# Find velocity of gun and bullet on frictionless surface

• dani123
In summary: You might want to double-check the rounding on the momenta when you introduce the signs, but I think you are okay there as well.
dani123

## Homework Statement

A 30.0-kg gun is standing on a frictionless surface. The gun fires a 50.0-g bullet with a muzzle velocity of 310 m/s.

a) calculate the momenta of the bullet and the gun after the fun was fired.

b) calculate the kinetic energy of both the bullet and the gun just after firing.

## Homework Equations

Mgun*Vgun + Mbullet*Vbullet= 0 before firing

KE= 1/2 M*V^2

## The Attempt at a Solution

a) Before the firing, the system is at rest and therefore the momentum is ZERO. After firing, the total momentum is still ZERO. There is no net momentum gained or lost in this system. ----> Here, I am just looking if anyone could let me know if my reasoning is correct, and I was also wondering if there are anything else I should show in order to get full mark value?

b) After firing
0= (30 kg) Vgun+ (0.05kg) (310 m/s)
Vgun=[(0.05kg)(310m/s)]/(30kg) = 0.517m/s

Ke=1/2 M*V^2
for bullet after firing: KE= 1/2 (0.05kg)(310m/s)^2=2402.5J= 2.40x10^3J

for the gun after firing: KE=1/2 (30kg)(0.517m/s)^2=4.01J

Also here, I am just looking for someone to check that I did this problem correctly and also to check that the SIGNIFICANT FIGURES are correct. Thank you so much in advance.

b)

a) You are correct that the NET momentum is zero, but the bullet and the gun still have momentum. They are simply acting in opposite directions, so you can still calculate the momentum.

b) Your answers look right to me, although without any rounding at all, I calculated the KE for the gun to be 4.00J. Your sig figs are fine.

dani123 said:

## Homework Statement

A 30.0-kg gun is standing on a frictionless surface. The gun fires a 50.0-g bullet with a muzzle velocity of 310 m/s.

a) calculate the momenta of the bullet and the gun after the fun was fired.

b) calculate the kinetic energy of both the bullet and the gun just after firing.

## Homework Equations

Mgun*Vgun + Mbullet*Vbullet= 0 before firing

KE= 1/2 M*V^2

## The Attempt at a Solution

a) Before the firing, the system is at rest and therefore the momentum is ZERO. After firing, the total momentum is still ZERO. There is no net momentum gained or lost in this system. ----> Here, I am just looking if anyone could let me know if my reasoning is correct, and I was also wondering if there are anything else I should show in order to get full mark value?
Yes, that describes the situation adequately. You might at this point introduce the coordinate system you are going to use for the next part; is the bullet's direction of motion taken to be positive or negative?
b) After firing
0= (30 kg) Vgun+ (0.05kg) (310 m/s)
Vgun=[(0.05kg)(310m/s)]/(30kg) = 0.517m/s

Ke=1/2 M*V^2
for bullet after firing: KE= 1/2 (0.05kg)(310m/s)^2=2402.5J= 2.40x10^3J

for the gun after firing: KE=1/2 (30kg)(0.517m/s)^2=4.01J

Also here, I am just looking for someone to check that I did this problem correctly and also to check that the SIGNIFICANT FIGURES are correct. Thank you so much in advance.

The momenta are vector quantities, so you should indicate their directions by appropriate sign. Note that when you solved for Vgun using the momentum law you dropped the sign change that should have happened when one term was moved to the other side of the equation.

Your significant figures look okay.

## 1. What is the equation for finding the velocity of a gun and bullet on a frictionless surface?

The equation for finding the velocity of a gun and bullet on a frictionless surface is v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time taken.

## 2. How is friction taken into account when finding the velocity of a gun and bullet on a frictionless surface?

Since the surface is frictionless, friction does not play a role in determining the velocity of the gun and bullet. This means that the velocity calculated using the above equation would be the theoretical maximum velocity that the gun and bullet could reach.

## 3. Is the velocity of the gun and bullet on a frictionless surface affected by the weight of the bullet?

No, the weight of the bullet does not affect the velocity of the gun and bullet on a frictionless surface. The velocity is determined by the initial velocity and the acceleration, which are not affected by the weight of the bullet.

## 4. Can the velocity of the gun and bullet on a frictionless surface be greater than the initial velocity of the gun?

Yes, it is possible for the final velocity of the gun and bullet to be greater than the initial velocity of the gun on a frictionless surface. This is because the acceleration can increase the velocity of the bullet as it travels along the frictionless surface.

## 5. How does the angle of the gun affect the velocity of the bullet on a frictionless surface?

The angle of the gun does not have a direct effect on the velocity of the bullet on a frictionless surface. However, it can affect the initial velocity of the bullet and therefore impact the final velocity calculated using the equation v = u + at.

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