Question 1

A particle with a mass of 400 g moving at 2.0 m/s collides elastically with a stationary particle whose mass is 240 g. After the collision, the 400 g mass is moving at 1.5 m/s. Through what angle is its path deflected?
A)35°
B)15°
C)25°
D)30°
E)20°

Accepted Answer

The answer of A particle with a mass of 400...

Question 2

A plate falls vertically to the floor and breaks up into three pieces, which slide along the floor. Immediately after the impact, a 200-g piece moves along the x-axis with a speed of 2.00 m/s and a 235-g piece moves along the y-axis with a speed of 1.50 m/s. The third piece has a mass of 100 g. In what direction does the third piece move?
A)216.9° from the x-axis
B)221.4° from the x-axis
C)36.9° from the x-axis
D)39.9° from the x-axis
E)41.4° from the x-axis

Accepted Answer

The total momentum before and after the impact must be conserved. The momentum of the third piece can be calculated using the conservation of momentum in both x and y directions. Solving for the angle gives approximately 221.4° from the x-axis.

Question 3

Two automobiles traveling at right angles to each other collide and stick together. Car A has a mass of 1200 kg and had a speed of 25 m/s before the collision. Car B has a mass of 1600 kg. The skid marks show that, immediately after the collision, the wreckage was moving in a direction making an angle of 40° with the original direction of car A. What was the speed of car B before the collision?
A)16 m/s
B)18 m/s
C)11 m/s
D)21 m/s
E)14 m/s

Accepted Answer

Explanation:Momentum is conserved in both the x and y directions.$$(1200	ext{ kg})(25	ext{ m/s})\cos0\degree+(1600	ext{ kg})(v_B)\cos90\degree=(1200	ext{ kg}+1600	ext{ kg})(v_f)\cos40\degree$$$$(1200	ext{ kg})(25	ext{ m/s})\sin0\degree+(1600	ext{ kg})(v_B)\sin90\degree=(1200	ext{ kg}+1600	ext{ kg})(v_f)\sin40\degree$$$$v_f=\frac{(1200	ext{ kg})(25	ext{ m/s})}{\cos40\degree(1200	ext{ kg}+1600	ext{ kg})}=16	ext{ m/s}$$$$v_B=\frac{(1200	ext{ kg}+1600	ext{ kg})(v_f)\sin40\degree}{\sin90\degree(1600	ext{ kg})}=16	ext{ m/s}$$

Question 4

A 1000-kg car is traveling north at 20.0 m/s. A 1500-kg car is traveling north at 36.0 m/s. The 1500-kg collides with the rear of the 1000-kg car and they lock together. Ignoring external forces acting during the collision, what is the velocity of the cars immediately after the collision?
A)56.0 m/s north
B)29.6 m/s north
C)13.6 m/s south
D)8.00 m/s south
E)28.0 m/s north

Accepted Answer

Momentum is conserved in the collision, so the total momentum before the collision is equal to the total momentum after the collision. The total momentum before the collision is:$$(1000	ext{ kg})(20.0	ext{ m/s}) + (1500	ext{ kg})(36.0	ext{ m/s}) = 82000	ext{ kg m/s}$$The total mass after the collision is:$$1000	ext{ kg} + 1500	ext{ kg} = 2500	ext{ kg}$$So the velocity of the cars immediately after the collision is:$$82000	ext{ kg m/s} / 2500	ext{ kg} = 29.6	ext{ m/s north}$$

Question 5

A 10.0-kg mass is located at (2.00 m)  + (3.00 m)  . A 15.0-kg mass is located at (4.00 m)  . A 25-kg mass is located at (2.00 m)  . What is the location of the center of mass of this system?
A)(3.20 m)  + (3.20 m) 
B)(1.60 m)  + (1.60 m) 
C)(80.0 m)  + (80.0 m) 
D)(3.20 m)  + (1.60 m) 
E)(1.60 m)  + (3.20 m)

Accepted Answer

The answer of A 10.0-kg mass is located at (2.00...

Question 6

A 2.00-m rod of negligible mass connects two small objects. The mass of one object is 1.00 kg and the other is 1.50 kg. How far is the center of mass of this system from the 1.00 kg mass?
A)0.800 m
B)0.670 m
C)1.25 m
D)1.33 m
E)1.20 m

Accepted Answer

The answer of A 2.00-m rod of negligible mass connects...

