Practice Quiz

wong (eyw89) – Quiz 2 Practice – sudarshan – (57415)

1

This print-out should have 59 questions.
Multiple-choice questions may continue on the next column or page – find all choices before answering.

face of the table? Assume the boxes each have masses of 2.0 kg, the coefficient of static friction is µs between table and box, and the acceleration due to gravity is 10 m/s2 .

001 10.0 points
A block accelerates 3 m/s2 down a plane inclined at angle 27.0◦.
The acceleration of gravity is 9.81 m/s2 .

1. The force of the static friction would have a vertical component in this situation, and that is impossible since it must be parallel to the table surface.

2

3

s m/ 2. 20 N
3. Very small, almost zero

m µk 27◦

4. 2.5 N
5. 5.0 N

Find µk between the block and the inclined plane. 1. 0.166

6. fs would have to be greater than 20 N, which is physically impossible, so this is not a realistic situation.
7. 10 N

2. 0.148

8. Impossible to say from the information given. 3. 0.510

003

4. 0.853

10.0 points

A block with an initial velocity v0 slides up and back down a frictionless incline.

5. 1.289
002

10.0 points

Two identical boxes are connected by a string of negligible mass, which runs across a frictionless peg. One box is on a horizontal table, while the other box hangs vertically.
If the hanging box is released from rest, it remains at rest. m m

What must be the force of static friction between the box on the table, and the sur-

v0

θ

Which graph best represents a description of the velocity of the block versus time? The initial position of the block is the origin;
i.e., x = 0 at t = 0 . Consider down the track to be the positive x-direction.

wong (eyw89) – Quiz 2 Practice – sudarshan – (57415) v v t 1.

2

t

8.

v v t

2.

t

9.

v t 3.

v
10.

t

v t 4.

v t 5.

004 10.0 points
If a car hits a tree, the car’s occupants (if the car has no seat belts or air bags) will be violently accelerated forward and strike the dashboard with murderous force, due to an initial forward force exerted on their bodies by the backs of their seats.
1. False
2. None of these

v t 6.

3. This may happen in a few cases, but it is very rare.
4. True
5. This may happen in many cases, but not in every case.

v
7.

t
005 (part 1 of 5) 10.0 points
A car travels at a speed of 30 m/s around a curve of radius 69 m.
The acceleration of gravity is 9.8 m/s2 .

wong (eyw89) – Quiz 2 Practice – sudarshan – (57415)

3

In this case, which of these two forces has the smaller magnitude?
1. m g
1. 9

g
M

2. None of these µ 36◦

3. Both have the same magnitude.
4. n
5. If a is downward, n = 0 .

What is the net centripetal force needed to keep the car from skidding sideways?
Answer in units of N
006 (part 2 of 5) 10.0 points
Were there no friction between the car’s tires and the road, what centripetal force could be provided just by the banking of the road?
Answer in units of N
007 (part 3 of 5) 10.0 points
Now suppose the friction force is sufficient to keep the car from skidding. Calculate the magnitude of the normal force exerted on the car by the road’s surface. Hint: Check the correctness of your answer to the first question before proceeding with this and the following questions. Answer in units of N
008 (part 4 of 5) 10.0 points
Calculate the magnitude of the friction force.
Answer in units of N
009 (part 5 of 5) 10.0 points
Calculate the lowest possible value of the static friction coefficient µs that would prevent the car from skidding.
010 10.0 points
Consider a person standing in an elevator that is moving at constant speed upward. The person, of mass m, has two forces acting upon him, the downward force m g due to gravity, and the upward supporting force n exerted by the floor of the elevator.

6. If a is downward, mg = 0 .
011 (part 1 of 3) 10.0 points
Consider a loop-the-loop system where the radius of the loop is R. A small block (of negligible size) is released from rest at the
1
point P , which is at a height of 4 R.
8
m
P

33
R
8

C
R
B

A
What is the kinetic energy KB at B? Friction between the block and the track is negligible.
19
mgR
5
18
2. KB = mgR 5
31
mgR
3. KB =
8
25
4. KB = mgR 8
1. KB =

wong (eyw89) – Quiz 2 Practice – sudarshan – (57415)
5. KB =

16 mgR 5

2. NA =

6. KB =

11 mgR 5

3. NA =

7. KB =

26 mgR 7

4. NA =

8. KB =

19 mgR 7

5. NA =

9. KB =

17 mgR 7

6. NA =

10. KB =

19 mgR 8

7. NA =

012 (part 2 of 3) 10.0 points
What is the tangential speed vC at C?

