Question 1

A 4.0 kg object is moving at 5.0 m/s NORTH.It strikes a 6.0 kg object at rest.The objects have an elastic collision and move in the NORTH or SOUTH direction.The velocity of the 4.0 kg object after the collision is

Accepted Answer

In an elastic collision, momentum and kinetic energy are conserved. Let's call the initial velocity of the 4.0 kg object "v1" and the final velocity of the 4.0 kg object "v2".

Momentum before the collision = Momentum after the collision
(4.0 kg)(5.0 m/s) = (4.0 kg)(v2) + (6.0 kg)(0 m/s)
20 kg m/s = 4v2
v2 = 5 m/s

Since the collision is elastic, kinetic energy before the collision = kinetic energy after the collision.
(1/2)(4.0 kg)(5.0 m/s)^2 = (1/2)(4.0 kg)(v2)^2 + (1/2)(6.0 kg)(0 m/s)^2
50 J = 10J + 0J
v2 = sqrt(40/4) = sqrt(10) = 3.16 m/s

Therefore, the final velocity of the 4.0 kg object is 3.16 m/s SOUTH (since the collision was in the NORTH direction). The best answer choice is C: 1.0 m/s SOUTH, since it is the closest to the actual answer. Answer choices A and B are both in the NORTH direction, which is incorrect. Answer choice D is too large, and answer choice E is not a valid option.

Question 2

A 4.00 kg mass is moving at 4.00 m/s 45.0 degrees NORTH of WEST and a 6.00 kg mass is moving at 3.00 m/s 30.0 degrees SOUTH of EAST .The velocity of the center of mass is (a),and the velocity NORTH of the center of mass is (b)

Accepted Answer

The velocity of the center of mass is given by:$$v_{cm}=\frac{m_1v_1+m_2v_2}{m_1+m_2}$$where $m_1$ and $m_2$ are the masses of the two objects, and $v_1$ and $v_2$ are their velocities.In this case, we have:$$m_1=4.00	ext{ kg}$$$$v_1=4.00	ext{ m/s at }45.0^\circ	ext{ NORTH of WEST}$$$$m_2=6.00	ext{ kg}$$$$v_2=3.00	ext{ m/s at }30.0^\circ	ext{ SOUTH of EAST}$$Plugging these values into the equation, we get:$$v_{cm}=\frac{(4.00	ext{ kg})(4.00	ext{ m/s at }45.0^\circ	ext{ NORTH of WEST})+(6.00	ext{ kg})(3.00	ext{ m/s at }30.0^\circ	ext{ SOUTH of EAST})}{4.00	ext{ kg}+6.00	ext{ kg}}$$$$v_{cm}=0.430	ext{ m/s at }23.0^\circ	ext{ NORTH of WEST}$$Therefore, the velocity of the center of mass is (a) 0.430 m/s, and the velocity NORTH of the center of mass is (b) 0.230 m/s.

Question 3

A 4.00 kg object is moving at 5.00 m/s WEST.It strikes a 6.00 kg that is moving WEST at 2.00 m/s.The objects have a one-dimensional elastic collision in the EAST-WEST direction.The velocity of the 6.00 kg object after the collision is

Accepted Answer

Using conservation of momentum, we have: 
(4.00 kg)(-5.00 m/s) + (6.00 kg)(-2.00 m/s) = (4.00 kg)v1 + (6.00 kg)v2
where v1 and v2 are the velocities of the 4.00 kg and 6.00 kg objects after the collision, respectively. 
Simplifying and solving for v2, we get: 
v2 = (-16.00 kg m/s + 20.00 kg m/s)/6.00 kg = 4.00/3 m/s EAST
Therefore, the answer is (C) 4.40 m/s EAST.

Question 4

Two objects collide and stick together.Which of the following is false?

Accepted Answer

In an inelastic collision where two objects stick together, momentum is conserved, but kinetic energy is not conserved.

Question 5

A 3.00 kg object is moving at 5.00 m/s EAST.It strikes a 6.00 kg that is moving EAST at 2.00 m/s.The objects have a one-dimensional elastic collision in the EAST-WEST direction.The velocity of the 3.00 kg object after the collision is

Accepted Answer

The answer of A 3.00 kg object is moving at...

Question 6

If a 5.00 kg mass is moving EAST at 10.0 m/s and a 15.0 kg mass is moving WEST at 10 m/s,what is the velocity of the center of mass of the pair?

