Mechanics
3. (25 pts) A 0.035 kg bullet is fired by a gun and embeds itself in a 2.50 kg block of
wood at rest at the base of a 20β¦ incline. The coefficient of kinetic friction between the
block and the incline is 0.19. After the collision, the block slides along the incline for
3.5 m before coming to rest.
(a) (12 pts) Draw a free-body diagram for the block after the collision has occurred.
Use this free-body diagram to determine the deceleration along the incline.
(b) (5 pts) What was the speed of the block immediately after the collision?
(c) (8 pts) What was the speed of the bullet before the collision? In one or two
sentences, explain in words your approach to this part, including any principles
you applied Draw a picture where you sketch out the trajectory of the engine as well as define a coordinate system and origin.
Q3 final exam practice
4. (25 pts) A particle of mass m moves under the influence of a potential energy
U (x) = 1/x + x.
(a) (10 pts) Evaluate the potential energy at the following positions: 0.25 m, 0.50 m,
1.00 m, 2.00 m, 4.00 m, and 8.00 m. Plot U (x) vs x. Sketch a curve through your
data points.
(b) (10 pts) What is the mathematical relation between force as a function of position
and potential energy as a function of position? Using this fact, find a point of
equilibrium for the particle. Given your graph in part (a), comment on the result.
(c) (5 pts) Is the point of equilibrium stable or unstable? Explain why
Q4 final exam practice
5) (25 pts) A baseball player swings a bat and accelerates it from rest to 10.0 rad/s in
0.15 s. When swung about one of its ends, the bat has rotational inertia 0.256 kg Β· m2.
(a) (6 pts) What is the angular acceleration of the bat?
(b) (6 pts) What torque was necessary to accelerate the bat as described above?
(c) (13 pts) A 0.145 kg baseball is moving in the opposite direction to the bat at 40
m/s and strikes perpendicular to the bat, 0.70 m from the batβs axis of rotation.
The ball ricochets backwards at 45 m/s. What is the angular velocity of the bat
after the collision? In one or two sentences, explain in words your approach to
this part, including any principles you applied
Q 5 final exam prac
6) (20 pts) The A string of a violin is 32 cm long between fixed points with a fundamental
frequency of 440 Hz and a mass per unit length of 7.2 Γ 10β4 kg/m.
(a) (8 pts) What are the wave speed and tension in the string?
(b) (4 pts) What is the length of the tube of a simple wind instrument (say, an organ
pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is
343 m/s in air?
(c) (8 pts) What are the frequencies of the first two overtones of each instrument?
Q 6 final exam prac
pg 2 review w
(25 pts) A block of mass m1 is released from rest and slides down a frictionless incline and collides with a
block of mass m2 = 3m1. The collision causes the two blocks to stick together and they fly horizontally
off of the table.
a. (8 pts) What is the velocity of m1 after it slides down the incline and immediately before
colliding with m2?
b. (8 points) What is the velocity of the blocks after the collision?
c. (9 points) How far do the blocks land from the base of the table? How much farther/shorter is
this compared to if block m1 had launched off the table with its speed before colliding with m2?
pg 2 review 2
7) (20 pts) The image below shows the position vs. time graph for two bicycles, A and
B.
(a) (5 pts) Are there any instant(s) at which the two bicycles have the same velocity?
On each position vs. time graph, circle these moment(s) in time and write the
letter a next to it. Explain how you know they have the same velocity.
(b) (5 pts) Which bicycle has the larger acceleration? Explain your answer.
(c) (5 pts) Do the bicycles pass each other at any moment(s) in time? On each
position vs. time graph, circle these moment(s) and write the letter c nearby.
Which bicycle is passing the other?
(d) (5 pts) Which bicycle achieves the highest instantaneous velocity? Explain your
answer.
Q 7 final exam prac
6 pts) You have two springs that are identical except that spring 1 is stiffer than
spring 2 (i.e. k1 is greater than k2). On which spring is more work done (a) if they
are stretched using the same force; (b) if they are stretched the same distance?