Question 7

A billiard ball traveling at 3.00 m/s collides perfectly elastically with an identical billiard ball initially at rest on the table. The initially moving billiard ball deflects 30.0°. What is the speed of the initially stationary billiard ball after the collision?
A)2.00 m/s
B)0.866 m/s
C)1.50 m/s
D)2.59 m/s
E)0.750 m/s

Accepted Answer

The answer of A billiard ball traveling at 3.00 m/s...

Question 8

Two ice skaters push off against one another starting from a stationary position. The 45-kg skater acquires a speed of 0.375 m/s. What speed does the 60-kg skater acquire?
A)0.500 m/s
B)0.281 m/s
C)0.375 m/s
D)0.750 m/s
E)0 m/s

Accepted Answer

Since momentum is conserved in the system, we can use the following equation:

m1v1 + m2v2 = 0

where m1 and v1 are the mass and velocity of the first skater, and m2 and v2 are the mass and velocity of the second skater.

Plugging in the given values, we have:

(45 kg)(0.375 m/s) + (60 kg)(v2) = 0

Solving for v2, we get:

v2 = - (45 kg)(0.375 m/s) / (60 kg) = -0.28125 m/s

Since the negative sign just indicates the direction of motion, we can take the absolute value to get the speed:

|v2| = 0.281 m/s

Therefore, the answer is B.

Question 9

A 1000-kg car approaches an intersection traveling north at 20.0 m/s. A 1200-kg car approaches the same intersection traveling east at 22.0 m/s. The two cars collide at the intersection and lock together. Ignoring any external forces that act on the cars during the collision, what is the velocity of the cars immediately after the collision?
A)29.7 m/s in a direction 47.7° east of north
B)21.1 m/s in a direction 47.7° west of south
C)15.1 m/s in a direction 52.8° east of north
D)21.1 m/s in a direction 52.8° east of north
E)21.1 m/s in a direction 47.7° east of north

Accepted Answer

The answer of A 1000-kg car approaches an intersection traveling...

Question 10

A uniform piece of wire, 20 cm long, is bent in a right angle in the center to give it an L-shape. How far from the bend is the center of mass of the bent wire?
A)2.5 cm
B)3.5 cm
C)4.5 cm
D)5.0 cm
E)7.1 cm

Accepted Answer

The center of mass of each segment of the wire (10 cm long) is at its midpoint, 5 cm from the bend. Since the wire is uniform and the segments are equal in length, the center of mass of the L-shape will be located at the point where the medians of the right triangle (formed by the two segments and the line connecting their midpoints) intersect. This point is 1/3 of the way along the median from the right angle, which is $\sqrt{5^2 + 5^2} = \sqrt{50}$ cm long. Therefore, the distance from the bend to the center of mass is $\frac{1}{3} \times \sqrt{50} \approx 3.5$ cm.

Question 11

A 0.400-kg ball approaches a very massive wall at 20.0 m/s perpendicular to wall and rebounds with 70.0% of its initial kinetic energy. What is the magnitude of the change in momentum of the wall?
A)14.7 kg∙m/s
B)13.6 kg∙m/s
C)2.40 kg∙m/s
D)1.31 kg∙m/s
E)0.00 kg∙m/s

Accepted Answer

The initial momentum of the ball is 0.400 kg * 20.0 m/s = 8.0 kg∙m/s. The final kinetic energy is 70% of the initial, so the final speed is √0.7 * 20.0 m/s ≈ 16.73 m/s. The final momentum is 0.400 kg * 16.73 m/s ≈ 6.69 kg∙m/s. The change in momentum is 8.0 kg∙m/s - (-6.69 kg∙m/s) = 14.7 kg∙m/s.

Question 12

A 2.00-m rod of negligible mass connects two small objects. The mass of one object is 1.00 kg and the mass of the other is unknown. The center of mass of this system is on the rod a distance 1.80 m from the 1.00-kg mass object. What is the mass of the other object?
A)4.11 kg
B)3.22 kg
C)9.00 kg
D)0.111 kg
E)0.900 kg

Accepted Answer

The answer of A 2.00-m rod of negligible mass connects...

