Physics Homework Ch8

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1. The fishing pole in the figure below makes an angle of 20.0° with the horizontal. What is hte magnitude of the torque exerted by the fish about the axis perpendicular to the page and passing through the angler's hand if the fish pulls on the fishing line with a force  = 103N at an angle 37.0° below the horizontal? The force is applied at a point L = 1.86 m from the angler's hands.

_________ N*m

2. Find the net torque on the wheel in the figure below about the axle through O perpendicular to the page, taking a = 7.00 cm and b = 21.0 cm (Indicate the direction with the sign of your answer. Assume that the positive direction is counterclockwise.)

________N*m

3. Calculate the net torque (magnitude and direction) on the beam in the figure below about the following axes.

a) an axis through O perpendicular to the page

magnitude ________ N*m

Direction: (Counterclockwise or Clockwise)

b). an axis through C perpendicular to the page
magnitude ________ N*m

Direction (Counterclockwise or Clockwise)

4. A uniform 33.5-kg beam of length l = 4.95 m is supported by a vertical rope located d = 1.20 m from its left end as in the figure below. The right end of the beam is supported by a vertical column.

a) Find the tension in the rope

__________ N upward

b) Find the force that the column exerts on the right end of the beam.
__________ N upward






http://www.youtube.com/watch?v=Y3kcxu3Qr8E
A "different" way to solve for Torque

5. A meter stick is found to balance at the 49.7-cm mark when placed on a fulcrum. When a 61.0-gram mass is attached at the 12.0 cm mark, the fulcrum must be moved to the 39.2-cm mark for balance. What is the mass of the meter stick?

__________ g

6. A 520-N uniform rectangular sign 4.00 m wide and 3.00 m high is suspended from a horizontal, 6.00-m-long, uniform, 140-N rod as indicated in the figure below. The left end of the rod is supported by a hinge and the right end is supported by a thin cable making a 30.0° angle with the vertical. (Assume the cable is connected to the very end of the 6.00-m-long rod, and that there are 2.00 m separating the wall from the sign.)

a) Find the (magnitude of the ) tension T in the cable.
_______ N 

b) Find the horizontal and vertical components of the force exerted on the left end of the rod by the hinge. (Take up and to the right to be the positive directions. Indicate the direction with the sign of your answer).
Horizontal Component ___________ N

Vertical Component ___________ N

7. A window washer is standing on a scaffold supported by a vertical rope at each end. The scaffold weighs 204 N and is 2.9 m long. What is the tension in each rope when the 710-N worker stands 1.90 m from one end?
Smaller tension ________N

Larger tension  ________N

8. Four objects are held in position at the corners of a rectangle by light rods as shown in the figure below. (The mass values are given in the table.)

m1 (kg)	m2 (kg)	m3 (kg)	m4 (kg)
2.7	1.7	3.5	1.5

a) Find the moment of inertia of the system about the x-axis

_________kg*m²

b) Find the moment of inertia of the system about the y-axis

_________kg*m²

c) Find the moment of inertia of the system about an axis through O and perpendicular to the page.

________kg*m²

9. If the system shown in the figure below is set in rotation about each of the axes listed below, find the torque that will produce an angular acceleration of 3.8 rad/² in each case.

x axis                                                           ________ N * m

y axis                                                           ________ N * m

axis through O and perpendicular to the page   ________ N * m

10. A large grinding wheel in the shape of a solid cylinder of radius 0.330 m is free to rotate on a frictionless, vertical axle. A constant tangential force of 230 N applied to its edge causes the wheel to have an angular acceleration of 0.872 rad/².

a) What is the moment of inertia of the wheel?
_________ kg * m²

b) What is the mass of the wheel?

_________ kg

c) If the wheeel starts from rest, what is its angular velocity after 4.30 s have elapsed, assuming the force is acting during that time?

________ rad/s

11. A 245-kg merry-go-round in the shape of a uniform, solid, horizontal disk of radius 1.50 m is set in motion by wrapping a rope about the rim of the disk and pulling on the rope. What constant force would have to be exerted on the rope to bring the merry-go-round from rest to an angular speed of 0.700 rev/s in 2.00 s? (State the magnitude of the force.)

