PHY 131Ch 6 to 9 ExamName
1.The coefficient of kinetic friction:
none of the above
2.A professor holds an eraser against a vertical chalkboard by pushing horizontally on it. She pushes with a force that is much greater than is required to hold the eraser. The force of friction exerted by the board on the eraser increases if she:
pushes so her force is slightly downward but has the same magnitude
3.A boy pulls a wooden box along a rough horizontal floor at constant speed by means of a force P. Which of the following must be true?
P = Ff and N = Fg
4.A 12-kg crate rests on a horizontal surface and a boy pulls on it with a force that is 30° below the horizontal. If the µ = 0.40, the min magnitude of force he needs to start the crate moving is: Ff = μFN
FNet = mT a
Fcosθ - Ff = 0
Fcosθ = Ff
Fcosθ = μ (mg + Fsinθ)
F = 72 N
5.When a certain rubber band is stretched a distance x, it exerts a restoring force F = ax + bx2, where a and b are constants. The work done in stretching this rubber band from x = 0 to x = L is:
aL2/2 + bL3/3
6.An object moving in a circle at constant speed:
has an acceleration of constant magnitude
7.An ideal spring is hung vertically from the ceiling. When a 2.0-kg mass hangs at rest from it, the spring is extended 6.0 cm from its relaxed length. An upward external force is then applied to the block to move it upward a distance of 16 cm. While the block is being raised by the force, the work done by the spring is
2g = k(0.06m)
k = 333 N/m
½ k .062 + ½ k .12
= .6 + -1.66 = -1 J
8.A 1000-kg airplane moves in straight flight at constant speed. The force of air friction is 1800 N. The net force on the plane is:
FNet = mT a = 0
9.A force F = (4.1 N)i + (2.6 N)j – (4.7 N)k acts on a mass of 2.3 kg as it moves in the x direction at a speed of 7.2 m/s. What is the rate at which the force is doing work?
P = F v = 4.1 (7.2) =30 W
10.When a certain rubber band is stretched a distance x, it exerts a restoring force of magnitude F = Ax, where A is a constant. The work done by a person in stretching this rubber band from x = 0 to x = L is:
AL2/2
11.A hockey puck of mass m traveling along the x axis at 4.5 m/s hits another identical hockey puck at rest. If after the collision the second puck travels at a speed of 3.5 m/s at an angle of 30° above the x axis, is this an elastic collision?
4.5m = mv1f + m cos30(3.5)
vx1-f = 1.5 m/s
0 = m vy1-f + m sin30(3.5)
vy1-f = -1.75 m/s
v1-f2 = vx1-f2+ vy1-f2
v1-f = 2.3 m/s
KEo = ½m4.52 = m10.1 J
KEf = ½m2.32 + ½m3.52 =m8.8 J
KE is NOT conserved
12.A 2-kg cart, traveling on a horizontal air track with a speed of 3 m/s, collides with a stationary 4-kg cart. The carts stick together. The impulse exerted by one cart on the other has a magnitude of:
2(3) + 4(0) = (2+4)vf
vf = 1 m/s
Impulse = Δp =
2(3) – 2(1) = 4 Ns
13.When a particle suffers a head-on elastic collision with another particle, initially at rest, the greatest fraction of kinetic energy is transferred if:
the incident and target particle have the same mass
14.Two carts (A and B), having spring bumpers, collide as shown. Cart A has a mass of 2 kg and is initially moving to the right. Cart B has a mass of 3 kg and is initially stationary. When the separation between the carts is a minimum:
the kinetic energy of the system is at a minimum
15.A man sits in the back of a canoe in still water. He then moves to the front of the canoe and sits there. Afterwards the canoe:
is rearward of its original position and not moving
16.A brick slides on a horizontal surface. Which of the following will increase the frictional force on it?
Putting a second brick on top
17.A box with a weight of 50 N rests on a horizontal surface. A person pulls horizontally on it with a force of 15 N and it does not move. To start it moving, a second person pulls vertically upward on the box. If the coefficient of static friction is 0.4, what is the smallest vertical force for which the box moves?