8. NA =
9. NA =

37 mg 5
23
mg
2
27 mg 4
39
mg
4
35 mg 4
73
mg
7
45 mg 4
55
mg
7
37 mg 4

1. vC =

16 gR 5

2. vC =

34 gR 7

3. vC =

38 gR 7

4. vC =

12 gR 5

5. vC =

17 gR 4

1. Twice as far

6. vC =

8 gR 3

2. Half as far

7. vC =

23 gR 4

8. vC =

20 gR 7

10. NA =

014 10.0 points
Car B has the same mass as Car A but is going twice as fast.
If the same constant force brings both cars to a stop, how far will car B travel in coming to rest as compared to the distance car A traveled? 3. Eight times as far
4. Three times as far
5. None of these

9. vC =

27 gR 4

6. The same distance

10. vC =

11 gR 2

7. A quarter as far

013 (part 3 of 3) 10.0 points
What is the force NA with which the track pushes up on the block at the point A (at the bottom of the loop)?
21
1. NA = mg 2

4

8. Insufficient information is given.
9. Four times as far
015

10.0 points

wong (eyw89) – Quiz 2 Practice – sudarshan – (57415)
A ball of mass M is suspended by a thin string (of negligible mass) from the ceiling of an elevator. The vertical motion of the elevator as it travels up and down is described in the statements below. Indicate for each of the situations described the relation between value of the tension T in the string and the weight of the ball M g, or whether one cannot tell. T v M

Elevator with a weight held by a string inside it

5

block is 9.78 kg and the acceleration of gravity is 9.8 m/s2 .
Answer in units of m/s2
017 10.0 points
A balloon of mass M is floating motionless in the air. A person of mass less than M is on a rope ladder hanging from the balloon. The person begins to climb the ladder at a uniform speed v relative to the ground.
How does the balloon move relative to the ground? 1. Up with a speed less than v
2. Down with speed v
3. Down with a speed less than v

The elevator is traveling upwards and its upwards velocity is increasing as it starts towards a higher floor.
1. T < M g
2. T = M g
3. T > M g
4. Cannot be determined.
016 10.0 points
The block is released from rest on the incline with the spring initially unstretched:
78.2 N/m x 8
9. 7

5. Up with speed v
018 10.0 points
Two carts are put back-to-back on a track.
Cart A has a spring-loaded piston; cart B, which has twice the inertial mass of cart A, is entirely passive. When the piston is released, it pushes against cart B, and the carts move apart. How do the magnitudes of the final momenta p and kinetic energies K compare?
1. pA = pB , KA > KB
2. pA < pB , KA = KB
3. pA < pB , KA < KB
4. pA > pB , KA > KB

kg

µ=

4. The balloon does not move.

0

30◦

5. pA > pB , KA < KB
6. pA = pB , KA < KB

Choosing down the incline as the positive direction, what is its acceleration at its lowest point? The angle of inclination is 30 ◦ , the spring constant is 78.2 N/m the mass of the

7. pA = pB , KA = KB
8. pA > pB , KA = KB

wong (eyw89) – Quiz 2 Practice – sudarshan – (57415)
9. pA < pB , KA > KB
019 10.0 points
Two blocks of masses M and 3M are placed on a horizontal, frictionless surface. A light spring is attached to one of them, and the blocks are pushed together with the spring between them.

3M

M
Before
(a) v impact lifts the block 0.23 m up. (That is, the block — with the bullet stuck in it — rises
0.23 m up above its initial position, and then falls back down.)
Given g = 9.8 m/s2 . What was the initial velocity of the bullet?
Answer in units of m/s
021 (part 1 of 2) 10.0 points
Consider the 693 N weight held by two cables shown below. The left-hand cable had tension T2 and makes an angle of 54 ◦ with the ceiling. The right-hand cable had tension T1 and makes an angle of 50◦ with the ceiling.