__________N

12. A horizontal 810-N merry-go-round of radius 1.70 m is started from rest by a constant horizontal force of 55 N applied tangentially to the merry-go-round. Find the kinetic energy of the merry-go-round after 2.0 s. (assume it is a solid cylinder)

___________ J

13. Four objects--a hoop, solid cylinder, a solid sphere, and a thin, spherical shell--each has a mass of 5.39 kg and a radius of 0.252 m

a) Find the moment of inertia for each object as it rotates about the axes shown in the table above.

hoop                         ________ kg * m²

Solid cylinder             ________ kg * m²

Solid sphere               ________ kg * m²

Thin, spherical shell    ________ kg * m²

b) Suppose each object is rolled down a ramp. Rank the translational speed of each object from highest to lowest.

c) Rank the objects's rotational kinetic energies from highest to lowest as the objects roll down the ramp.

i. Solid cylinder> thin spherical> Solid Cylinder> Solid sphere> hoop
ii. hoop > thin spherical > solid cylinder > Solid sphere
iii. hoop > Solid Cylinder > solid Sphere> Thin spherical
iv. thin spherical > solid sphere > solid cylinder > hoop

14. A light rod of length  l = 1.00 m rotates about an axis perpendicular to its length and passing through its center as in the figure below. Two particles of masses m₁ = 4.45 kg and m₂ = 3.00 kg are connected to the ends of the rod.

a) Neglecting the mass of the rod, what is the system's kinetic energy when its angular speed is 2.7 rad/s?

___________ J

b) Repeat the problem, assuming the mass of the rod is taken to be 1.60 kg.

__________ J

15. A 240-N sphere 0.20 m in radius rolls without slipping 6.0 m down a ramp that is inclined at 37° with the horizontal. What is the angular speed of the sphere at the bottom of the slope if it starts from rest?

_________ rad/s

16. Each of the following objects has a radius of 0.184 m and a mass of 2.50 kg, and each rotates about an axis through its center (as in the table below) with an angular speed of 35.9 rad/s. Find the magnitude of the angular momentum of each object

a) a hoop

_______ kg * m²/s
b) a solid cylinder
__________ kg * m²/s

c) a solid sphere

__________ kg * m²/s

d) a hollow spherical shell

_______ kg * m²/s

17.

a) Calculate the angular momentum of Earth that arises from its spinning motion on its axis, treating Earth as a uniform solid sphere.
__________ J * s

b) Calculate the angular momentum of Earth that arises from its orbital motion about the Sun, treating Earth as a point particle.

18. A light rigid rod of lenth l = 1.00 m in length rotates about an axis perpendicular to its length and through its center, as shown in the figure below. Two particles of masses m₁ = 4.55 kg and m₂ = 3.00 kg are connected to the ends of the rod. What is the angular momentum of the system if the speed of each particle is 6.40 m/s? (Neglect the rod's mass).

19. A student sits on a rotating stool holding two 2.8-kg objects. When his arms are extended horizontally, the objects are 1.0 m from the axis of rotation and he rotates with an angular speed of 0.75 rad/s. The moment of inertia of the student plus stool is 3.0 kg * m² and is assumed to be constant. The student then pulls in the objects horizontally to 0.28 m from the rotation axis.

a) Find the new angular speed of the student

_________ rad/s

b) Find the kinetic energy of the student before and after the objects are pulled in.

Before: __________ J

After  ___________ J

BONUS QUESTION:
+Dr-Mohammed Salah El-Gazzar asked me (in the comments below)
A ball of mass M and radius R starts from rest at a height of 2.00 m and rolls down a 30.0° slope, as in the figure. What is the linear speed of the ball when it leaves the incline? Assume that the ball rolls without slipping.

Repeat this example for a solid cylinder of the same mass and radius as the ball and released from the same height.


BONUS ANSWER:Here is your answer:

1st Principle:

The Work-Energy theorem:

Sum of all Changes of energy is equal to work

 -- If there is no friction, heat transfer, etc -- that is, if all forces acting are conservative forces, then the work will equal ZERO (0)

So:

Sum of changes in Linear kinetic Energy + Sum of changes in Rotational kinetic energy = - (negative) changes in potential energy

ΔKE(linear) + ΔKE(rotational) = ΔPE

ΔKE(linear) = (1/2)(m)(Δv^2)

2nd Principle:

For every linear variable, there is a rotational copy-cat. 

 - Mass, in linear kinematics is like "I" (represents moment of inertia --AKA rotational mass or rotational inertia--

 - Velocity, in linear kinematics is like "ω" (Omega represents angular velocity) 

ΔKE(rotational) = (1/2)(I)(Δω^2)

ω = velocity/radius

3rd Principle:

 the Moment of inertia is a quantity that describes the mass as it is distributed around the axis of rotation. 