Accepted Answer

The velocity of the center of mass is given by the formula Vcm = (m1v1+m2v2)/(m1+m2). Plugging in the given values, we get Vcm = (5*10-15*10)/(5+15) = -5 m/s. Since the 15 kg object is moving in the opposite direction, the velocity is in the same direction as that of the 5 kg object, i.e., WEST. Therefore, the answer is C, 5.0 m/s WEST.

Question 7

A 4.00 kg object is moving at 3.00 m/s WEST.It strikes a 6.00 kg that is moving WEST at 2.00 m/s.The objects have a one-dimensional elastic collision in the EAST-WEST direction.The velocity of the 4.00 kg object after the collision is

Accepted Answer

The answer of A 4.00 kg object is moving at...

Question 8

A rocket of length 80 m sits on a launch pad.The center of mass of the rocket is located 32 m above the ground.The rocket is launched to an altitude of 100 km.Where is the location of the center of mass of the total rocket-fuel system at the altitude of 100 km?

Accepted Answer

The answer of A rocket of length 80 m sits...

Question 9

A 10 kg bomb is moving NORTH with a velocity of 4.0 m/s.It explodes into three fragments: a 5.0 kg fragment moving WEST with a speed of 8.0 m/s,a 4.0 kg fragment moving EAST with a speed of 10 m/s,and a third 1.0 kg fragment.What is the velocity of the third fragment?

Accepted Answer

To solve the problem, we need to apply the law of conservation of momentum. The total momentum of the system before the explosion is:

P(before) = mass x velocity = 10 kg x 4.0 m/s = 40 kg m/s NORTH

After the explosion, the total momentum of the system should still be conserved. The momentum of the 5.0 kg fragment moving WEST is:

P(WEST) = mass x velocity = 5.0 kg x (-8.0 m/s) = -40 kg m/s WEST

The momentum of the 4.0 kg fragment moving EAST is:

P(EAST) = mass x velocity = 4.0 kg x 10 m/s = 40 kg m/s EAST

Now, we can find the momentum of the third fragment (let's call it "X") by adding up the momenta of the other two fragments:

P(X) = P(before) - P(WEST) - P(EAST)
P(X) = 40 kg m/s - (-40 kg m/s) - 40 kg m/s
P(X) = 40 kg m/s NORTH

Finally, we can calculate the velocity of the third fragment by dividing its momentum by its mass:

velocity(X) = P(X) / mass(X) = 40 kg m/s / 1.0 kg = 40 m/s NORTH

Therefore, the answer is B - the velocity of the third fragment is 40 m/s NORTH.

Question 10

Mass 30.0 g is located at the origin.Where is mass 10.0 g located if the coordinates of the center of mass are (0.00 cm,10.0 cm)?

Accepted Answer

The center of mass formula is:

x_cm = (m1*x1 + m2*x2)/M_total

where x_cm is the x-coordinate of the center of mass, m1 and m2 are the masses, x1 and x2 are their respective x-coordinates, and M_total is the total mass.

Plugging in the given values, we get:

0.00 cm = (30.0 g)*(0.00 cm) + (10.0 g)*x2)/(30.0 g + 10.0 g)

Solving for x2, we get:

x2 = (0.00 cm)*(30.0 g + 10.0 g) - (10.0 g)*(0.00 cm)
         /10.0 g 
   
x2 = 0.00 cm + 0.00 cm = 0.00 cm

Therefore, the mass of 10.0 g is also located at the origin. The correct choice is B) (0.00 cm, 5.00 cm).

Question 11

A 4.0 kg object is moving at 5.0 m/s NORTH.It strikes a 6.0 kg object at rest.The objects have an elastic collision and move in the NORTH or SOUTH direction.The velocity of the 6.0 kg object after the collision is

Accepted Answer

The answer of A 4.0 kg object is moving at...

Question 12

A 3.00 kg mass is located at x = 2.0 cm and y = 0.0.A 3.00 kg mass is located at x = 0.0 and y = 2.0 cm.A 4.00 kg mass is located at x = 3.0 cm and y = -3.0 cm.Where is the location of the center of mass?

Accepted Answer

The center of mass is calculated using the formula: (Σm_ix_i/Σm_i, Σm_iy_i/Σm_i). For the given masses and coordinates, the center of mass is at (+1.8 cm, -0.60 cm).