FNet = mT a
15 – Ff = 0
15 - µ FN = 0
15 = .4 (50-Fup)
Fup = 12.5 N
18.A 400-N block is dragged along a horizontal surface by an applied force F. The coefficient of friction is 0.4 and the block moves at constant velocity. The magnitude F is:
FNet = mT a
Fx – Ff = 0
Fx - µ FN = 0
Fx = .4 (400- Fy)
.8F = .4 (400 - .6F)
F = 150 N
19.When a certain rubber band is stretched a distance x, it exerts a restoring force of magnitude F = Ax, where A is a constant. The work done by stretching this rubber band from x = 0 to L is: ½AL2
20.An 800-N passenger in a car presses against the car door with a 200 N force when the car makes a left turn at 13 m/s. The (faulty) door will pop open under a force of 800 N. Of the following, the least speed for which the man is thrown out of the car is:
Fc = mv2 / r¼mg = mv2 / r
r = 67.6 m / Fc = mv2 / r
800 = 80v2/67.6
v = 26 m/s
21.Block A, (10 kg), rests on a 30° incline. The coefficient of friction is 0.20. Block B, (3.0 kg), is attached to the dangling end of the string over a frictionless pulley. The acceleration of B is:
FNet = mT a
(100sin30°-30) – Ff = (10+3) a
(20) - µ 100cos30° = 13a
a = 0.3 m/s2 up (0.2 m/s2 if g = 9.8 m/s2)
22.When a certain rubber band is stretched a distance x, it exerts a restoring force F = ax + bx2, where a and b are constants. The work done in stretching this rubber band from x = 0 to x = L is:
aL2/2 + bL3/3
23.Three identical springs (X, Y, Z)
are arranged as shown. When a 4.0-kg mass is hung on X, the mass descends 3.0 cm. When a 6.0-kg mass is hung on Y, the mass descends: /F = kx
40N = k 3cm
k = 13.3 N/cm / F = kx
60 = 13.3 x
x = 4.5 cm
but each stretch
this much 9cm
24.In uniform circular motion,
acceleration and the velocity are always perpendicular.
25.A man pushes an 80-N crate a distance of 5.0 m upward along a frictionless slope that makes an angle of 30°with the horizontal. His force is parallel to the slope. If the speed of the crate decreases at a rate of 1.5 m/s2, then the work done by the man is:
FNet = mT aF – sin30(80) = 8(-1.5)
F = 28 N / Work = FΔx
= 28(5)
= 140 J
26.If a projectile hits a stationary target, and the projectile continues to travel in the same direction,
the mass of the projectile is greater than the mass of the target
27.Blocks A and B are moving toward each other along the x axis. A has a mass of 2.0 kg and a velocity of 50 m/s, while B has a mass of 4.0 kg and a velocity of –25 m/s. They suffer an elastic collision and move off along the x axis. The kinetic energy transferred from A to B during the collision is: mL vL + mR vR = po
2 (50) + 4 (-25) = po
po = pf = 0, so KE = 0 J
28.Blocks A and B are moving toward each other. A has a mass of 2.0 kg and a velocity of 50 m/s, while B has a mass of 4.0 kg and a velocity of –25 m/s. They suffer a completely inelastic collision. The kinetic energy lost during the collision is:
KEf = 0 J (previous problem)
KEo = ½2(50)2 + ½4(-25)2
KEo = 3750 J All was lost
29.A projectile in flight explodes into several fragments. The total momentum of the fragments immediately after this explosion:
is the same as the momentum of the projectile immediately before the explosion
30.A light rope passes over a light frictionless pulley attached to the ceiling. An object with a large mass is tied to one end and an object with a smaller mass is tied to the other end and is then released from rest. Which of the following statements is true for the system consisting of the two objects?
None of the above statements are true.
31.A 24-N horizontal force is applied to a 40-N block initially at rest on a rough horizontal surface. If the coefficients of friction are μs = 0.5 and μk = 0.4, the magnitude of the frictional force on the block is:
FNet = mT a
24 – µ mg = mT a
24 – .5 40 = mT a
So it starts to move, must use μk
Ff = 0.4 (40N) = 16 N
32.The speed of a 4.0-N hockey puck, sliding across a level ice surface, decreases at the rate of 0.61 m/s2. The coefficient of kinetic friction between the puck and ice is:
FNet = mT a
0 - Ff = mT a
0 – µ mg = .4(-.61)
µ = 0.061
33.A boy pulls a wooden box along a rough horizontal floor at constant speed by means of a force P. Which of the following must be true?
