The kinetic energy EK of a moving object varies jointly with its mass m and the square of its velocity v. The constant of proportionality is ½. A particle with mass m and velocity v has EK = 4 J. What is the mass of another particle with velocity 2v and EK = 4 J? Question options:

Question

0.5m (0.5M INCORRECT)
2m
0.25m

Answer 1

Using the information given, we can write the equation for the kinetic energy (EK) as:

EK = 1/2 * m * v^2

We are given that EK = 4 J for the first particle. Let's substitute this into the equation:

4 = 1/2 * m * v^2

Now, we need to find the mass of another particle with a velocity of 2v and EK = 4 J. Let's denote the mass of the second particle as M. We can write the equation for its kinetic energy as:

EK = 1/2 * M * (2v)^2

Simplifying this equation:

EK = 1/2 * M * 4v^2
EK = 2M * v^2

We are given that EK = 4 J for the second particle. Let's substitute this into the equation:

4 = 2M * v^2

Now, we can compare the equations for the two particles:

1/2 * m * v^2 = 4
2M * v^2 = 4

Simplifying both equations:

m * v^2 = 8
M * v^2 = 2

Now, let's compare the equations:

m * v^2 = 8
M * v^2 = 2

We can divide the two equations to find the relationship between M and m:

(M * v^2) / (m * v^2) = 2 / 8
M / m = 2 / 8
M / m = 1 / 4

So, the mass of the second particle (M) is 1/4 of the mass of the first particle (m):

M = 1/4 * m

Therefore, the mass of the second particle with velocity 2v and EK = 4 J is 1/4 of the mass of the first particle.