a) What is the ratio of the momentum of a 3kg mass moving at 3 m/s to that of a 2 kg mass moving at 4 m/s?
b) What is the ratio of the respective kinetic energies?
Help ASAP please!! Step by step to get the answers
(3*3)/(2*4) = ratio of momenta
(3*9)/(2*16) = ratio of energies
Where did 9 and 16 come from??
a) To find the ratio of the momentum, we'll use the formula for momentum:
Momentum = mass * velocity
First, let's calculate the momentum for the 3kg mass moving at 3 m/s:
Momentum_1 = mass_1 * velocity_1
Momentum_1 = 3 kg * 3 m/s
Momentum_1 = 9 kg·m/s
Now, let's calculate the momentum for the 2kg mass moving at 4 m/s:
Momentum_2 = mass_2 * velocity_2
Momentum_2 = 2 kg * 4 m/s
Momentum_2 = 8 kg·m/s
The ratio of momentum_1 to momentum_2 is:
Momentum ratio = Momentum_1 / Momentum_2
Momentum ratio = 9 kg·m/s / 8 kg·m/s
Momentum ratio = 1.125
Therefore, the ratio of the momentum of the 3kg mass moving at 3 m/s to that of the 2kg mass moving at 4 m/s is 1.125.
b) To find the ratio of the respective kinetic energies, we'll use the formula for kinetic energy:
Kinetic Energy = (1/2) * mass * velocity^2
First, let's calculate the kinetic energy for the 3kg mass moving at 3 m/s:
Kinetic Energy_1 = (1/2) * mass_1 * velocity_1^2
Kinetic Energy_1 = (1/2) * 3 kg * (3 m/s)^2
Kinetic Energy_1 = (1/2) * 3 kg * 9 m^2/s^2
Kinetic Energy_1 = (1/2) * 27 kg·m^2/s^2
Kinetic Energy_1 = 13.5 kg·m^2/s^2
Now, let's calculate the kinetic energy for the 2kg mass moving at 4 m/s:
Kinetic Energy_2 = (1/2) * mass_2 * velocity_2^2
Kinetic Energy_2 = (1/2) * 2 kg * (4 m/s)^2
Kinetic Energy_2 = (1/2) * 2 kg * 16 m^2/s^2
Kinetic Energy_2 = (1/2) * 32 kg·m^2/s^2
Kinetic Energy_2 = 16 kg·m^2/s^2
The ratio of kinetic energy_1 to kinetic energy_2 is:
Kinetic Energy ratio = Kinetic Energy_1 / Kinetic Energy_2
Kinetic Energy ratio = 13.5 kg·m^2/s^2 / 16 kg·m^2/s^2
Kinetic Energy ratio = 0.84375
Therefore, the ratio of the respective kinetic energies is approximately 0.84375.
a) To find the ratio of the momentum of the two masses, you need to calculate the momentum of each mass separately and then divide one by the other.
The formula to calculate momentum is given by:
Momentum = mass * velocity
For the 3kg mass moving at 3 m/s,
Momentum1 = 3 kg * 3 m/s = 9 kg m/s
For the 2 kg mass moving at 4 m/s,
Momentum2 = 2 kg * 4 m/s = 8 kg m/s
To find the ratio, divide the momentum of the first mass by the momentum of the second mass:
Ratio = Momentum1 / Momentum2
Ratio = 9 kg m/s / 8 kg m/s
Ratio = 1.125
Therefore, the ratio of the momentum of the 3kg mass to that of the 2 kg mass is 1.125.
b) To find the ratio of the respective kinetic energies, you need to calculate the kinetic energy of each mass separately and then divide them.
The formula to calculate kinetic energy is given by:
Kinetic Energy = 0.5 * mass * velocity^2
For the 3kg mass moving at 3 m/s,
Kinetic Energy1 = 0.5 * 3 kg * (3 m/s)^2 = 13.5 J
For the 2 kg mass moving at 4 m/s,
Kinetic Energy2 = 0.5 * 2 kg * (4 m/s)^2 = 16 J
To find the ratio, divide the kinetic energy of the first mass by the kinetic energy of the second mass:
Ratio = Kinetic Energy1 / Kinetic Energy2
Ratio = 13.5 J / 16 J
Ratio = 0.84375
Therefore, the ratio of the respective kinetic energies is approximately 0.84375.
These are the step-by-step calculations to find the answers.