Question 13

Three masses are located in the x-y plane as follows: a mass of 6 kg is located at (0 m, 0 m), a mass of 4 kg is located at (3 m, 0 m), and a mass of 2 kg is located at (0 m, 3 m). Where is the center of mass of the system?
A)(1 m, 2 m)
B)(2 m, 1 m)
C)(1 m, 1 m)
D)(1 m, 0.5 m)
E)(0.5 m, 1 m)

Accepted Answer

The center of mass can be found by taking the weighted average of the position vectors of the masses. 
Let's denote the position vectors of the masses as r1, r2, and r3, with masses m1, m2, and m3, respectively.
r1 = (0 m, 0 m)
r2 = (3 m, 0 m)
r3 = (0 m, 3 m)
m1 = 6 kg
m2 = 4 kg
m3 = 2 kg

The center of mass, denoted as R, can be found using the following equation:

R = (m1*r1 + m2*r2 + m3*r3)/(m1 + m2 + m3)

Substituting in the values, we get:

R = (6 kg * (0 m, 0 m) + 4 kg * (3 m, 0 m) + 2 kg * (0 m, 3 m))/(6 kg + 4 kg + 2 kg) 
  = (12 mkg/12 kg, 6 mkg/12 kg)
  = (1 m, 0.5 m)

Therefore, the center of mass of the system is at position (1 m, 0.5 m), which corresponds to choice D.

Question 14

Two objects of the same mass move along the same line in opposite directions. The first mass is moving with speed v. The objects collide in a perfectly inelastic collision and move with speed 0.100v in the direction of the velocity of the first mass before the collision. What was the speed of the second mass before the collision?
A)1.200v
B)10.0v
C)0.900v
D)0.800v
E)0.00v

Accepted Answer

The answer of Two objects of the same mass move...

Question 15

A neutron with a mass of 1.67 × 10^-²⁷ kg traveling east with a kinetic energy of 2.00 × 10^-²¹ J collides perfectly elastically with a helium nucleus with a mass 6.68 × 10^-²⁷ kg that is initially at rest. After the collision, the neutron has a kinetic energy 1.80 × 10^-²¹ J. What angle was the neutron deflected during the collision? A)142° B)117° C)38.0° D)180° E)32.8°

Accepted Answer

The answer of A neutron with a mass of 1.67...

Question 16

A 2.3-kg object traveling at 6.1 m/s collides head-on with a 3.5-kg object traveling in the opposite direction at 4.8 m/s. If the collision is perfectly elastic, what is the final speed of the 2.3-kg object?
A)0.48 m/s
B)7.1 m/s
C)3.8 m/s
D)4.3 m/s
E)6.6 m/s

Accepted Answer

The answer of A 2.3-kg object traveling at 6.1 m/s...

Question 17

A 3.00-kg object traveling 20.0 m/s west collides with a 5.00-kg mass object traveling 12.0 m/s west. The collision is perfectly elastic, what is the velocity of the 3.00-kg object after the collision?
A)20.0 m/s east
B)8.00 m/s west
C)12.0 m/s west
D)12.0 m/s east
E)10.0 m/s west

Accepted Answer

The answer of A 3.00-kg object traveling 20.0 m/s west...

Question 18

A 2.00-kg mass object traveling east at 20.0 m/s collides with a 3.00-kg mass object traveling west at 10.0 m/s. After the collision, the 2.00-kg mass has a velocity 5.00 m/s to the west. How much kinetic energy was lost during the collision? A)(^{0.00 J}) B)458 J C)516 J D)(^{91.7 J}) E)175 J

Accepted Answer

The answer of A 2.00-kg mass object traveling east at...

Question 19

A 4.00-kg mass and a 9.00-kg mass are being held at rest against a compressed spring on a frictionless surface. When the masses are released, the 4.00-kg mass moves to the east with a speed of 2.00 m/s. What is the velocity of the 9.00-kg mass after the masses are released?
A)2.00 m/s west
B)0.888 m/s west
C)0.500 m/s east
D)4.50 m/s west
E)0.500 m/s west

Accepted Answer

The answer of A 4.00-kg mass and a 9.00-kg mass...

Question 20

A 620-g object traveling at 2.1 m/s collides head-on with a 320-g object traveling in the opposite direction at 3.8 m/s. If the collision is perfectly elastic, what is the change in the kinetic energy of the 620-g object?
A)It loses 0.23 J.
B)It gains 0.69 J.
C)It loses 0.47 J.
D)It loses 1.4 J.
E)The energy of the object is unchanged.

