# Rotational Question

Paymemoney

## Homework Statement

An astronaut on the surface of the Moon fires a cannon to launch an experiment package, which leaves the barrel moving horizontally. Assume that the free-fall acceleration on the Moon is one-sixth that on the Earth. Radius of moon = 1.74 * 10^6 m
a) What must be the muzzle speed of the probe so that it travels completely around the Moon and returns to its original location? Found out to be 1.68km/s
b) How long does this trip around the Moon take?

## Homework Equations

$$a=\omega^2r$$

$$v=\omega r$$

## The Attempt at a Solution

I tired to solve with constant acceleration formulas.
a=1.62m/s^2
vi=0
vf=1.68km/s => 1678.928m/s

vf=vi+at
16878.928=0+1.62t
t=10419.09136s

2)A crate of eggs is located in the middle of the flat bed of a pickup truck as the truck negotiates an unbanked curve in the road. The curve may be regarded as an arc of a circle of radius 35.0m. If the coefficient of static friction between crate and truck is 0.600, how fast can the truck be moving without the crate sliding?

I have tried to do the following:

i know the static friction: 0.600

i need to know $$\omega$$

which is $$\sqrt{9.8}{35}$$, $$\omega=0.529$$

find velocity

$$v=r\omega$$
v=0.529 * 35
v=18.52m/s

i know this is incorrect, someone tell me how i can approach this.

Last edited:

Mentor

## Homework Statement

An astronaut on the surface of the Moon fires a cannon to launch an experiment package, which leaves the barrel moving horizontally. Assume that the free-fall acceleration on the Moon is one-sixth that on the Earth. Radius of moon = 1.74 * 10^6 m
a) What must be the muzzle speed of the probe so that it travels completely around the Moon and returns to its original location? Found out to be 1.68km/s
b) How long does this trip around the Moon take?

## Homework Equations

$$a=\omega^2r$$

$$v=\omega r$$

## The Attempt at a Solution

I tired to solve with constant acceleration formulas.
a=1.62m/s^2
vi=0
vf=1.68km/s => 1678.928m/s

vf=vi+at
16878.928=0+1.62t
t=10419.09136s
This is a circular motion/orbit problem. Use Newton's 2nd law and the formula for centripetal acceleration.

Paymemoney
how can i find the time with the centripetal acceleration formula?

Mentor
how can i find the time with the centripetal acceleration formula?
OK. Looks like you solved for the speed (but didn't show your work). The speed is constant. What distance does it travel in going around once?

Paymemoney
do you mean $$\omega = 9.649 * 10^{4} rad/s$$?

Mentor
do you mean $$\omega = 9.649 * 10^{4} rad/s$$?
You could certainly use that if you like. But that should be 10-4!

I was thinking of distance = speed * time. You have the speed. And you should be able to calculate the distance, then solve for the time.

Paymemoney
How can i find the distance if i only have velocity, acceleration?

Mentor
How can i find the distance if i only have velocity, acceleration?
What path does it take? Hint: Make use of the moon's radius.

Paymemoney
would you find the diameter of the moon, which is 3480000?

Mentor
Answer this: What is the shape of the package's orbit around the moon?

Paymemoney
well the shape of a car....

Mentor
well the shape of a car....

It goes all the way around the moon in a big circle!

Paymemoney

Mentor
Do you understand what I mean now? How can you find the length of that path? (Remember that this is a question about circular motion.)

(You could also solve for the time using ω, which you've already calculated.)

Paymemoney
yes, i understand it took me awhile -_-.

So from the equation: $$\omega = \frac{\theta}{t}$$

derived from the linear $$v=\frac{x}{t}$$

where:

$$\theta = 2\pi$$ because it go around once.

$$\omega = 9.649 * 10^{-4}$$

$$t=\frac{2\pi}{9.649*10^{-4}}$$

t=6511.74765s

$$t=\frac{6511.74765}{3600}$$ turn into hours

t=1.81hrs however book's answer has a slight difference in 1.80hrs. Edit** i know why because of my rounding off.

Paymemoney
would someone answer my second question?

Last edited:
Mentor
yes, i understand it took me awhile -_-.

So from the equation: $$\omega = \frac{\theta}{t}$$

derived from the linear $$v=\frac{x}{t}$$
You used the first equation, but you could also have used the second one directly. When it goes around once, the package traces the circumference of a circle. So $x = 2\pi r$.

Mentor
2)A crate of eggs is located in the middle of the flat bed of a pickup truck as the truck negotiates an unbanked curve in the road. The curve may be regarded as an arc of a circle of radius 35.0m. If the coefficient of static friction between crate and truck is 0.600, how fast can the truck be moving without the crate sliding?

I have tried to do the following:

i know the static friction: 0.600

i need to know $$\omega$$

which is $$\sqrt{9.8}{35}$$, $$\omega=0.529$$

find velocity

$$v=r\omega$$
v=0.529 * 35
v=18.52m/s

i know this is incorrect, someone tell me how i can approach this.
How did you solve for ω?

Again, this is a circular motion problem that can be solved using Newton's 2nd law and what you know about centripetal acceleration.

What force acts on the eggs? What's the expression for its acceleration?

FYI: ac = ω²r = v²/r

Paymemoney
How did you solve for ω?

Again, this is a circular motion problem that can be solved using Newton's 2nd law and what you know about centripetal acceleration.

What force acts on the eggs? What's the expression for its acceleration?

FYI: ac = ω²r = v²/r

the mass and the centripetal force.

Don't i need to use the static friction?

Mentor
Don't i need to use the static friction?
Yes. Static friction is the only force available to provide the centripetal acceleration.

Paymemoney
So would i start by finding the fsmax by using the equation

coefficient of static friction = $$\frac{fsmax}{n}$$

Mentor
So would i start by finding the fsmax by using the equation

coefficient of static friction = $$\frac{fsmax}{n}$$
Right. The static friction will be at its maximum, so F = μN. (What's N?)

Now apply Newton's 2nd law.

Paymemoney
the normal

Paymemoney
how do i find the N???

Mentor
how do i find the N???
To find an expression for the normal force, analyze the vertical force components. What's the net vertical force?

Paymemoney
would it be F=N -mg

Mentor
would it be F=N -mg
Right. And what must F equal in this case?

Paymemoney
the static friction force

Mentor
the static friction force
No. We're talking about vertical forces here. What's the net vertical force? (Is there any vertical acceleration?)

The purpose is just so you can find the normal force.

Paymemoney
wouldn't that be mg???

Mentor
wouldn't that be mg???
Sure. That's all you need.

Paymemoney
but how do i know the mass??

Homework Helper
You don't need it. Use call the mass "m" and you'll see it cancels out.

Paymemoney
so if i use the F= N - mg

mg = N - mg

9.8 = N -9.8

N= 19.6N

Mentor
but how do i know the mass??
You don't and it doesn't matter. Just use N = mg.

so if i use the F= N - mg

mg = N - mg

9.8 = N -9.8

N= 19.6N
No. The vertical forces add to zero, so 0 = N - mg, thus N = mg.

Now go back to analyzing the friction force. Now that you have an expression for N, how would you express the maximum static friction? Plug that into Newton's 2nd law.