What is the speed and mass of the object?

The recoil of a projectile launcher finds that the linear momentum of an ejected object is 26.1 kg m/s, and the target is equipped with an energy detector that determines that the object has a kinetic energy of 200 J.

2 Answers
Feb 28, 2018

speed = 15.3256705m/s
mass = 1.703025 kg

Explanation:

From the Kinetic Energy and momentum formulas
K.E=1/2*m*v^2

and momentum
P=mv

we can get
K.E = 1/2*P*v

and we can get
K.E = P^2/(2m)
because v=P/m

so

for the speed, I will use K.E = 1/2*P*v

200J = 1/2*26.1kg m/s*v
V = (200J)/((26.1kgm/s)*1/2) = 15.3256705 m/s

for the mass, I will use K.E = P^2/(2m)
m = P^2/(2K.E)
m = (26.1^2kgm/s)/(2*200J) = 1.703025kg

Feb 28, 2018

m = 1.70 kg

v = 15.32 m/s away from the launcher.

By solving a system of equations.

Explanation:

We know the following based on the equations for momentum and kinetic energy.

m*v = 26.1 (kg m)/s (this is equation1)

1/2 m*v^2 = 200J (this is equation2)

To solve the above system of equations, we need to isolate a variable. Let us first isolate mass to solve for velocity.

m=26.1/v (this is equation1)

m=400/v^2 (this is equation2)

And because mass is equal we can combine the equations to solve for v.

26.1/v = 400/v^2

v = 400/26.1

v = 15.32 m/s away from the launcher.

Finally, we can solve for mass by plugging our velocity back in to the momentum equation You could also find it other ways too.

p = m * v

26.1 = m * 15.32

m = 1.70 kg