(4 pts) A car rounds a curve at a steady 50 km/h. If it rounds the same curve at
a steady 70 km/h, will its acceleration be any different? Explain
Q 8a final exam prac
3 pts) A guitar string vibrates at a frequency of 330 Hz with wavelength 1.40 m.
The frequency and wavelength of this sound in air as it reaches our ears is
(i) same frequency, same wavelength.
(ii) higher frequency, same wavelength.
(iii) lower frequency, same wavelength.
(iv) same frequency, longer wavelength.
(v) same frequency, shorter wavelength
Q 8f final exam prac
pg 3 review 2
A rod of length 2.00 m and mass 5.00 kg is free to rotate about its center. A force of F = 50 N is
applied at a distance of 0.50 m from the axis of rotation. The rod begins to rotate, but the force is
always applied with the same angle with respect to the rod. There is a frictional torque of 3.20 mβN.
a. (5 pts) Calculate the net torque exerted on the rod.
b. (5 pts) Determine the angular acceleration of the rod.
c. (5 pts) After rotating 180π = π πππ, what is the angular velocity of the rod?
d. (10 pts) After rotating clockwise for 180π , the force F is shut off, and a block of mass 2.00 kg is
placed in the way of the rod. The mass is placed right at one of the ends of the rod, and the rod
collides with it. The collision causes the rod and block to stick together. What is their angular
velocity after the collision?
pg 3 review 2
The position as a function of time for an object moving along a line is given by:
π₯(π‘) = β5.2π‘ β 22π‘2 + 0.80π‘3
(a) (9 pts) Calculate the position of the object at t = 0.0 s, t = 2.0 s, and t = 6.0 s. What is the
average velocity from 0.0 s to 2.0 s, and what is the average velocity from 2.0 s to 6.0 s?
(b) (8 pts) Determine π£(π‘), the velocity as a function of time. Calculate the instantaneous velocity
at t = 1.0 s and t = 4.0 s.
(c) (8 pts) Are there moments when the velocity is zero? If yes, at what times?
pg 1 review 2
3 pts) Several objects listed below roll without slipping down an incline of vertical
height H, all starting from rest at the same moment. Which object makes it to
the bottom of the incline first?
(i) Sphere
(ii) Hoop
(iii) Solid cylinder
(iv) Empty can
Q 8h
(e) (4 pts) Describe several situations in which an object is not in equilibrium, even
though the net force on it is zero.
Q 8e final exam prac
3 pts) The sound level near a cooling fan is 30 dB. If four such units operate side
by side, the sound level near them would be
(i) 30 dB
(ii) 120 dB
(iii) 36 dB
(iv) 60 dB
3 pts) Two children float motionlessly in a space station. The 20 kg child pushes
on the 40 kg child and the 40 kg child sails away at 1.0 m/s. The 20 kg child
(i) remains motionless;
(ii) moves in the same direction at 1.0 m/s;
(iii) moves in the opposite direction at 1.0 m/s;
(iv) moves in the opposite direction at 2.0 m/s;
(v) none of these.
Q 8c final exam prac
4 pts) A block is given a brief push so that it slides up a ramp. After the block
reaches its highest point, it slides back down, but the magnitude of its acceleration
is less on the descent that on the ascent. Why?
Q 8i
(g) (3 pts) The sound level near a cooling fan is 30 dB. If four such units operate side
by side, the sound level near them would be
(i) 30 dB
(ii) 120 dB
(iii) 36 dB
(iv) 60 dB
Q 8g final exam prac
A package falls out of an airplane that is flying in a straight line at a
constant altitude and speed. If you could ignore air resistance, what would be
the path of the package as observed by the pilot? As observed by a person on the
ground? Explain your answer.
Q 8d final exam prac
15 pts) A bridge has a stiffness constant of 1.00 Γ 108 N/m. Soldiers walk in lockstep across the bridge
at the bridgeβs natural frequency, adding 1.00 Γ 104 joules of vibrational energy to the bridge each
second. How long will it take the oscillations of the bridge to increase from an amplitude of 0.050 m to
0.400 m?
pg 4 review 2