 So, different geometries of mass will have slightly different equations for "I"

 -- In our case, we need to be able to calculate "I" for a Sphere and a Solid cylinder:

There is ONE big problem with your question at this point. 

 1. Is the "ball" a solid sphere (like a bowling ball) or a shell-like sphere (like a basket ball)?

I(solid sphere) = 2/5M(R^2)

I(hollow sphere) = 2/3M(R^2)

And Then finally

I(solid cylinder) = 1/2M(R^2)

So, let's do the equation for the solid cylinder, first, since we know exactly what formula to use:

--Start with the equation for the work energy theorem (shown in Eq 1, modified for all conservative forces).

Eq 1:

ΔKE(linear) + ΔKE(rotational) = -ΔPE

Eq 2/3/4

ΔKE(linear) = (1/2)(m)(Δv^2)

ΔKE(rotational) = (1/2)(I)(Δω^2)

ΔPE = mgΔh

Substitution of Eq 2/3/4 into Eq 1 gives the following: 

Eq 5

(1/2)(m)(Δv^2) + (1/2)(I)(Δω^2) = -mgΔh

Convert the rotational variables into 

Conversion 1

I = 1/2M(R^2)

Conversion 2

ω = v/r*

* NOTE: the use of capital "R" and lower case "r" both refer to the "radius", but convention has them being either capital or lower case in different conversions... They are the same  variable, here: r = R

Subsitute conversion 1 and conversion 2 into equation 5 provides:

Eq 6

(1/2)(m)(Δv^2) + (1/2)(1/2M(R^2))((Δv/r)^2) = -mgΔh

The mass can be divided out of this problem (all terms have mass)

Eq 7

(1/2)(Δv^2) + (1/2)(1/2(R^2))((Δv/r)^2) = -gΔh

This can be reduced via the following steps:

 - multiply both sides by "2"

 - Allow R^2 to cancel itself out

 - divide both sides by 1.5

Eq 8

Δv^2 = (-2/1.5)gΔh

Take the square root of both sides to solve for the change in linear velocity. Since we are assuming the ball started at rest (zero velocity), then the Δv is equal to the final velocity (when it leaves the incline)

v = Square root((-2/1.5)gΔh)

 -- Remember that the change in height (final height = 0, intial height was 2 meters) will be a negative number (final minus intial-- 0 - 2 = -2), so the negatives will cancel each other out.

Or

 v = Square root ((-1.333)*(9.8)*(-2)) = 26.13268 m/s (FOR THE CYLINDER)

Now, assume the ball is solid sphere (not hollow) -- everything starts the same:

Eq 1:

ΔKE(linear) + ΔKE(rotational) = -ΔPE

Eq 2/3/4

ΔKE(linear) = (1/2)(m)(Δv^2)

ΔKE(rotational) = (1/2)(I)(Δω^2)

ΔPE = mgΔh

Substitution of Eq 2/3/4 into Eq 1 gives the following: 

Eq 5

(1/2)(m)(Δv^2) + (1/2)(I)(Δω^2) = -mgΔh

HERE IS WHERE THINGS CHANGE -- "I" HAS A DIFFERENT CONVERSION EQUATION

Convert the rotational variables into 

Conversion 1

I = 2/5M(R^2)

Conversion 2

ω = v/r*

Subsitute conversion 1 and conversion 2 into equation 5 provides:

Eq 6

(1/2)(m)(Δv^2) + (1/2)(2/5M(R^2))((Δv/r)^2) = -mgΔh

- Again, divide out the "mass"

 - multiply both sides by "2"

 - Allow R^2 to cancel itself out

 - divide both sides by 1.5

 - take the square root of both sides

v = Square root( (10/7) X (9.8) X (2) )

v = 5.291502622129181 m/s (for a solid sphere)

By now, I think you probably understand what I'm doing -- just use a different conversion factor for 

"I" and all of the other steps will be the exact same.

Physics Homework Ch7

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Questions and comments are welcome!

