How to Calculate Impulse in Various Scenarios

[jigoku_snow]

Homework Statement

1) a girl applies a steady force to a stationary trolley which has a mass of 18 kg for 6 s. she moves it 36 m in this time. determine the impulse which she produced.

2) a satellite of mass 240kg moving in a free space at velocity of 600 m /s is struck by an unknown object which causes it to be deflected onto a new path at right angles to its original direction of motion in 0.5 s. find the impulse which acted upon the satellite if it continued to move at 600 m/s after deflection.

3) the impulse of a force causes a stationary mass to move at 4 m/s in the direction of the force. the same impulse causes a 2nd body also at rest to move at 6 m/s in the direction of the force. what velocity would be produced if the impulse were to act on the combined masses initially at rest?

4) a block of mass 100kg is being moved steadily by pulling on a rope attached to the block making an angle of 30 degree with the horizontal.if the tension in the rope is 120 N,what are the force of friction and the coefficient of friction?

Homework Equations

1) 2) 3) F=ma, Ft=m(v-u)
4) T- (mg sin theta + frictional force) = ma

The Attempt at a Solution

1) v of trolley= 36/6= 6 m/s
18 x 6 = 108 Ns ( answer given = 220 Ns)

2) p b4 collision =240 x 600 = 144000 kg m/s
p after collision = 240 x 600 = 144000 kg m/s
change in momentum = impulse = 0 ( answer 2.04 x 10^6)

3) impulse on 1st body= m(v-u) = m(4-0) = 4m
impulse on 2nd body = m(6-0)= 6m [ans : 2.4 m/s]

4) a=0, 120 = 500+ friction
friction = 380
coefficient of friction = 380/ mg cos 30= 0.438 [ answer 0.113]

 

[Doc Al]

1) v of trolley= 36/6= 6 m/s
18 x 6 = 108 Ns ( answer given = 220 Ns)

The velocity is not constant (but the acceleration is). What's the final velocity?

2) p b4 collision =240 x 600 = 144000 kg m/s
p after collision = 240 x 600 = 144000 kg m/s
change in momentum = impulse = 0 ( answer 2.04 x 10^6)

Momentum is a vector. To find the change in momentum, you must subtract the two momentum vectors, not just their magnitudes.

3) impulse on 1st body= m(v-u) = m(4-0) = 4m
impulse on 2nd body = m(6-0)= 6m [ans : 2.4 m/s]

The impulse on each body is the same. What's different is their mass. Figure out the total mass (in terms of the impulse), then use it to find the speed.

4) a=0, 120 = 500+ friction
friction = 380
coefficient of friction = 380/ mg cos 30= 0.438 [ answer 0.113]

What's the component of the rope tension pulling the block forward? What's the normal force on the block?

 

[jigoku_snow]

The velocity is not constant (but the acceleration is). What's the final velocity?
i don't get what 'the velocity is not constant but the acceleration is' means. isn't to find a variable (a or v) from the formula a=(v-u)/t ,we will get the same answer ?
i'm stuck here :
a=(v-u)/t, v=s/t=6.
a=1 m/s^2.
u=0 (at rest) , 1=v/6, final v= 6 m/s

Momentum is a vector. To find the change in momentum, you must subtract the two momentum vectors, not just their magnitudes.
is it a need to find the displacement traveled by the satellite after collision first of all? "to be deflected onto a new path at right angles to its original direction of motion" . we will have a resultant velocity. SQRT (600)^2 + (-600)^2 = 849 . is that the final velocity? The impulse on each body is the same. What's different is their mass. Figure out the total mass (in terms of the impulse), then use it to find the speed.
impulse acted on the first body = 4m.
impulse on the 2nd body = 6m. is that means the mass of these 2 bodies differ by 2? i have an unknown which is m. how to identify the value of m?

What's the component of the rope tension pulling the block forward? What's the normal force on the block?

component of the rope tension= mg sin theta = 500N . given the tension of the rope is 120 N. is that means the total pulling force = 120 + 500= 620 ?
'moved steadily' which means a=0 ? then pulling force = sliding? if yes then mg sin theta + friction force = 620. friction force = 120 N. coefficient of friction = 120/ mg cos theta.

 

[Doc Al]

component of the rope tension= mg sin theta = 500N . given the tension of the rope is 120 N. is that means the total pulling force = 120 + 500= 620 ?

The rope tension is only 120 N. So what's the horizontal component of that force?