3M

M

54 ◦

◦

50

The two blocks are at rest first. Then the cord holding them together is burned, after which the block of mass 3M moves to the right with a speed of 2 m/s. What is the speed of the block of mass M?
1. 0 m/s

T1

T2

After
(b)

6

693 N
a) What is the tension in the cable labeled
T1 slanted at an angle of 50◦ ?
Answer in units of N
022 (part 2 of 2) 10.0 points
a) What is the tension in the cable labeled T2 slanted at an angle of 54◦ ?
Answer in units of N

2. 6 m/s
3. 2 m/s
4. impossible to determine
5. 1.5 m/s
6. 0.67 m/s
7. 4 m/s
020 10.0 points
A 11.7 g bullet is fired vertically into a 1.65 kg block of wood.

023 10.0 points
You are given two carts, A and B. They look identical and you are told that they are made of the same material. You place A at rest on an air track and give B a constant velocity directed to the right so that it collides elastically with A. After the collision, both carts move to the right, the velocity of B being smaller than what it was before the collision.
What do you conclude?
1. Cart A is hollow.

v0

The bullet gets stuck in the block, and the

2. need more information
3. Cart B is hollow.

wong (eyw89) – Quiz 2 Practice – sudarshan – (57415)
4. The two carts are identical.

1. 0.2

024 10.0 points
You are on a rooftop and you throw one ball straight down and another straight up. The second ball, after rising, falls and also strikes the ground below.
If air resistance can be neglected and if your downward and upward initial speeds are the same, how will the speed of the balls compare upon striking the ground?
1. They have same speed.
2. The speed of the second ball is smaller than that of the first one.
3. The speed of the second ball is larger than that of the first one.

2. 0.05
3. 20
4. 2
5. 0.5
027 10.0 points
On the surface of the earth is a pendulum of mass m and length ℓ.
If the pendulum is allowed to swing down from rest starting from an initial horizontal position, with the forces acting being T, the tension in the string, and m g , the force of gravity, how much work has been done on the pendulum as it swings through the vertical position? 4. More information is needed
1. m g +T times
025 10.0 points
A block starts at rest and slides down a frictionless track except for a small rough area on a horizontal section of the track (as shown in the figure below).
It leaves the track horizontally, flies through the air, and subsequently strikes the ground.
The acceleration of gravity is 9.81 m/s2 .
9.81 m/s2

2.2 m

h

v

1.2 m µ=0.2 4.15 m
At what height h above the ground is the block released?
Answer in units of m
026 10.0 points
A horizontal force of 100 N is used to pull a crate, which weighs 500 N, at constant velocity across a horizontal floor.
What is the coefficient of kinetic friction?

π
ℓ, the distance traveled.
2

2. T ℓ
3. m g ℓ, with the pendulum’s KE increasing by this amount.
4. Zero; energy is conserved.
028

512 g

7

10.0 points

A 7 kg mass slides to the right on a surface having a coefficient of friction 0.15 as shown.
The mass has a speed of 4 m/s when contact is made with a spring that has a spring constant
101 N/m. The mass comes to rest after the spring has been compressed a distance d. The mass is then forced toward the left by the spring and continues to move in that direction beyond the unstretched position. Finally the mass comes to rest a distance D to the left of the unstretched spring.

wong (eyw89) – Quiz 2 Practice – sudarshan – (57415) v 101 N/m

7 kg
4 m/s
7 kg d v⊃ = 0

8

How long does it take Tperiod for the ball to rotate once around the axis?
Answer in units of s
031 10.0 points
A block is at rest on the incline shown in the figure. The coefficients of static and kinetic friction are µs = 0.6 and µk = 0.51, respectively.
The acceleration of gravity is 9.8 m/s2 .

7 kg

43

vf

kg µ 28◦

7 kg v⊢ = 0
7 kg

101 N/m

D

µ = 0.15
Find the compressed distance d. The acceleration of gravity is 9.8 m/s2 .
Answer in units of m
029 (part 1 of 2) 10.0 points
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 describes a cone.
The acceleration of gravity is 9.8 m/s2 .

What is the frictional force acting on the
43 kg mass?
Answer in units of N
032 10.0 points
Two crates are touching, resting on a practically frictionless surface. If you apply a force
F with your hand against the larger crate of mass M , both crates accelerate across the surface, and remain in contact. a F′
F
M m Which statement is wrong?

