Question 1

A 0.50 kg block (A) moving at $$2.0\ \mathrm{m/s}$$ collides head-on with a 0.30 kg block (B) moving at $$-2.0\ \mathrm{m/s}. $$After a completely inelastic collision, what is the final velocity of the combined blocks?

Accepted Answer

$$v_f = 0.25\ \mathrm{m/s}$$

Question 2

Which of the following best describes the center of mass of a homogeneous sphere?

Accepted Answer

It is located at the geometric center of the sphere.

Question 3

A stationary bomb explodes into two fragments of unequal mass. What happens to the center of mass of the system immediately after the explosion?

Accepted Answer

It remains stationary.

Question 4

Given three particles with masses $$m_A$$, $$m_B$$, and $$m_C at $$positions $$(x_A, y_A)$$, $$(x_B, y_B)$$, and $$(x_C, y_C)$$, what is the $$x-$$coordinate of the center of mass?

Accepted Answer

$$x_{cm} = \dfrac{m_A x_A + m_B x_B + m_C x_C}{m_A + m_B + m_C}$$

Question 5

In a two-dimensional collision, which conservation law(s) must be applied to solve for the final velocities of the objects?

Accepted Answer

Conservation of momentum in both $$x$$ and $$y$$ directions

Question 6

A disk and a donut (torus) are both homogeneous and have an axis of symmetry. Where is the center of mass located for each?

Accepted Answer

Along the axis of symmetry for both

Question 7

A 1 kg block (A) and a 3 kg block (B) are compressed together with a spring and released from rest on a frictionless surface. If block B moves away at $$2\ \mathrm{m/s}$$ after the spring is released, what is the final speed of block A?

Accepted Answer

$$v_A = 6\ \mathrm{m/s}$$

Question 8

Which equation correctly relates the net external force to the acceleration of the center of mass for a system of particles?

Accepted Answer

$$\sum F_{ext} = M \vec{a}_{cm}$$

Question 9

In a perfectly elastic head-on collision between two objects of equal mass, what happens to their velocities?

Accepted Answer

They exchange velocities.

Question 10

A projectile explodes in mid-air into two fragments. If air resistance is negligible, what can be said about the motion of the center of mass after the explosion?

Accepted Answer

It continues along the original projectile path.

Question 11

A 5 kg ball (A) moving at $$2\ \mathrm{m/s}$$ collides with a stationary 3 kg ball (B) on a frictionless surface. After the collision, ball A moves at $$1\ \mathrm{m/s} at$$ $$30^\circ$$ above the x-axis. What is the $$x-$$component of ball B's velocity after the collision?

Accepted Answer

$$v_{Bf,x} = 0.5\ \mathrm{m/s}$$

Question 12

Which of the following is true about the center of gravity and center of mass for an object in a uniform gravitational field?

Accepted Answer

They coincide.

Question 13

A spring is compressed between two blocks of mass $$m_A$$ and $$m_B$$ and then released. If the spring has negligible mass and the system starts from rest, which conservation law allows you to find the final velocities of the blocks?

Accepted Answer

Conservation of momentum

Question 14

Which of the following is a correct expression for the $$y-$$coordinate of the center of mass for three particles?

Accepted Answer

$$y_{cm} = \dfrac{m_A y_A + m_B y_B + m_C y_C}{m_A + m_B + m_C}$$

Question 15

In a completely inelastic collision, which of the following is true?

Accepted Answer

The objects stick together and move with a common velocity.

Question 16

A homogeneous cylinder has its center of mass located:

Accepted Answer

At the midpoint of its axis of symmetry.

Question 17

If a system of particles is acted on by no external forces, what can be said about the velocity of the center of mass?

Accepted Answer

It remains constant.

Question 18

Which of the following is NOT a property of the center of mass?

Accepted Answer

It always coincides with the geometric center for any object.

Question 19

A system consists of two particles, one of mass $$2\ \mathrm{kg} at$$ $$(1,2)$$ and one of mass $$3\ \mathrm{kg} at$$ $$(4,6). $$What are the coordinates of the center of mass?

Accepted Answer

$$(2.6, 4.4)$$

Momentum, Collisions, and Center of Mass – Study Notes

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