Q: A 0.2 kg arrow is shot into a 1.0 kg block suspended as a pendulum. After the collision, the block and arrow rise to a height of 0.5 m. What was the initial speed of the arrow? (Assume a completely inelastic collision and $$g = 9.8\ \mathrm{m/s^2$})$$

$$v_\text{arrow} = 7.7\ \mathrm{m/s}$$

Question 1

Newton's second law can be expressed in terms of momentum. Which equation correctly represents this law?

Accepted Answer

$$\sum \vec{F} = \frac{d\vec{p}}{dt}$$

Question 2

A 0.2 kg arrow is shot into a 1.0 kg block suspended as a pendulum. After the collision, the block and arrow rise to a height of 0.5 m. What was the initial speed of the arrow? (Assume a completely inelastic collision and $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v_	ext{arrow} = 7.7\ \mathrm{m/s}$$

Question 3

Which of the following statements is true for an elastic collision?

Accepted Answer

Both momentum and kinetic energy are conserved.

Question 4

In a two-dimensional collision, which property of momentum is conserved?

Accepted Answer

Both the $$x$$ and $$y$$ components of momentum are conserved.

Question 5

A ball of mass $$m$$ moving at $$v$$ collides elastically with a stationary ball of equal mass. After the collision, what are the velocities of the two balls?

Accepted Answer

The first ball stops, and the second ball moves at velocity $$v.$$

Question 6

Which equation gives the center of mass $$x_{cm}$$ for two particles of masses $$m_1$$ and $$m_2 at $$positions $$x_1$$ and $$x_2$$?

Accepted Answer

$$x_{cm} = \frac{m_1$ x_1$ + m_2$ x_2$}{m_1$ + m_2$}$$

Question 7

A uniform rod of length $$L$$ and mass $$M$$ has its center of mass located at:

Accepted Answer

$$\frac{L}{2}$$

Question 8

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

Accepted Answer

The colliding objects stick together after the collision.

Question 9

A 3.0 kg ball moving at $$3.0\ \mathrm{m/s} in $$the $$+x$$ direction collides with a stationary ball of equal mass. After the collision, both balls move off at $$45^\circ$$ above and below the $$x-$$axis. What is the speed of each ball after the collision?

Accepted Answer

$$2.12\ \mathrm{m/s}$$

Question 10

Which of the following best describes what happens to kinetic energy in an inelastic collision?

Accepted Answer

Some kinetic energy is converted into other forms of energy, such as heat or sound.

Question 11

For a continuous rod of length $$L$$ and mass $$M$$ with non-uniform density $$\lambda = Ax^2$, which integral gives the center of mass?

Accepted Answer

$$x_{cm} = \frac{1}{M} \$$int_0$$^L x \lambda dx$$

Question 12

Which equation relates the rate of change of momentum to force for a particle of mass $$m$$?

Accepted Answer

$$\frac{dp}{dt} = m \frac{dv}{dt} = ma$$

Question 13

In a ballistic pendulum experiment, why is the collision considered completely inelastic?

Accepted Answer

Because the projectile and block stick together after the collision.

Question 14

Which of the following is NOT a consequence of the conservation of momentum in an isolated system?

Accepted Answer

External forces can change the total momentum of the system.

Question 15

A system consists of two particles with masses $$m_1$$ and $$m_2$$ moving with velocities $$v_1$$ and $$v_2. $$What is the velocity of the center of mass?

Accepted Answer

$$v_{cm} = \frac{m_1$ v_1$ + m_2$ v_2$}{m_1$ + m_2$}$$

Question 16

Which of the following is a correct statement about the center of mass of a system?

Accepted Answer

It is the point where all external forces can be considered to act.

Question 17

In a real-world car crash, why is the collision typically considered inelastic?

Accepted Answer

Because some kinetic energy is converted into deformation, heat, and sound.

Question 18

If a force acts on a system of particles, how does it affect the center of mass?

Accepted Answer

The center of mass accelerates according to the net external force.

Momentum, Collisions, and Center of Mass – Study Notes

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