◦

20

9.8 m/s2

1. The force F ′ = −m a.

1. 8 m v
5.1 kg
What is the speed of the ball when it is in circular motion?
Answer in units of m/s
030 (part 2 of 2) 10.0 points

2. The smaller crate exerts a force F ′ backward on the larger crate, equal and opposite to the force (not shown) that the larger crate exerts forward on the smaller one to accelerate it.
3. The forces F and F ′ are equal and opposite, as required by Newton’s third law.
4. The magnitude of the acceleration of the

wong (eyw89) – Quiz 2 Practice – sudarshan – (57415)
F
, where F
M +m is the magnitude of F and m is the mass of the smaller crate. two crates will be given by

033 10.0 points
Five ramps lead from the ground to the second floor of a workshop, as sketched below. All five ramps have the same height; ramps B,
C, D and E have the same length; ramp A is longer than the other four. You need to push a heavy cart up to the second floor and you may choose any one of the five ramps.

9

034 10.0 points
A box is attached to an unstretched spring of force constant k and rests on a horizontal tabletop. The box is moved out to the right a distance ℓ along the table, stretching the spring, and released. It remains at rest when released. k m ℓ

A

B

C

What is the force of static friction in this situation? 1. fs = µs m g to the right.
2. fs = k ℓ to the right.

D

3. fs = k ℓ to the left.
E

Assuming no frictional forces on the cart, which ramp would require you to do the least work? 1. Unable to determine without knowing the exact profiles of ramps C, D or E.
2. Ramp D.
3. Same work for all five ramps.
4. Ramp B.
5. Ramp A.
6. Same work for the straight ramps A and
B; less work for ramps C, D, and E.
7. Same work for ramps B, C, D or E; more work for ramp A.
8. Ramp C.
9. Ramp E.

4. fs = µs m g to the left.
035 10.0 points
A bowling ball is hanging in mid-air at rest in a room on board the International Space
Station. An astronaut throws a golf ball directly at the bowling ball, and they collide elastically. Compared to its values before the collision, the golf ball after the collision has a
1. All of these
2. momentum that has changed from p to roughly −p .
3. slightly less momentum.
4. slightly less kinetic energy.
5. None of these
036 10.0 points
Static friction 0.49 between a 0.9 kg block and a 3.9 kg cart. There is no kinetic friction

wong (eyw89) – Quiz 2 Practice – sudarshan – (57415)

F

3.9 kg

µ = 0.49

9.8 m/s2

between the cart and the horizontal surface.
The acceleration of gravity is 9.8 m/s2 .

10

3.27 m

0.9 kg

What minimum force F must be exerted on the 3.9 kg cart in order for the 0.9 kg block not to fall?

What minimum coefficient of friction between a rider’s clothing and the wall of the cylinder is needed to keep the rider from slipping? The acceleration due to gravity is 9.81 m/s2 .

1. F = 91 N
2. F = 76 N
3. F = 94 N

038 10.0 points
A 4.2 kg block is pushed along the ceiling with a constant applied force of 80 N that acts at an angle of 56◦ with the horizontal. The block
2
accelerates to the right at 5.4 m/s2 .

4. F = 77 N µ 5. F = 96 N

4.2 kg

6. F = 49 N

5.4 m/s2

80

7. F = 66 N

N

◦

56

8. F = 70 N
9. F = 68 N
10. F = 74 N
037 10.0 points
In a popular amusement-park ride, a cylinder of radius 3.27 m is set in rotation at an angular speed of 5.36 rad/s, as shown in the figure. The floor then drops away, leaving the riders suspended against the wall in a vertical position. What is the coefficient of kinetic friction between the block and the ceiling? The acceleration due to gravity is 9.81 m/s2 .
039

10.0 points

A box of mass M is being accelerated up a vertical wall by a constant force F applied at an angle θ with the vertical, as shown. a M
F

θ

µk

wong (eyw89) – Quiz 2 Practice – sudarshan – (57415)
If the coefficient of kinetic friction between the box and wall is µk , what is the magnitude of the acceleration of the box?
F
from Newton’s Second Law
M
F
(cos θ − µk sin θ) − g
2. a =
M
F sin θ
3. a =
M

1. a =

4. a = µk g
F
(sin θ − µk cos θ) + g
M
F
(cos θ + µk sin θ) − g
6. a =
M
F sin θ
7. a = g −
M
F
8. a =
−g
M
F
(sin θ − µk cos θ) − g
9. a =
M

11

Find the speed of the bullet. The acceleration due to gravity is 9.81 m/s2 .
Answer in units of m/s
041 10.0 points
A pendulum made of a string and a sphere is able to swing in a vertical plane. The pendulum is released from a position of 70 ◦ from vertical as shown in the figure below.
The string hits a peg located a distance d below the point of suspension and rotates about the peg.
The acceleration of gravity is 9.8 m/s2 .