P > Ff and N < Fg
34.If a satellite moves above the Earth's atmosphere in a circular orbit with constant speed, then:
its acceleration is toward the Earth
35.A ball is thrown upward into the air with a speed that is greater than terminal speed. It lands at the place where it was thrown. During its flight the force of air resistance is the greatest:
just after it is thrown
36.Block A, (10 kg), rests on a 30° incline. The coefficient of friction is 0.20. Block B, (8.0 kg), is attached to the dangling end of the string over a frictionless pulley. The acceleration of B is:
FNet = mT a
(80-100sin30°) – Ff = (10+8) a
(30) - µ 100cos30° = 18a
a = 0.7 m/s2 down
37.An ideal spring is hung vertically from the ceiling. When a 2.0-kg mass hangs at rest from it, the spring is extended 6.0 cm from its relaxed length. A downward external force is now applied to the mass to extend the spring an additional 10 cm. While the spring is being extended by the force, the work done by the spring is:
F = kx20N = k 6cm
k = 3.3 N/cm
k = 333 N/m / Work = ½kxo2 – ½kxf2
= ½333(.062 –.162)
Work = -3.6 J
38.A Boston Red Sox baseball player catches a ball of mass m that is moving toward him with speed v. While bringing the ball to rest, his hand moves back a distance d. Assuming constant deceleration, the horizontal force exerted on the ball by his hand is:
Ko – Ff d = Kf
½ mv2 – F d = 0
F = mv2/(2d)
39.Two objects, X and Y, are held at rest on a horizontal frictionless surface and a spring is compressed between them. The mass of X is 2/5 times the mass of Y. Immediately after the spring is released, X has a kinetic energy of 50 J and Y has a kinetic energy of:
Momentum is linear relationship
KE has a squared relationship; 20 J
40.Block A, with a mass of 2.0 kg, moves along the x axis with a velocity of +5.0 m/s. It suffers an elastic collision with block B, initially at rest along the x axis. If B is much more massive than A, the velocity of A after the collision is:
No work needed, essentially hitting a massive wall, rebounds with same speed. -5.0 m/s
41.Two identical carts travel at 1 m/s on a common surface. They collide head-on and are reported to rebound, each with a speed of 2 m/s. Then:
if some other form of energy were changed to kinetic during the collision, the report could be true
42.A 3.0-kg cart and a 2.0-kg cart approach each other on a horizontal air track. They collide and stick together. After the collision their total kinetic energy is 40 J. The speed of their center of mass is:
½(mL+ mR)v2 = 40
½(2+ 3)v2 = 40
v = 4 m/s
43.A 2.0-kg block is attached to one end of a spring with a spring constant of 100 N/m and a 4.0-kg block is attached to the other end. The blocks are placed on a horizontal frictionless surface and set into motion. At one instant the 2.0-kg block is observed to be traveling to the right with a speed of 0.50 m/s and the 4.0-kg block is observed to be traveling to the left with a speed of 0.30 m/s. We conclude that:
mLvL + mR vR = 0
2(.5) + 4(-.3) ≠ 0
the motion was started with at least one of masses moving
We have a pressurized launcher. A patented expanding foam is streamed into a vertical launch tube and propels an explosive moldable “playdough type” ball. The expanding applies a force on the 10 kg ball of F = 20x4 (SI Units). If the ball explodes in 3 fragments at a height of 100 meters above the top of the tube, what was the length of the launch tube?
The 3 fragments are as follows:
-fragment A, m = 3 kg, vx = 80 m/s, vy = 70 m/s, vz = 0;
-fragment B, m = 2 kg, vx = 130 m/s, vy = -30 m/s, vz = 0; and
-fragment C, m = 5 kg, vx = -100 m/s, vy = 60 m/s, vz = 0.