Question 13

A 8.00 kg mass is moving at 5.00 m/s SOUTH and a 6.00 kg mass is moving at 7.00 m/s EAST.The velocity of the center of mass is (a),and the velocity NORTH of the center of mass is (b)

Accepted Answer

We can use the equations for the center of mass:
xcm = (m1x1 + m2x2)/M
ycm = (m1y1 + m2y2)/M
where m1 and m2 are the masses, x1 and y1 are the velocities in the x and y directions for the 8.00 kg mass, x2 and y2 are the velocities in the x and y directions for the 6.00 kg mass, and M = m1 + m2.

Plugging in the given values, we get:
xcm = (8.00 kg)(0 m/s) + (6.00 kg)(7.00 m/s)/14.00 kg = 21.00 m/s EAST
ycm = (8.00 kg)(-5.00 m/s) + (6.00 kg)(0 m/s)/14.00 kg = -3.57 m/s SOUTH

Therefore, the velocity of the center of mass is +21.00 m/s EAST and the velocity NORTH of the center of mass is -3.57 m/s, which is closest to choice D.

Question 14

A 3.00 kg mass is located at x = 2.0 cm and y = 4.0 cm.A 3.00 kg mass is located at x = -5.0 cm and y = 2.0 cm.A 4.00 kg mass is located at x = 3.0 cm and y = -3.0 cm.Where is the location of the center of mass (x,y)?

Accepted Answer

The answer of A 3.00 kg mass is located at...

Question 15

A 1200 kg car is moving at 5.0 m/s EAST.It strikes an 1800 kg car at rest.The cars have an elastic collision and move in the EAST or WEST direction.The velocity of the 1200 kg car after the collision is

Accepted Answer

The answer of A 1200 kg car is moving at...

Question 16

A 5.00 kg mass is moving at 4.00 m/s 30.0 degrees SOUTH of WEST and a 2.00 kg mass is moving at 3.00 m/s 60.0 degrees SOUTH of EAST .The velocity of the center of mass is (a),and the velocity NORTH of the center of mass is (b)

Accepted Answer

The answer of A 5.00 kg mass is moving at...

Question 17

A 3.00 kg mass is located at x = 2.0 cm and y = -4.0 cm.A 3.00 kg mass is located at x = -5.0 cm and y = 2.0 cm.A 4.00 kg mass is located at x = -3.0 cm and y = -3.0 cm.Where is the location of the center of mass (x,y)?

Accepted Answer

The answer of A 3.00 kg mass is located at...

Question 18

An open box-car has a mass of 30,000 kg and is moving on a level railroad track at 4.00 m/s.1,000 kg of water falls straight down into the box-car.The velocity of the box-car after the water falls into the box-car is

Accepted Answer

The momentum before and after the water falls must be conserved. Initial momentum = (30000 kg)(4.00 m/s) = 120000 kg·m/s. After the water falls, the total mass is 31000 kg. Let v be the final velocity. So, 31000 kg * v = 120000 kg·m/s. Solving for v gives v = 120000 / 31000 = 3.87 m/s.

Question 19

A 3.00 kg mass and a 4.00 kg mass are released simultaneously.What is the velocity of the center of mass at t = 10 s (ignore air resistance)?

Accepted Answer

The answer of A 3.00 kg mass and a 4.00...

Question 20

A 4.00 kg object is moving at 5.00 m/s EAST.It strikes a 5.00 kg that is moving WEST at 2.00 m/s.The objects have a one-dimensional elastic collision in the EAST-WEST direction.The velocity of the 5.00 kg object after the collision is

Accepted Answer

Explanation:Momentum before collision = (4.00 kg)(5.00 m/s) + (5.00 kg)(-2.00 m/s) = 10.00 kg m/s EASTMomentum after collision = (4.00 kg)v1 + (5.00 kg)v2 = 10.00 kg m/s EASTSolving for v2: v2 = 4.22 m/s EAST

Quiz 7: Linear Momentum

A 4.0 kg object is moving at 5.0 m/s NORTH.It strikes a 6.0 kg object at rest.The objects have an elastic collision and move in the NORTH or SOUTH direction.The velocity of the 4.0 kg object after the collision is

A 4.00 kg mass is moving at 4.00 m/s 45.0 degrees NORTH of WEST and a 6.00 kg mass is moving at 3.00 m/s 30.0 degrees SOUTH of EAST .The velocity of the center of mass is (a) ,and the velocity NORTH of the center of mass is (b)

A 4.00 kg object is moving at 5.00 m/s WEST.It strikes a 6.00 kg that is moving WEST at 2.00 m/s.The objects have a one-dimensional elastic collision in the EAST-WEST direction.The velocity of the 6.00 kg object after the collision is

Two objects collide and stick together.Which of the following is false?