5. a =

10. a = 0 since kinetic friction makes the box slide at constant velocity
040

◦

33
2.8 m

vi

5.2 kg

d

70 ◦
9.8 m/s2
Find the smallest value of d (highest peg position) in order for the sphere to swing in a full circle centered on the peg.
Answer in units of m

10.0 points

A bullet of mass 3 g is fired into the bob of a ballistic pendulum of mass 5.2 kg. When the bob is at its maximum height, the strings make an angle of 33 ◦ with the vertical. The length of the pendulum is 2.8 m.

3g

m
7 kg 10

vf

042 10.0 points
Note: The pendulum bob is released at a height below the height of the peg.
A pendulum made of a string of length
10.5 m and a spherical bob of mass 7.3 kg and negligible raius swings in a vertical plane.
The pendulum is released from an angular position 39 ◦ from vertical as shown in the figure below. The string hits a peg located a distance 6 m below the point of suspension and swings about the peg up to an angle α on the other side of the peg. Then, the bob proceeds to oscillate back and forth between these two angular positions.
The acceleration of gravity is 9.8 m/s2 .

7.3 kg

39 ◦

α
9.8 m/s2

What is the maximum angle α which the pendulum will swing to the right after hitting the peg as shown above?
Answer in units of ◦
043 10.0 points
Consider the acceleration of block with mass m across the frictionless table towards the pulley.

Case I

m

In case I a block of mass m is attached to the end of the string. m Case II

vx

1.3 m µ=0.3 ∆x
What is the speed v of the block when it leaves the track?
Answer in units of m/s
045 (part 2 of 3) 10.0 points
What is the horizontal distance x the block travels in the air?
Answer in units of m
046 (part 3 of 3) 10.0 points
What is the total speed of the block when it hits the ground?
Answer in units of m/s

mg

In case II a force of m g is acts on the end of the string.
The acceleration of block m is
1. greater in case I.

8.1 kN/m 501 g
5.3 cm

m

12

044 (part 1 of 3) 10.0 points
A block is pushed against the spring with spring constant 8.1 kN/m (located on the lefthand side of the track) and compresses the spring a distance 5.3 cm from its equilibrium position (as shown in the figure below).
The block starts at rest, is accelerated by the compressed spring, and slides across a frictionless track except for a small rough area on a horizontal section of the track (as shown in the figure below).
It leaves the track horizontally, flies through the air, and subsequently strikes the ground.
The acceleration of gravity is 9.8 m/s2 .

2.3 m

10

.5

m

6m

wong (eyw89) – Quiz 2 Practice – sudarshan – (57415)

047 (part 1 of 2) 10.0 points
A wooden block hangs on a string. A bullet hits and sticks in the block.
What is conserved in the collision of the bullet with the block?
1. neither momentum nor mechanical energy

2. greater in case II.
2. momentum and mechanical energy
3. the same in both cases.
3. only mechanical energy

wong (eyw89) – Quiz 2 Practice – sudarshan – (57415)

13

A

4. only momentum
048 (part 2 of 2) 10.0 points
After the bullet collides and sticks in the wooden block that hangs on a string, the block swings out from its lowest position and reaches its highest position.
What is conserved in the motion after the bullet has collided with the block and the block swings up to the highest position?
1. momentum and mechanical energy
2. neither momentum nor mechanical energy
3. only momentum
4. only mechanical energy
049 (part 1 of 2) 10.0 points
Consider the 40 N weight held by two cables shown below. The left-hand cable is horizontal.

