A frog is jumping around its pond. At some time t , the frog is in mid-jump and has a kinetic energy of 1 J and a momentum of magnitude 0.5 kg⋅m/s . What is the mass of the frog in kg?
0.5 m V^2 = 0.5*(1/m)*(mV)^2
Kinetic energy = ( 0.5)*(1/m)*(momentum)^2
1 = (1/m)*0.125
m = 0.125 kg
To find the mass of the frog, we can use the equations for kinetic energy and momentum.
The equation for kinetic energy is:
Kinetic Energy (KE) = 1/2 * mass * velocity^2
And the equation for momentum is:
Momentum (p) = mass * velocity
We are given that the kinetic energy of the frog is 1 J and the magnitude of momentum is 0.5 kg⋅m/s.
First, let's find the velocity of the frog using the momentum equation:
0.5 kg⋅m/s = mass * velocity
Now, let's rearrange the equation to solve for the velocity:
velocity = 0.5 kg⋅m/s / mass
We know that kinetic energy is given by the equation:
1 J = 1/2 * mass * velocity^2
Substituting the value of velocity, we get:
1 J = 1/2 * mass * (0.5 kg⋅m/s / mass)^2
Now, simplify the equation:
1 J = 1/2 * mass * (0.5)^2 kg^2⋅m^2/s^2
1 J = 1/2 * 0.25 kg^2⋅m^2/s^2
Simplifying further, we get:
1 J = 0.125 kg^2⋅m^2/s^2
Now, we can solve for mass by isolating it in the equation:
mass = √ (2 * 1 J / 0.125 kg^2⋅m^2/s^2)
mass = √ (16 kg)
mass = 4 kg
Therefore, the mass of the frog is 4 kg.