# Impulse and Momentum

by Gary Gende and Owen "O-Dog" Zahorcak, January 1998

## 1.

What is the momentum of a 23 Kg cannon shell going 530 m/s?

`23 * 530 = 12190 kgm/s....p = mV`
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## 2.

`What speed must a 5 Kg object go to have 24 Kgm/s of momentum?`
```24 = 5 * V....p = mV

V = 24/5 or 4.8 m/s```
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## 3.

`A bullet going 640 m/s has 42 Kgm/s of momentum. What is its mass?`
```42 = 640 * m....p = mV

m = 42/640 or .066 kg```
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## 4.

`What is the impulse imparted by a rocket that exerts 4.8 N for 1.63 seconds?`
`4.8 * 1.63 = 7.824 or 7.8 Ns..../\p = Ft`
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## 5.

`For what time must you exert a force of 45 N to get an impulse of 16 Ns?`
```16 = 45 * t..../\p = Ft

t = 16/45 or .36 s```
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## 6.

`What force exerted over 6 seconds gives you an impulse of 64 Ns?`
```64 = 6 * N..../\p = Ft

N = 64/6 or 10.7 N```
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## 7.

```What is the change in velocity of a .35 Kg air track cart if you exert a force of 1.2 N on

it for 3 seconds?```
```.35 * /\V = 1.2 * 3....F = m(/\V/t)

/\V = 3.6/.35 or 10.3 m/s```
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## 8.

```A rocket engine exerts a force of 500 N on a space probe (in outer space!) for 5 seconds.

The probe speeds up from rest to a speed of 21 m/s.  What is its mass?```
```21 * m = 500 * 5....F = m(/\V/t)

m = 2500/21 or 119 kg```
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```

## 9.

`What force exerted for .12 seconds will make a .54 Kg baseball change its velocity 80 m/s.`
```N * .12 = .54 * 80....F = m(/\V/t)

N = 43.2/.12 or 360 N```
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## 10.

`How long must the space probe in question 8 fire its engine to change its velocity by 3 m/s?`
```500 * t = 119 * 3....F = m(/\V/t)

t = 357/500 or .71 s```
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## 11.

```A rocket engine burns 5 Kg of fuel per second. The exhaust gas velocity is 608 m/s. What is

the thrust of the engine? What time must it burn to impart an impulse of 12,000 Ns? How much

fuel will it burn to do this?```
```a.  5 * 608 = 3040 N....F = m(/\V/t)

b.  12000 = 3040 * t..../\p = Ft

t = 12000/3040 or 3.95 s

c.  3.95 * 5 = 19.7 s....fuel burned per second multiplied by the number of seconds it is

burning```
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```

## 12.

`An 11 Ns rocket engine has 12.5 g of fuel. What is the exhaust velocity?`
```11 = .0125 * V....F = m(/\V/t)

V = 11/.0125 or 880 m/s```
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## 13.

```A rocket generates 25 N of thrust, and the exhaust gas velocity is 1250 m/s. At what rate

does it consume fuel in Kg/s? How much fuel has it burned in 5 minutes?```
```a.  25 = 1250 * V....F = m(/\V/t)

kg/s = 25/1250 or .02 Kg/s

b.  .02 * 5 min * 60 sec/min = 6 kg....fuel burned per second multiplied by the number of

seconds it is burning```
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```

## 14.

```A small rocket probe in deep space has a mass of 68.5 Kg, 45.2 Kg of which is fuel. Its engine
consumes .250 Kg of fuel per second, and it has an exhaust velocity of 720 m/s. For how much
time will the engine burn? What is the initial acceleration of the rocket engine? What is the
acceleration just before it runs out of fuel?```
```a.  rate = mass/time, time = mass/rate = (45.2 kg)/(.25 kg/s) = 180.8 s

b.  Dp = FDt = mDv, F(1.0 s) = (.25 kg)(720 m/s), F = 180 N
Initial mass = 68.5 kg
<180 N> = (68.5 kg)a, a  = 2.63 m/s/s
c.  F = (720 * .25) = 180....F = m(/\V/t)
Final Mass = 23.3 kg
<180 N> = (23.3 kg)a, a  = 7.73 m/s/s```
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```

## 15.

```A rocket takes off from the surface of the Earth straight up.  The total mass of the
rocket is 5000 Kg, 3500 Kg of which is fuel. The exhaust gas velocity is 3000 m/s ,
and the rocket consumes 25 Kg of fuel per second. For how long do the engines burn?
What is the thrust of the engine? What are the initial and final accelerations of the
rocket? (don't forget gravity) ```
```a.  rate = mass/time, time = mass/rate = (3500 kg)/(25 s) = 140 s

b.  Dp = FDt = mDv,  F(1.0 s) = (25 kg)(3000 m/s), F = 75,000 N

c1. Initial acceleration:
Mass = 5000 kg (no fuel has been burned)
Weight = (5000 kg)(9.8 N/kg) = 49,000 N
<75,000 N - 49,000 N> = (5000 kg)a, a = 5.2 m/s/s

c2. Final acceleration:
mass = 5000 kg - 3500 kg = 1500 kg  (Fuel is gone)
weight = (1500 kg)(9.8 N/kg) = 14,700 N
<75,000 N - 14,700 N> = (1500 kg)a, a = 40.2 m/s/s