1. A wheel has a radius of 3.6 m. How far (path length) does a point on the circumference travel if the wheel is rotated through the following angles, respectively
a) 31 °
_____ m

b) 31 rad
_____m

c) 31 rev
_____m






2. The tires on a new compact car have a diameter of 2.0 ft and are warranted for 64,000 miles.
 a) Determine the angle (in radians) through which one of these tires will rotate during the warranty period
_________ rad

b) How many revolutions of the tire are equivalent to your answer in (a)?
________ rev






3. A potter's wheel moves uniformly from rest to an angular speed of 0.19 rev/s in 29.0 s.
a) Find its angular acceleration in radians per second per second
 ________ rad/s²






4. A race car starts from rest on a circular track of radius 433 m. The car's speed increases at the constant rate of 0.320 m/s² . At the point where the magnitudes of the centripital and tangential accelerations are equal, find the following.
a) the speed of the race car
________m/s

b) the distance traveled
______ m

c) The elapsed time
______ s






5. A dentist drill starts from rest. After 3.30 s of constant angular acceleration it turns at a rate of 2.9 X 10⁴ rev/min.
a) Find the drill's angular acceleration
______ rad/s²

b) Determine the angle (in radians) through which the drill rotates during this period
_________ rad






6. A 53.4-cm diameter disk rotates with a constant angular acceleration of 2.60 rad/s². It starts from rest at t = 0, and a line drawn from the center of the disk to point p on the rim of the disk makes an angle of 57.3° with the positive x-axis at this time.
a) Find the angular speed of the wheel at t = 2.30 s
______ rad/s

b) Find the linear velocity and tangential acceleration of p at t = 2.30 s.
linear velocity _______ m/s
tangential acceleration  _____ m/s²

c) Find the position of P (in degrees, with respect to the positive x-axis) at t = 2.30 s
________ °




7. A rotating wheel requires 6.00 s to rotate 25.0 revolutions. Its angular velocity at the end of the 6.00-s interval is 96.0 rad/s. What is the constant angular acceleration (in rad/s^2/) of the wheel
______ rad/s^2/






8. A car initially traveling eastward turns north by traveling in a circular path at uniform speed as in the figure. The length of the arc ABC is 249 m, and the car completes the turn in 33.0 s

a) Determine the car's speed
_______ m/s

b) What is the magnitude and direction of the acceleration when the car is at point B?
magnitude _________ m/s²
direction   _________ ° counterclockwise from the +x-axis





9. It has been suggested that rotating cylinders about 11 mi long and 3.6 mi in diameter be placed in space and used as colonies. What angular speed must the cylinder have so that the centripetal acceleration at its ssurface equals the free-fall acceleration on Earth?
__________ rad/s






10. An adventurous archeologist (m = 80.5 kg) tries to cross a river by swinging from a vine. The vine is 11.0 m long, and his speed at the bottom of the swing is 8.5 m/s. The archeologist doesn't know that the vine has a breaking strength of 1,000 N. Does he make it safely across he river without falling in?
Yes
No






11. A 55.0-kg ice skater is moving at 4.03 m/s when she grabed the loose end of a rope, the opposite end of which is tied to a pole. She then moves in a circle of radius 0.805 m around the pole
a) Determine the force exerted by the horizontal rope on her arms.
_______N
b) Compare this force with her weight by finding the ratio of the force to her weight
_________







12. A certain light truck can go around a flat curve having a radius of 150 m with a maximum speed of 30.5 m/s. With what maximum speed can it go around a curve having a radius of 85.5 m?
_________m/s






13. A 50.0-kg child stands at the rim of a merry-go-round of radius 2.10 m, rotating with an angular speed of 2.6 rad/s
a) What is the child's centripetal acceleration?
________ m/s²
b) What is the minimum force between her feet and the floor of the carousel that is required to keep her in the circular path?
________N
c) What minimum coefficient of static friction is required?
__________
Is the answer you found reasonable? In other words, is she likely to stay on the merry-go-round?

Yes
No






14. An air puck of mass m₁ = 0.30 kg is tied to a string and allowed to revolve in a circle of radius R = 1.3 m on a frictionless horizontal table. The other end of the string passes through a hole in the center of the table, and a mass of m₂ = 1.1 kg is tied to it (see the figure below). The suspended mass remains in equilibrium while the puck on the tabletop revolves.

a) What is the tension in the string?
_______ N
b) What is the horizontal force acting on the puck?
_______N
c) What is the speed of the puck?
_______m/s






15. The average distance separating Earth and the moon (center to center) is 384,000 km. Use the data in the table to find the net gravitational force exerted by the Earth and the Moon on a 3.00 x 104-kg spaceship located halfway between them.
________ N

