Lesson test: Centre of mass and rockets

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Centre of mass and rockets

1.[2p]
Two particles, 3.0 kg at $x = 0$ and 5.0 kg at $x = 2.4$ m, lie on a line. Where is the centre of mass, in metres from the origin?

CorrectNot quite: 1.5

2.[3p]
A shell fired on a parabolic path explodes into many fragments in mid air. What does the centre of mass of the fragments do?

It carries on along the original parabola until the first fragment lands

Correct

It stops, because the explosion destroys the momentum

The answer is: It carries on along the original parabola until the first fragment lands

It follows the largest fragment

The answer is: It carries on along the original parabola until the first fragment lands

It falls vertically from the point of the explosion

The answer is: It carries on along the original parabola until the first fragment lands

3.[1p]
The centre of mass of a body must lie inside the material of the body.

True

The answer is: False

False

Correct

4.[2p]
Why do the internal forces of a system drop out of $\sum {\vec{F}}_{ext} = M {\vec{A}}_{cm}$ ?

They occur in equal and opposite third law pairs, so they cancel in the total

Correct

They are always much smaller than the external forces

The answer is: They occur in equal and opposite third law pairs, so they cancel in the total

They do no work

The answer is: They occur in equal and opposite third law pairs, so they cancel in the total

They act only for very short times

The answer is: They occur in equal and opposite third law pairs, so they cancel in the total

5.[3p]
A rod of length 3.0 m has a density that increases in proportion to the distance from one end. How far from that end is its centre of mass, in metres?

CorrectNot quite: 2.0

6.[3p]
A rocket in free space has an exhaust speed of 3200 m s⁻¹ and burns until its mass has fallen to one quarter of its initial value. What velocity change does it gain, in metres per second?

CorrectNot quite: 4436

7.[3p]
Which of these follow from the rocket equation $Δ v = v_{e x} \ln (m_{0} / m)$ ?

Select all that apply

Each further increment of velocity costs exponentially more propellant

Correct

A higher exhaust speed raises the velocity change in direct proportion

Correct

Staging helps because emptied tanks need not be accelerated further

Correct

The velocity change grows in direct proportion to the mass of propellant burned

The answer is: Each further increment of velocity costs exponentially more propellant, A higher exhaust speed raises the velocity change in direct proportion, Staging helps because emptied tanks need not be accelerated further

8.[2p]
A 1200 kg car at 20 m s⁻¹ strikes a stationary 900 kg car. What is the speed of the centre of mass of the pair, in metres per second, both before and after the impact?

CorrectNot quite: 11.43

9.[3p]
Match each system to what its centre of mass does while the motion proceeds.

A wrench thrown spinning across a room
A skater pulling their arms in on frictionless ice
The Earth and Moon
Two colliding cars, during the impact

keeps moving at constant velocity
traces a smooth parabola
stays where it is
both orbit it, about 1700 km below the Earth's surface

Show the answer

A wrench thrown spinning across a room: traces a smooth parabola A skater pulling their arms in on frictionless ice: stays where it is The Earth and Moon: both orbit it, about 1700 km below the Earth's surface Two colliding cars, during the impact: keeps moving at constant velocity

1.[2p] Two particles, 3.0 kg at x=0 and 5.0 kg at x=2.4 m, lie on a line. Where is the centre of mass, in metres from the origin?

2.[3p] A shell fired on a parabolic path explodes into many fragments in mid air. What does the centre of mass of the fragments do?

3.[1p] The centre of mass of a body must lie inside the material of the body.

4.[2p] Why do the internal forces of a system drop out of ∑F→ext=MA→cm?

5.[3p] A rod of length 3.0 m has a density that increases in proportion to the distance from one end. How far from that end is its centre of mass, in metres?

6.[3p] A rocket in free space has an exhaust speed of 3200 m s⁻¹ and burns until its mass has fallen to one quarter of its initial value. What velocity change does it gain, in metres per second?

7.[3p] Which of these follow from the rocket equation Δv=vexln(m0/m)?

8.[2p] A 1200 kg car at 20 m s⁻¹ strikes a stationary 900 kg car. What is the speed of the centre of mass of the pair, in metres per second, both before and after the impact?

9.[3p] Match each system to what its centre of mass does while the motion proceeds.

1.[2p]
Two particles, 3.0 kg at $x = 0$ and 5.0 kg at $x = 2.4$ m, lie on a line. Where is the centre of mass, in metres from the origin?

2.[3p]
A shell fired on a parabolic path explodes into many fragments in mid air. What does the centre of mass of the fragments do?

3.[1p]
The centre of mass of a body must lie inside the material of the body.

4.[2p]
Why do the internal forces of a system drop out of $\sum {\vec{F}}_{ext} = M {\vec{A}}_{cm}$ ?

5.[3p]
A rod of length 3.0 m has a density that increases in proportion to the distance from one end. How far from that end is its centre of mass, in metres?

6.[3p]
A rocket in free space has an exhaust speed of 3200 m s⁻¹ and burns until its mass has fallen to one quarter of its initial value. What velocity change does it gain, in metres per second?

7.[3p]
Which of these follow from the rocket equation $Δ v = v_{e x} \ln (m_{0} / m)$ ?

8.[2p]
A 1200 kg car at 20 m s⁻¹ strikes a stationary 900 kg car. What is the speed of the centre of mass of the pair, in metres per second, both before and after the impact?

9.[3p]
Match each system to what its centre of mass does while the motion proceeds.