - k N ) D m 2 (F cos + m g sin - k N ) D m 2 (F cos - m g sin ) D m 2 (F cos - m g sin - k N ) D m 2 (F sin - k N ) D m 2 (F cos - m g sin + k N ) D m Question 15 part 1 of 1 10 points
7. v = 8. v =
m
27.1
13.1
Given the angles = 27.1 > = 13.1 , calculate the boxcar's acceleration a. Answer in units of m/s2 . Question 14 part 1 of 1 10 points A block of mass m is pushed a distance D up an inclined plane by a horizontal force F . The plane is inclined at an angle with respect to the horizontal. The block starts from and rest the coefficient of kinetic friction is k .
D
At a certain point, when a spring is stretched near its elastic limit, the spring force satisfies the equation
F = - x + x3 ,
where = 16 N/m and = 3400 N/m3 . Calculate the work done by the spring when it is stretched from its equilibrium position to 0.092 m past its equilibrium. Answer in units of mJ. Question 16 part 1 of 2 10 points Note: Using the Pythagorean theorem, the length of the front-face diagonal is
F
m
k
What is the final speed of the block?
(40 m)2 + (49 m)2 = 63.2535 m . Consider a rectangular parallel piped (block) with sides A = 40 m, B = 49 m, and C = 102 m, as shown in the figure below.
practice 05 ALIBHAI, ZAHID 102 m D A
6
49 m
(maximum) speed. How much air resistance acts on the nails? Answer in units of N. 40 m Question 20 part 1 of 2 10 points A particle moving in the xy plane undergoes a displacement s = (sx ^ + sy ^), with sx = i 3.29 m, sy = 5.01 m, while a constant force F = (Fx ^ + Fy ^), with Fx = 6.61 N, Fy = i 1.23 N, acts on the particle. Calculate the magnitude of the displacement. Answer in units of m. Question 21 part 2 of 2 10 points Calculate the work done by F . Answer in units of J. Question 22 part 1 of 3 10 points A small, spherical bead of mass 3.3 g is released from rest at t = 0 in a bottle of liquid shampoo. The differential equation of motion is dv b = g- v. dt m The terminal speed is observed to be 2.2 cm/s. The acceleration of gravity is 9.8 m/s2 . Find the value of the constant b in the integral form of the above equation mg 1 - e-b t/m . v= b Answer in units of N s/m. Question 23 part 2 of 3 10 points
C B The figure is not drawn to scale. What is the length of the body diagonal D ? Answer in units of m. Question 17 part 2 of 2 10 points What is the angle between the body diagonal D and the front-left edge A of the block? Answer in units of . Question 18 part 1 of 1 10 points The pulley system is in equilibrium and the pulleys are weightless and frictionless. The spring constant is 5 N/cm, the suspended weights are 36 N and 6 N. The acceleration of gravity is 9.8 m/s2 . 5 N/cm
36 N
6N
How much will the spring stretch? Answer in units of cm. Question 19 part 1 of 1 10 points A 145 N bag of nails falls at its terminal
Find the time it takes to reach 0.283 vt . Answer in units of s. Question 24 part 3 of 3 10 points Find the value of the resistive force when the bead reaches terminal speed.
practice 05 ALIBHAI, ZAHID Answer in units of N. Question 25 part 1 of 1 10 points A box of mass m with an initial velocity of v0 slides down a plane, inclined at with respect to the horizontal. The coefficient of kinetic friction is . The box stops after sliding a distance x. vertically downward. Fhand
7
m
v0
k
How far does the box slide? 1. x = 2. x = 3. x = 4. x = 5. x = 6. x = 7. x = 8. x = 9. x = 10. x =
2 v0 g ( sin + cos ) 2 v0 g (sin - cos ) 2 v0 2 g ( sin - cos ) 2 v0 2 g cos 2 v0 2 g ( sin + cos ) 2 v0 2 g sin 2 v0 g ( sin - 2 cos ) 2 v0 2 g ( cos - sin ) 2 v0 2 g ( cos + sin ) 2 v0 2 g (sin - cos )
The following figures show several attempts at drawing free-body diagrams for the book. Which figure has the correct directions for each force? Note: The magnitude of the forces are not necessarily drawn to scale.
1.
force normal
2.
friction force weight normal
3.
force friction normal weight
Question 26 part 1 of 2 10 points A book is at rest on an incline as shown above. A hand, in contact with the top of the book, produces a constant force Fhand
4.
friction force
B oo k
friction weight normal weight
practice 05 ALIBHAI, ZAHID 5. the pull of the book on the earth 5. weight force normal friction
8
6. the normal force exerted on the wedge by the book 7. the component of gravity pointing parallel to the surface of the incline Question 28 part 1 of 1 10 points A 2.67 kg block is pushed 1.59 m up a vertical wall with constant speed by a constant force of magnitude F applied at an angle of 55.8 with the horizontal. The acceleration of gravity is 9.8 m/s2 .
6.
normal friction
force weight
7.
normal force
friction weight
2.67 kg
8.
force friction
normal weight
Question 27 part 2 of 2 10 points For the normal force exerted on the book by the wedge in the diagram, which force(s) complete(s) the force pair for Newton's third law (action-reaction)? 1. the sum of the component of gravity perpendicular to the surface of the incline and the component of Fhand perpendicular to the surface of the incline 2. the pull of the earth on the book 3. the component of Fhand pointing perpendicular to the surface of the incline 4. the component of gravity pointing perpendicular to the surface of the incline
If the coefficient of kinetic friction between the block and wall is 0.551, find the work done by F . Answer in units of J. Question 29 part 1 of 1 10 points A 1910 kg pile driver is used to drive a steel I-beam into the ground. The pile driver falls 2.6 m before contacting the beam, and it drives the beam 6.22 cm into the ground before coming to rest. The acceleration of gravity is 9.8 m/s2 . Using the work-energy theorem, calculate the magnitude of the average force the beam exerts on the pile driver while the pile driver is brought to rest. Answer in units of N. Question 30 part 1 of 2 10 points
F
8 55.
practice 05 ALIBHAI, ZAHID A 4.5 g mass is released from rest at C which has a height of 0.8 m above the base of a loop-the-loop and a radius of 0.13 m . The acceleration of gravity is 9.8 m/s2 . C 4.5 g B 0.13 m 0.8 m A lowest point. Note: Neglect the mass of the seat. Answer in units of m/s.
9
D Find the normal force pressing on the track at A, where A is at the same level as the center of the loop. Answer in units of N. Question 31 part 2 of 2 10 points Consider a different situation when the initial height at C has not yet been specified. What is the minimum kinetic energy of the block at B, which is located at the top of the loop, so that the block can pass by this point without falling off from the track? Answer in units of J. Question 32 part 1 of 1 10 points A bucket full of water is rotated in a vertical circle of radius 0.672 m (the approximate length of a person's arm). What must be the minimum speed of the pail at the top of the circle if no water is to spill out? Answer in units of m/s. Question 33 part 1 of 1 10 points A 20 kg child sits in a swing supported by two chains, each 1.5 m long. The acceleration of gravity is 9.8 m/s2 . If the tension in each chain at the lowest point is 137 N, find the child's speed at the