Useful Planetary Data
Body	Mass (kg)	Mean Radius (m)	Period (s)	Distance from Sun (m)	T2/r3 (s2/m3)
Mercury	3.18 x 1023	2.43 x 106	7.60 x 106	5.79 x 1010	2.97 x 10−19
Venus	4.88 x 1024	6.06 x 106	1.94 x 107	1.08 x 1011	2.99 x 10−19
Earth	5.98 x 1024	6.37 x 106	3.156 x 107	1.496 x 1011	2.97 x 10−19
Mars	6.42 x 1023	3.37 x 106	5.94 x 107	2.28 x 1011	2.98 x 10−19
Jupiter	1.90 x 1027	6.99 x 107	3.74 x 108	7.78 x 1011	2.97 x 10−19
Saturn	5.68 x 1026	5.85 x 107	9.35 x 108	1.43 x 1012	2.99 x 10−19
Uranus	8.68 x 1025	2.33 x 107	2.64 x 109	2.87 x 1012	2.95 x 10−19
Neptune	1.03 x 1026	2.21 x 107	5.22 x 109	4.50 x 1012	2.99 x 10−19
Pluto	~1.4 x 1022	~1.5 x 106	7.82 x 109	5.91 x 1012	2.96 x 10−19
Moon	7.36 x 1022	1.74 x 106	-	-	-
Sun	1.991 x 1030	6.96 x 108	-	-	-

16. A satelite has a mass of 99 kg and is located at 2.05 x 10⁶ m above the surface of the Earth.
a) What is the potential energy associated with the satelite at this location?
________ J
b) What is the magnitude of the gravitational force on the satelite?
_______ N






17. A coordinate system (in meters) is constructed on the surface of a pool table, and three objects are placed on the table as follows: a 7.0-kg object at the origin of the coordinate system, a 16.0-kg object at (0, 2.0), and a 25.0-kg object at (4.0, 0). Find the resultant gravitational force exerted by the other two objects on the object at the origin.
Magnitude _________ N
direction    ________°






18. Objects with masses of 190 kg and a 490 kg are separated by 0.430 m.
a) Find the net gravitational force exerted by these objects on a 65.0-kg object placed midway between them.
magnitude _______ N
direction
 - Toward the 190-kg mass
 - Toward the 490-kg mass
 - The magnitude is zero






19. A satelite is in a circular orbit around the Earth at an altitude of 2.52 x 10⁶ m.

a) find the period of the orbit. (Hint: Modify Kepler's third law:

                               T² = 

4π2

GMS

r³
 so it is suitable for objects orbiting the Earth rather than the Sun. The radius of the Earth is 6.38 x 10⁶ m, and the mass of the Earth is 5.98 x 10²⁴ kg.)
__________ h
b) Find the speed of the satellite
_______km/s
c) Find the acceleration of the satelite.
_______ m/s² toward the center of the earth






20. A satellite of Mars, called Phobos, has an orbital radius of 9.4 x 10⁶ m and a period of 2.8 x 10⁴ s. Assuming the orbit is circular, determine the mass of Mars
___________ kg






21. A 549-kg satellite is in a circular orbit about the Earth at a height above the Earth equal to the Earth's mean radius.
a) Find the satellite's orbital speed
_________m/s
b) Find the period of its revolution.
________ h
c) Find the gravitational force acting on it.
_________ N

Physics Homework Ch6

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1. Calculate the magnitude of the linear momentum for the following cases.
a) a proton with mass 1.67 X 10^-27 kg, moving with a speed of 5.45 X 10⁶ m/s
__________kg * m/s
b) a 12.5 g bullet moving with a speed of 350 m/s
_________kg * m/s
c) a 71.5 kg sprinter running with a speed of 11.5 m/s
________kg *m/s
d) the Earth (mass = 5.98 X 10²⁴ kg) moving with an orbital speed equal to 2.98 X 10⁴ m/s
_________kg * m/s




2. A pitcher claims he can throw a 0.159-kg baseball with as much momentum as a 2.10-g bullet moving with a speed of 1.50 X 10³ m/s
a). What mus the baseball's speed be if the pitcher's claim is valid?
______m/s
b). Which has greater kinetic energy, the ball the or the bullet?