Accepted Answer

Explanation:The total kinetic energy before the collision is:$$KE_i = \frac{1}{2}mv_1^2 + \frac{1}{2}mv_2^2 = \frac{1}{2}(0.620 kg)(2.1 m/s)^2 + \frac{1}{2}(0.320 kg)(3.8 m/s)^2 = 2.72 J$$The total kinetic energy after the collision is:$$KE_f = \frac{1}{2}mv_3^2 + \frac{1}{2}mv_4^2$$where v3 and v4 are the velocities of the two objects after the collision. Since the collision is perfectly elastic, the total kinetic energy is conserved, so:$$KE_i = KE_f$$$$2.72 J = \frac{1}{2}(0.620 kg)v_3^2 + \frac{1}{2}(0.320 kg)v_4^2$$Solving for v3, we get:$$v_3 = \pm 1.4 m/s$$Since the 620-g object is traveling in the opposite direction after the collision, its velocity is -1.4 m/s. Therefore, the change in its kinetic energy is:$$\Delta KE = KE_f - KE_i = \frac{1}{2}(0.620 kg)(-1.4 m/s)^2 - 2.72 J = -0.23 J$$So, the correct answer is A: It loses 0.23 J.

Quiz 9: Linear Momentum

A particle with a mass of 400 g moving at 2.0 m/s collides elastically with a stationary particle whose mass is 240 g. After the collision, the 400 g mass is moving at 1.5 m/s. Through what angle is its path deflected?

A 1000-kg car is traveling north at 20.0 m/s. A 1500-kg car is traveling north at 36.0 m/s. The 1500-kg collides with the rear of the 1000-kg car and they lock together. Ignoring external forces acting during the collision, what is the velocity of the cars immediately after the collision?

A 10.0-kg mass is located at (2.00 m) + (3.00 m) . A 15.0-kg mass is located at (4.00 m) . A 25-kg mass is located at (2.00 m) . What is the location of the center of mass of this system?

A 2.00-m rod of negligible mass connects two small objects. The mass of one object is 1.00 kg and the other is 1.50 kg. How far is the center of mass of this system from the 1.00 kg mass?

A billiard ball traveling at 3.00 m/s collides perfectly elastically with an identical billiard ball initially at rest on the table. The initially moving billiard ball deflects 30.0°. What is the speed of the initially stationary billiard ball after the collision?

Two ice skaters push off against one another starting from a stationary position. The 45-kg skater acquires a speed of 0.375 m/s. What speed does the 60-kg skater acquire?

A uniform piece of wire, 20 cm long, is bent in a right angle in the center to give it an L-shape. How far from the bend is the center of mass of the bent wire?

A 0.400-kg ball approaches a very massive wall at 20.0 m/s perpendicular to wall and rebounds with 70.0% of its initial kinetic energy. What is the magnitude of the change in momentum of the wall?

A 2.00-m rod of negligible mass connects two small objects. The mass of one object is 1.00 kg and the mass of the other is unknown. The center of mass of this system is on the rod a distance 1.80 m from the 1.00-kg mass object. What is the mass of the other object?

Three masses are located in the x-y plane as follows: a mass of 6 kg is located at (0 m, 0 m) , a mass of 4 kg is located at (3 m, 0 m) , and a mass of 2 kg is located at (0 m, 3 m) . Where is the center of mass of the system?

A 2.3-kg object traveling at 6.1 m/s collides head-on with a 3.5-kg object traveling in the opposite direction at 4.8 m/s. If the collision is perfectly elastic, what is the final speed of the 2.3-kg object?

A 3.00-kg object traveling 20.0 m/s west collides with a 5.00-kg mass object traveling 12.0 m/s west. The collision is perfectly elastic, what is the velocity of the 3.00-kg object after the collision?

A 2.00-kg mass object traveling east at 20.0 m/s collides with a 3.00-kg mass object traveling west at 10.0 m/s. After the collision, the 2.00-kg mass has a velocity 5.00 m/s to the west. How much kinetic energy was lost during the collision?

A 4.00-kg mass and a 9.00-kg mass are being held at rest against a compressed spring on a frictionless surface. When the masses are released, the 4.00-kg mass moves to the east with a speed of 2.00 m/s. What is the velocity of the 9.00-kg mass after the masses are released?

A 620-g object traveling at 2.1 m/s collides head-on with a 320-g object traveling in the opposite direction at 3.8 m/s. If the collision is perfectly elastic, what is the change in the kinetic energy of the 620-g object?