Two 2.0 g bullets are fired with speeds of 40.0 m/s and 80.0 m/s, respectively. What are their kinetic energies? Which bullet has more kinetic energy? What is the ratio of their kinetic energies?
A car has kinetic enery of 4.32* 10^5 when traveling at a speed of 23m/s. What is its masss?
I have around 12 problems of these and I am not very good with formulas. Please someone just do these and then I will be able to do the other ones, but please step by step.
I can help you with those problems step by step! Let's start with the first one.
To find the kinetic energy of an object, you use the formula:
Kinetic energy = 1/2 * mass * velocity^2
For the first bullet:
Mass = 2.0 g = 0.002 kg (since 1 g = 0.001 kg)
Velocity = 40.0 m/s
Substituting these values into the formula, we get:
Kinetic energy = 1/2 * 0.002 kg * (40.0 m/s)^2
Simplifying, we have:
Kinetic energy = 0.0004 kg * 1600 m^2/s^2
= 0.64 Joules
For the second bullet:
Mass = 2.0 g = 0.002 kg
Velocity = 80.0 m/s
Substituting these values into the formula, we get:
Kinetic energy = 1/2 * 0.002 kg * (80.0 m/s)^2
Simplifying, we have:
Kinetic energy = 0.0004 kg * 6400 m^2/s^2
= 2.56 Joules
Therefore, the kinetic energy of the first bullet is 0.64 Joules and the kinetic energy of the second bullet is 2.56 Joules.
To determine which bullet has more kinetic energy, you compare their values. In this case, the second bullet has a higher kinetic energy, as 2.56 Joules is greater than 0.64 Joules.
To find the ratio of their kinetic energies, you divide the kinetic energy of the second bullet by the kinetic energy of the first bullet:
Ratio = (Kinetic energy of the second bullet) / (Kinetic energy of the first bullet)
= 2.56 Joules / 0.64 Joules
= 4
Therefore, the ratio of their kinetic energies is 4:1.
Now let's move on to the second problem.
The formula for kinetic energy is the same as before:
Kinetic energy = 1/2 * mass * velocity^2
Given information:
Kinetic energy = 4.32 * 10^5 J
Velocity = 23 m/s
We can rearrange the formula to solve for mass:
Mass = (2 * Kinetic energy) / (velocity^2)
Substituting the values into the formula, we have:
Mass = (2 * 4.32 * 10^5 J) / (23 m/s)^2
Simplifying, we get:
Mass = (8.64 * 10^5 J) / (529 m^2/s^2)
= 1.635 kg
Therefore, the mass of the car is approximately 1.635 kg.
I hope this helps! If you have any more questions or need further clarification, please let me know.
Sure, let's solve these step by step:
1. Kinetic energy is given by the formula: K.E. = 1/2 * m * v^2, where m is the mass and v is the velocity.
For the first bullet:
Mass (m) = 2.0 g = 0.002 kg (converting grams to kilograms)
Velocity (v) = 40.0 m/s
Kinetic Energy (K.E.) bullet1 = 1/2 * 0.002 kg * (40.0 m/s)^2
= 0.04 J
For the second bullet:
Mass (m) = 2.0 g = 0.002 kg (converting grams to kilograms)
Velocity (v) = 80.0 m/s
Kinetic Energy (K.E.) bullet2 = 1/2 * 0.002 kg * (80.0 m/s)^2
= 0.32 J
Therefore, the kinetic energy of the first bullet is 0.04 J and the kinetic energy of the second bullet is 0.32 J.
To determine which bullet has more kinetic energy, we compare their values:
K.E. bullet1 = 0.04 J
K.E. bullet2 = 0.32 J
Clearly, the second bullet has more kinetic energy compared to the first bullet.
The ratio of their kinetic energies can be calculated by dividing the kinetic energy of the second bullet by the kinetic energy of the first bullet:
Ratio = K.E. bullet2 / K.E. bullet1
= 0.32 J / 0.04 J
= 8
2. The formula to calculate kinetic energy is the same as mentioned above: K.E. = 1/2 * m * v^2
Given:
Kinetic Energy (K.E.) = 4.32 * 10^5 J
Speed (v) = 23 m/s
We need to find the mass (m).
Rearranging the formula:
Mass (m) = K.E. / (1/2 * v^2)
= 4.32 * 10^5 J / (1/2 * (23 m/s)^2)
= 4.32 * 10^5 J / (1/2 * 529 m^2/s^2)
= 4.32 * 10^5 J / (1/2 * (23^2) m^2/s^2)
= 8.64 * 10^5 J / (23^2) kg
= 8.64 * 10^5 J / 529 kg
≈ 1635.503 kg
Therefore, the mass of the car is approximately 1635.503 kg.
Hope this helps! Let me know if you have any further questions.
the only formula you will need for both of these questions is :
E = 0.5mv^2
E = kinetic energy (J)
m = mass of object (kg)
v = velocity of object (m/s)
you should be able to go from here, just sub in the values.