Mode:
The bullet has greater kinetic energy
The ball has greater kinetic energy
Both have the same kinetic energy





3. An object has a kinetic energy of 232 J and a momentum of magnitude 21.6 kg * m/s.
a). Find the speed of the object
______m/s
b) Find the mass of the ojbect
_______ kg




4. A 0.252 kg volleyball approaches a player horizontally with a speed of 12.9 m/s. The player strikes the ball with her fist and causes the ball to move in the opposite direction with a speed of 22.0 m/s
a). What impulse is delivered to the ball by the player?
___________kg * m/s
b). If the player's fist is in contact with the ball for 0.0600 s, find the magnitude of the average force exerted on the player's fist.
___________ N





5. A ball of mass 0.120 kg is dropped from rest from a height of 1.25 m. It rebounds from the floor to reach a height of 0.600 m. What impulse was given to the ball by the floor?
magnitude _____ kg * m/s

Direction: (upward or downward)





6. A tennis player receives a shot with a ball (0.0600 kg) traveling horizontally at 54.0 m/s and returns the shot with the ball traveling horizontally at 32.0 m/s in the opposite direction.
a). What is the impulse delivered to the ball by the racket?
__________N*s  (direction: +x or -x)
b) What work does the racket do on the ball?





7. High speed stroboscopic photographs show that the head of a 210 - g golf club is traveling at 41 m/s just before it strikes a 46-g golf ball at rest on a tee. After the collision, the club head travels (in the same direction) at 30 m/s. Find the speed of the golf ball just after impact
________m/s





8. A rifle with a weight of 40 N fires a 6.0-g bullet with a speed of 230 m/s
a) Find the recoil speed of the rifle
______m/s
b) If a 750-N man holds the rifle firmly with his shoulder, find the recoil of the man and rifle.
________m/s






9. A 78-kg fisherman in a 119-kg boat throws a package of mass m = 15 kg horizontally toward the right with a speed of v_i = 4.3 m/s as in the figure below. Neglecting water resistance, and assuming the boat is at rest before the package is thrown, find the velocity of the boat after the package is thrown.
magnitude _______m/s
Direction (toward the right or toward the left)

 

10. A 70.0-kg person throws a 0.0470-kg snowball forward with a ground speed of 29.0 m/s. A second person with a mass of 59.0 kg, catches the snowball. Both people are on skates. The first person is initially moving forward with a speed of 2.00 m/s, and the second person is initially at rest. What are the velocities of the two peopel after the snowball is exchanged?
Disregard the friction between the skates and the ice.
Thrower _______ m/s
Catcher _______ m/s





11. A railraod car of mass 3.5 X 10⁴ kg moving at 4.00 m/s collides and couples with two coupled railroad cars, each of the same mass as the single car and moving in the same direction at 1.2 m/s
a). What is the speed of the three coupled cars after the collision?
________m/s
b) How much kinetic energy is lost in the collision?
_______ J






12. In a Broadway performance, an 71.6-kg actor swings from a 3.80-m-long cable that is horizontal when he starts. At the bottom of his arc, he picks up his 55.0 kg costar in an inelastic collision. What maximum height do they reach after their upward swing?
_________m






13. Two shuffleboard disks of equal mass, one orange and the other green, are involved in a perfectly elastic glancing collision. The green disk is initially at rest and is stuck by the orange disk moving initially to the right at _oi = 3.35 m/s as in figure (a) shown below. After the collision, the orange disk moves in a direction that makes an angle of θ = 39.0 ° with the horizontal axis while the green disk makes an angle of = 51.0°with this axis as in figure (b). Determine the speed of each disk after the collision.
_of = _______ m/s
_gf = _______ m/s

 

14. A 0.032-kg bullet is fired vertically at 215 m/s into a 0.15-kg baseball that is initially at rest. How high does the combined bullet and baseball rise after teh collision, assuming the bullet embeds itself in the ball?
__________m





15. A 26.0 g object moving to the right at 18.0 cm/s overtakes and collides elastically with a 10.0-g object moving in the same direction at 15.0 cm/s. Find the velocity of each object after the collision.
26.0 g object ________ cm/s
10.0 g object ________ cm/s






16. A billiard ball rolling across a table at 1.55 m/s makes a head on elastic collision with an identical ball. Find the speed of each ball after the collision when each of the following occurs.

a) The second ball is initially at rest.
frist ball _________m/s
second ball ________m/s

b) The second ball is moving toward the first at speed of 1.05 m/s
first ball ___________m/s
second ball ___________m/s

c) The second ball is moving away from the first at a speed of 1.10 m/s
first ball _________ m/s
second ball _________ m/s