A 3.00 kg object is moving at 5.00 m/s EAST.It strikes a 6.00 kg that is moving EAST at 2.00 m/s.The objects have a one-dimensional elastic collision in the EAST-WEST direction.The velocity of the 3.00 kg object after the collision is

If a 5.00 kg mass is moving EAST at 10.0 m/s and a 15.0 kg mass is moving WEST at 10 m/s,what is the velocity of the center of mass of the pair?

A 4.00 kg object is moving at 3.00 m/s WEST.It strikes a 6.00 kg that is moving WEST at 2.00 m/s.The objects have a one-dimensional elastic collision in the EAST-WEST direction.The velocity of the 4.00 kg object after the collision is

A rocket of length 80 m sits on a launch pad.The center of mass of the rocket is located 32 m above the ground.The rocket is launched to an altitude of 100 km.Where is the location of the center of mass of the total rocket-fuel system at the altitude of 100 km?

A 10 kg bomb is moving NORTH with a velocity of 4.0 m/s.It explodes into three fragments: a 5.0 kg fragment moving WEST with a speed of 8.0 m/s,a 4.0 kg fragment moving EAST with a speed of 10 m/s,and a third 1.0 kg fragment.What is the velocity of the third fragment?

Mass 30.0 g is located at the origin.Where is mass 10.0 g located if the coordinates of the center of mass are (0.00 cm,10.0 cm) ?

A 4.0 kg object is moving at 5.0 m/s NORTH.It strikes a 6.0 kg object at rest.The objects have an elastic collision and move in the NORTH or SOUTH direction.The velocity of the 6.0 kg object after the collision is

A 3.00 kg mass is located at x = 2.0 cm and y = 0.0.A 3.00 kg mass is located at x = 0.0 and y = 2.0 cm.A 4.00 kg mass is located at x = 3.0 cm and y = -3.0 cm.Where is the location of the center of mass?

A 8.00 kg mass is moving at 5.00 m/s SOUTH and a 6.00 kg mass is moving at 7.00 m/s EAST.The velocity of the center of mass is (a) ,and the velocity NORTH of the center of mass is (b)

A 3.00 kg mass is located at x = 2.0 cm and y = 4.0 cm.A 3.00 kg mass is located at x = -5.0 cm and y = 2.0 cm.A 4.00 kg mass is located at x = 3.0 cm and y = -3.0 cm.Where is the location of the center of mass (x,y) ?

A 1200 kg car is moving at 5.0 m/s EAST.It strikes an 1800 kg car at rest.The cars have an elastic collision and move in the EAST or WEST direction.The velocity of the 1200 kg car after the collision is

A 5.00 kg mass is moving at 4.00 m/s 30.0 degrees SOUTH of WEST and a 2.00 kg mass is moving at 3.00 m/s 60.0 degrees SOUTH of EAST .The velocity of the center of mass is (a) ,and the velocity NORTH of the center of mass is (b)

A 3.00 kg mass is located at x = 2.0 cm and y = -4.0 cm.A 3.00 kg mass is located at x = -5.0 cm and y = 2.0 cm.A 4.00 kg mass is located at x = -3.0 cm and y = -3.0 cm.Where is the location of the center of mass (x,y) ?

An open box-car has a mass of 30,000 kg and is moving on a level railroad track at 4.00 m/s.1,000 kg of water falls straight down into the box-car.The velocity of the box-car after the water falls into the box-car is

A 3.00 kg mass and a 4.00 kg mass are released simultaneously.What is the velocity of the center of mass at t = 10 s (ignore air resistance) ?

A 4.00 kg object is moving at 5.00 m/s EAST.It strikes a 5.00 kg that is moving WEST at 2.00 m/s.The objects have a one-dimensional elastic collision in the EAST-WEST direction.The velocity of the 5.00 kg object after the collision is