# Conservation of Linear Momentum and Impulse

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1)Impulse and momentum change/varying force. A 10-kg asteroid is traveling through space at 2 m/s toward a spaceship. To avoid a collision, an astronaut, with the help of a backpack rocket, exerts a force of 20 N on the asteroid in the opposite direction for 5 s. (a) find the asteroid's final speed?

(b) How long should she have pushed in order to just stop the asteroid?

2) Conservation of linear momentum. A toy cannon having a mass of 4.0 kg sits on a frictionless level surface. It fires a 250-g projectile horizontally and immediately recoils westward at 1.5 m/s. (a) Find the change in momentum of the cannon? (b) Determine the change in momentum of the projectile? (c) What was the muzzle velocity of the projectile?

3)A fireworks rocket rises straight up to its maximum altitude of 50.0 m. At that point it explodes into two equal-mass pieces; one heads straight down at 20.0 m/s, the other travels straight upward. What is the maximum altitude attained by the second upwardly-moving fragment?

4) Collisions> In an arrangement for measuring the muzzle velocity of a rifle or pistol, the bullet is fired up at a wooden mass, into which it imbeds. The wood is blasted straight up into the air to a measured height h. Assuming negligible losses to friction, write an expression for the velocity in terms of the known masses and height. If a 100-grain (6.48-g) 25-06 Remington rifle bullet is fired into a 5.00-kg block that then rises 4.0 cm into the air, what was the muzzle speed of that bullet?

5)A soft clay block is suspended so as to form a so-called ballistic pendulum. A bullet is fired point blank into the block, imbedding itself therin and raising the latter to a height h. Write an expression for the muzzle speed of the bullet in terms of g, h, and the masses. Note that although the friction on the pendulum is negligible, clay-bullet friction losses are not, and mechanical energy is not conserved in the collision.

6)Referring to the above problem, Derive an expression for the percentage of kinetic energy converted into internal energy during the bullet-clay impact.

#### Solution Preview

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* denotes multiplication

P= momentum

m, M Mass

g= Acceleration due to gravity= 10 m/s2

u,v= velocity

F*t= Impulse

a acceleration

h,x= distance

1)Impulse and momentum change/varying force. A 10-kg asteroid is traveling through space at 2 m/s toward a spaceship. To avoid a collision, an astronaut, with the help of a backpack rocket, exerts a force of 20 N on the asteroid in the opposite direction for 5 s. (a) find the asteroid's final speed?

P= m v

Initial momentum of the asteroid= 20 * 2=40 kg-m/sec direction

Final momentum = 20 V direction

F*t= change in momentum

20 V-(-40)=F * t

0r 20 V+ 40 =20*t=20*5=100

or 20 V=100-40=60

or V=60/20= 3 m/s

(b) How long should she have pushed in order to just stop the asteroid?

20 V-(-40)=F * t

If V=0

40= F*t

0r 40=20*t

or t= 2 s

2) Conservation of linear momentum. A toy cannon having a mass of 4.0 kg sits on a frictionless level surface. It fires a 250-g projectile horizontally and immediately recoils westward at 1.5 m/s. (a) Find the ...

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Answers questions on Impulse, momentum, conservation of linear momentum