'moved steadily' which means a=0 ?

Yes. So what's the net force in any direction?

 

[jigoku_snow]

The rope tension is only 120 N. So what's the horizontal component of that force?
F cos theta?

Yes. So what's the net force in any direction?

net force =0

 

[Doc Al]

Yes. Keep going. (Careful with quotes.)

 

[jigoku_snow]

The velocity is not constant (but the acceleration is). What's the final velocity?

i don't get what 'the velocity is not constant but the acceleration is' means. isn't to find a variable (a or v) from the formula a=(v-u)/t ,we will get the same answer ?
i'm stuck here :
a=(v-u)/t, v=s/t=6.
a=1 m/s^2.
u=0 (at rest) , 1=v/6, final v= 6 m/s

Momentum is a vector. To find the change in momentum, you must subtract the two momentum vectors, not just their magnitudes.

is it a need to find the displacement traveled by the satellite after collision first of all? "to be deflected onto a new path at right angles to its original direction of motion" . we will have a resultant velocity. SQRT (600)^2 + (-600)^2 = 849 . is that the final velocity?

The impulse on each body is the same. What's different is their mass. Figure out the total mass (in terms of the impulse), then use it to find the speed.

impulse acted on the first body = 4m.
impulse on the 2nd body = 6m. is that means the mass of these 2 bodies differ by 2? i have an unknown which is m. how to identify the value of m?

* hope this time i quote them correctly ;)

 

[Doc Al]

i don't get what 'the velocity is not constant but the acceleration is' means. isn't to find a variable (a or v) from the formula a=(v-u)/t ,we will get the same answer ?
i'm stuck here :
a=(v-u)/t, v=s/t=6.
a=1 m/s^2.
u=0 (at rest) , 1=v/6, final v= 6 m/s

v = s/t gives the average velocity, not the final velocity. How are they related?

is it a need to find the displacement traveled by the satellite after collision first of all? "to be deflected onto a new path at right angles to its original direction of motion" . we will have a resultant velocity. SQRT (600)^2 + (-600)^2 = 849 . is that the final velocity?

You are subtracting vectors, not finding displacement. You are finding the change in velocity, not the final velocity. (The final speed is given.)

impulse acted on the first body = 4m.
impulse on the 2nd body = 6m. is that means the mass of these 2 bodies differ by 2? i have an unknown which is m. how to identify the value of m?

Call the impulse I.
For the first mass alone: I = m₁4
For the second mass alone: I = m₂6
What's the total mass?

* hope this time i quote them correctly ;)

Not quite, but I fixed it.

 

[jigoku_snow]

v = s/t gives the average velocity, not the final velocity. How are they related?

okay. now i know that the final velocity is twice the average velocity. i thought the average v will be the final v (OMG)



You are subtracting vectors, not finding displacement. You are finding the change in velocity, not the final velocity. (The final speed is given.)

arent to get the change in v , first we need to have final v? ( final v - initial v= change in v)



Call the impulse I.
For the first mass alone: I = m₁4
For the second mass alone: I = m₂6
What's the total mass?

m1 + m2 = total mass.
m1/m2=6/4.
is that means that m1=6?

Not quite, but I fixed it.

lol

 

[jigoku_snow]

v = s/t gives the average velocity, not the final velocity. How are they related?

okay. now i know that the final velocity is twice the average velocity. i thought the average v will be the final v (OMG)

You are subtracting vectors, not finding displacement. You are finding the change in velocity, not the final velocity. (The final speed is given.)

arent to get the change in v , first we need to have final v? ( final v - initial v= change in v)

Call the impulse I.
For the first mass alone: I = m14
For the second mass alone: I = m26
What's the total mass?

m1 + m2 = total mass.
m1/m2=6/4.
is that means that m1=6?

Not quite, but I fixed it.

lol... at last i know how ;)

 

[Doc Al]

okay. now i know that the final velocity is twice the average velocity. i thought the average v will be the final v (OMG)

Good.

arent to get the change in v , first we need to have final v? ( final v - initial v= change in v)

You are given the final v. If initial v = 600 x, then final v is 600 y (for example).

m1 + m2 = total mass.

OK

m1/m2=6/4.
is that means that m1=6?

Here's what I meant:
If I = m1*4, then m1 = I/4. Now apply the same impulse to the total mass to get the velocity. (You don't have enough information to solve for the actual masses, but you don't need that anyway.)

 

[jigoku_snow]

all right . i got it ;) thanks .