◦

43

40 N
a) What is the tension in the cable slanted at an angle of 43◦ ?
Answer in units of N
050 (part 2 of 2) 10.0 points
b) What is the tension in the horizontal cable?
Answer in units of N
051 10.0 points
Consider a frictionless roller coaster such as depicted. C hA 16 m
B
Passenger cars start at point A with zero initial speed, accelerate as they go down to point B, swing around the circular vertical loop B → C → B of radius 16 m, then go on towards further adventures (not shown).
When a car goes through the top of the loop
(point C), the passengers feel weightless (for just a moment).
What is the height hA of the starting point A above the loop’s bottom B? The acceleration of gravity is 9.8 m/s2 .
Answer in units of m
052 10.0 points
Consider a loop-the-loop system where the radius of the loop is R. A small block (of negligible size) is released from rest at the
4
point P , which is at a height of 4 R.
5
m
P

24
R
5

C
R
B

A
What is the force NA with which the track

wong (eyw89) – Quiz 2 Practice – sudarshan – (57415) pushes up on the block at the point A (at the bottom of the loop)? Consider friction between the block and the track to be negligible.
1. NA =
2. NA =
3. NA =
4. NA =
5. NA =

53 mg 5
65
mg
7
47 mg 5
21
mg
4
33 mg 4

14

054 10.0 points
Which of these systems is NOT an “isolated system” to which conservation of momentum can be applied?
1. A ball falls freely toward the floor. (Ignore air friction.) System: the ball
2. Two masses connected by a spring oscillate on a frictionless tabletop. System: the two masses and the spring
3. A ball falls freely toward the ground.
(Ignore air friction.) System: the ball and the earth 6. NA = 12 m g
7. NA =
8. NA =
9. NA =
10. NA =

31 mg 3
49
mg
5
35 mg 4
41
mg
5

053 10.0 points
Consider a frictionless track as shown in the figure. A block of mass 3.411 kg is released on the track at a height 5.08 m above the level surface. It slides down the track and makes a head-on elastic collision with a block of mass
6.822 kg, initially at rest.
The acceleration of gravity is 9.8 m/s2 .

5. All of these in fact are isolated systems.
6. A single car slips on an icy road. (Friction with the ice is negligible.) System: the car
7. Two cars slipping on an icy road collide with one another. (Friction with the ice is negligible.) System: the two cars
055 (part 1 of 3) 10.0 points
An air puck of mass 0.12 kg is tied to a string and allowed to revolve in a circle of radius
1.4 m on a horizontal, frictionless table. The other end of the string passes through a hole in the center of the table and a mass of 0.43 kg is tied to it. The suspended mass remains in equilibrium while the puck revolves.

5.08 m

3.411 kg

4. A billiard ball collides with another billiard ball on a level pool table. (Ignore friction with the table during the instant of the collision.) System: the two balls

0.12 kg
1.4 m
6.822 kg v Calculate the height to which the block with mass 3.411 kg rises after rebounding from the collision.
Answer in units of m

0.43 kg

wong (eyw89) – Quiz 2 Practice – sudarshan – (57415)
What is the tension in the string? The acceleration due to gravity is 9.8 m/s2 .
Answer in units of N
056 (part 2 of 3) 10.0 points
What is the horizontal force acting on the puck? Answer in units of N
057 (part 3 of 3) 10.0 points
What is the speed of the puck?
Answer in units of m/s
058

Find the distance D where the mass comes to rest. The acceleration due to gravity is
9.8 m/s2 .
Answer in units of m
059

v

A 6 kg mass slides to the right on a surface having a coefficient of friction 0.25 as shown in the figure. The mass has a speed of 6 m/s when contact is made with a spring that has a spring constant 107 N/m. The mass comes to rest after the spring has been compressed a distance d. The mass is then forced toward the left by the spring and continues to move in that direction beyond the unstretched position. Finally the mass comes to rest a distance
D to the left of the unstretched spring. v 107 N/m
6 kg

At the position shown in the figure, which arrow best represents the direction of the acceleration of the mass? The acceleration of gravity is 9.8 m/s2 and no external forces act on the system.
1.

2.

6 m/s

3.

6 kg

4.

d v⊃ = 0

5.

6 kg
6. The mass is traveling at a constant velocity, so it has no acceleration.

vf
6 kg

6 kg

7.
8.

D

10.0 points

A mass slides with negligible friction on a circular track of 1 m radius oriented vertically.
Its speed at the position shown in the figure is 3.13 m/s.

10.0 points

v⊢ = 0

15

107 N/m
9.
µ = 0.25