# Simple and basic momentum and work done Qs

• nonthesecond
In summary, Mr Green stepped off a boat of mass 35 kg at a speed of 3m/s. To find the speed of the boat in the opposite direction, we can use the conservation of momentum for the total system. The initial momentum of the system is 0, and after the man steps off, his momentum will be equal and opposite to that of the boat. Using the formula p=m*v, we can calculate the momentum of Mr Green and use this value as the momentum for the boat. Rearranging the formula for velocity, we get the speed of the boat to be 6.9 m/s. Therefore, the boat moved at a speed of 6.9 m/s in the opposite direction.
nonthesecond
Mr Green, mass 80 kg, stepped off a boat of mass 35 kg at a speed of 3m/s. how fast did the boat move in the opposite direction?

As this sounds like a homework problems I'll just give you a few hints abut the problem.

Conservation of momentum for the total system states that the momentum before and after must be equal as there are no external forces acting upon the system.

So before he steps off as I'm assuming the boat is at rest, the total momentum of the system will be 0.

So after the man steps off the boat his momentum will be equal and opposite to that of the boat as the 2 momentums will cancel out to be zero.

rollcast said:
As this sounds like a homework problems I'll just give you a few hints abut the problem.

Conservation of momentum for the total system states that the momentum before and after must be equal as there are no external forces acting upon the system.

So before he steps off as I'm assuming the boat is at rest, the total momentum of the system will be 0.

So after the man steps off the boat his momentum will be equal and opposite to that of the boat as the 2 momentums will cancel out to be zero.

thanks which formulae do i use?

m = mass x v

or

mom before = mom after

?

You can use either but probably working out the momentum of the man using p = m * v, then use that value of p to work out the momentum of the boat, v = m / p. If you were working out the velocity of the boat afterwards you would need to make momentum negative but as it only asks for the speed you can keep momentum positive.

rollcast said:
You can use either but probably working out the momentum of the man using p = m * v, then use that value of p to work out the momentum of the boat, v = m / p. If you were working out the velocity of the boat afterwards you would need to make momentum negative but as it only asks for the speed you can keep momentum positive.

is this correct?

80 x 3 = 240

80/240 = 0.3 (which is the velocity) so it's 0.3m/s^2

rollcast said:
You can use either but probably working out the momentum of the man using p = m * v, then use that value of p to work out the momentum of the boat, v = m / p. If you were working out the velocity of the boat afterwards you would need to make momentum negative but as it only asks for the speed you can keep momentum positive.

nonthesecond said:
is this correct?

80 x 3 = 240

80/240 = 0.3 (which is the velocity) so it's 0.3m/s^2

Sorry I made a mistake rearranging the formula for velocity.

It should be v=p/m

Your calculation for the momentum is correct and you should get the right answer if you use the right formula for the velocity.

rollcast said:
Sorry I made a mistake rearranging the formula for velocity.

It should be v=p/m

Your calculation for the momentum is correct and you should get the right answer if you use the right formula for the velocity.

how can it be 3m/s^2 because that ids already given in the question.

i think i remeber my teacher saying that it's: 80 + 35= 115
115 x 3 = 375
375/35 = 1.3...m/s

is that correct?

nonthesecond said:
how can it be 3m/s^2 because that ids already given in the question.

i think i remeber my teacher saying that it's: 80 + 35= 115
115 x 3 = 375
375/35 = 1.3...m/s

is that correct?

Thats how you would calculate the initial momentum for the system as the 2 masses are together and have the same velocity.

Initial momentum for the system = m * v = (80 + 35) * 0Then you need to treat the 2 masses separate for the after stage as the 2 masses are not together anymore and will be moving in opposite directions (Newtons 3rd Law)

rollcast said:
Thats how you would calculate the initial momentum for the system as the 2 masses are together and have the same velocity.

Initial momentum for the system = m * v = (80 + 35) * 0

Then you need to treat the 2 masses separate for the after stage as the 2 masses are not together anymore and will be moving in opposite directions (Newtons 3rd Law)

ok thanks so what would i have to do to find how fast the boat moved in the opposite direction?

nonthesecond said:
ok thanks so what would i have to do to find how fast the boat moved in the opposite direction?

Work out the momentum for Mr Green.

p = m * v

Then use this value as the momentum for the boat (You can ignore the fact it should be opposite as we are only working out speed not velocity) Rearrange the momentum formula to work out velocity (or speed in this case).

p = m * v
v = p / m

rollcast said:
Work out the momentum for Mr Green.

p = m * v

Then use this value as the momentum for the boat (You can ignore the fact it should be opposite as we are only working out speed not velocity) Rearrange the momentum formula to work out velocity (or speed in this case).

p = m * v
v = p / m

3 m/s is it squared but how can that be the answer when it's already written in the question?

nonthesecond said:
3 m/s is it squared but how can that be the answer when it's already written in the question?

For the second step you need to use the mass of the boat.

rollcast said:
For the second step you need to use the mass of the boat.

so it's 240/35 ? = 6.9m/s is that the final answer and it's not squared?

rollcast said:
For the second step you need to use the mass of the boat.

did i get the question right?

## What is momentum?

Momentum is a measure of an object's motion, defined as the product of its mass and velocity. It is a vector quantity, meaning it has both magnitude and direction.

## How is momentum related to force?

According to Newton's Second Law of Motion, force is equal to the rate of change of an object's momentum. This means that the greater the force applied to an object, the greater its change in momentum will be.

## What is work done?

Work done is the measure of energy transfer that occurs when a force is applied to an object and causes it to move in the direction of the force. It is calculated by multiplying the force applied by the distance the object moves.

## What is the relationship between work done and energy?

Work done and energy are closely related, as work done is the transfer of energy from one object to another. The amount of work done is equal to the change in an object's energy.

## How is work done calculated?

Work done is calculated by multiplying the magnitude of the force applied by the distance the object moves in the direction of the force. In mathematical terms, it is represented by the equation W = Fd, where W is work done, F is the applied force, and d is the distance moved.

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