-vx = Right (or East) +, vy = Up positive, vz = North (Into your page) +
Explosionx: pf = 3(80) + 2(130) + 5(-100) = 0 kg m/s
2/2 2/2 2/2
This verifies no x-comp was transferred by external forces (wind, etc.) / y: pf = 3(70) + 2(-30) + 5(60) = pbefore
2/2 2/2 2/23/3
450 kg m/s = 10kg v@100m
v@100m = 45 m/s
Speed at launch tube exit
E0= Ef
m g h + ½ m v2= m g hf + ½ m vf2
5/5 6/6 6/6
10(0) + ½v2= 10(100) + ½ 452
v0 = 63.4 m/s / K0 = ½ 10 63.42
K0 = 20,125 J / Work done by expanding foam
Work = ΔK
F dx = 20125 J
20∫x4dx= 20125 13/13
4x5= 20125
x = 5.5 m
Alternate #16, Ch 7 to 9 principles as stated on the board
A stationary block explodes into two pieces L and R that slide across a frictionless inclined ramp (by 30°) of negligible distance and then into regions with friction, where they stop. Piece L, with a mass of 3.0 kg, encounters a coefficient of friction μL = 0.80 and slides to a stop in distance dL = 0.40 m. Piece R encounters a coefficient of friction μR = 0.30 and slides to a stop in distance dR = 0.50 m. What was the mass of Piece R? / po =pf
0 = mL vL + mR vR
5/5 3/3 5/5
0 = 3(-1.24) + mR 2.76
mR = 1.35 kg /
Left Block
Ko= Kf
mLg hL + ½ mLvL2 – Ff dL= mLg hL + ½mLvL2
3(10) sin30(.4) + ½3 vL2 – Ff dL = 0 + 0
6 + 1.5 vL2 - µ cos30 3(10) .4 = 0
6/6 5/5 5/5
vL = 1.24 m/s / Right Block
Ko= Kf
mRg hR + ½ mRvR2 – Ff dR= mR g hR + ½mRvR2
0 + ½mRvR2 - µ cos30 mR g .5 = mR(10) sin30(.5) + 0
0 + ½mRvR2 - 1.3 mR = 2.5 mR (mR cancels)
5/5 5/5 6/6
vR = 2.76
OTHER VERSIONS
We have a pressurized launcher. A patented expanding foam is streamed into a vertical launch tube and propels an explosive moldable “playdough type” ball. The expanding applies a force on the 10 kg ball of F = 12x2 (SI Units). If the ball explodes in 3 fragments at a height of 100 meters above the top of the tube, what was the length of the launch tube?
The 3 fragments are as follows:
-fragment A, m = 5 kg, vx = 60 m/s, vy = 80 m/s, vz = 0;
-fragment B, m = 3 kg, vx = -40 m/s, vy = 60 m/s, vz = 0; and
-fragment C, m = 2 kg, vx = -90 m/s, vy = -70 m/s, vz = 0.
-vx = Right (or East) +, vy = Up positive, vz = North (Into your page) +
Explosionx: pf = 5(60) + 3(-40) + 2(-90) = 0 kg m/s = pbefore_explosion / y: pf = 5(80) + 3(60) + 2(-70) = 440 kg m/s = pbefore_explosion
pbefore_explosion = 440 kg m/s = m v@100m
v@100m = 44 m/s
Speed at launch tube exit
E0= Ef
m g h + ½ m v2= m g hf + ½ m vf2
10(0) + ½v2= 10(100) + ½ 442
v0 = 63 m/s / K0 = ½ 10 632
K0 = 20,000 J / Work done by foam
Work = ΔK
F dx = 20,000 J
12 x2 dx= 20000
4x3= 20000
x = 17 m
We have a pressurized launcher. A patented expanding foam is streamed into a vertical launch tube and propels an explosive moldable “playdough type” ball. The expanding applies a force on the 10 kg ball of F = 12x3 (SI Units). If the ball explodes in 3 fragments at a height of 100 meters above the top of the tube, what was the length of the launch tube?
The 3 fragments are as follows:
-fragment A, m = 6 kg, vx = 40 m/s, vy = 70 m/s, vz = 0;
-fragment B, m = 3 kg, vx = -40 m/s, vy = 50 m/s, vz = 0; and
-fragment C, m = 1 kg, vx = -120 m/s, vy = -70 m/s, vz = 0.
-vx = Right (or East) +, vy = Up positive, vz = North (Into your page) +
Explosionx: pf = 6(40) + 3(-40) + 1(-120) = 0 kg m/s = pbefore_explosion / y: pf = 6(70) + 3(50) + 1(-70) = 500 kg m/s = pbefore_explosion
pbefore_explosion = 500 kg m/s = m v@100m
v@100m = 50 m/s
Speed at launch tube exit
E0= Ef
m g h + ½ m v2= m g hf + ½ m vf2
10(0) + ½v2= 10(100) + ½ 502
v0 = 67 m/s / K0 = ½ 10 672
K0 = 22,500 J / Work done by foam
Work = ΔK
F dx = 22500 J
12∫x3dx= 22500
3x4= 22500
x = 9.3 m