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 = 15.3256705#m/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#