1. How much work is necessary to accelerate a bullet having a mass of 5.0 g to a velocity of 1000. m/sec?

This was on a chemistry problem set of mine, and it seems like a very physics-oriented question [I have not taken physics.] Could someone point me in the right direction as to which formulas to use/when?

What is the difference in kinetic energies at the two speeds? That energy came from the work to accelerate.

To calculate the work necessary to accelerate the bullet, we need to use the formula for work, which is defined as the product of force and displacement.

However, in this particular case, we don't have the force directly. Instead, we need to use the concept of kinetic energy. The kinetic energy of an object is given by the formula KE = (1/2)mv^2, where m is the mass of the object and v is its velocity.

The difference in kinetic energies at the two speeds is the work done to accelerate the bullet. To find this difference, we need to calculate the kinetic energy at each speed and then subtract the initial kinetic energy from the final kinetic energy.

First, let's convert the mass of the bullet to kilograms. Since 1 gram is equal to 0.001 kilograms, the mass of the bullet is 5.0 g * 0.001 kg/g = 0.005 kg.

Now let's calculate the initial kinetic energy. Considering the bullet starts with an initial velocity of 0 m/s, the initial kinetic energy is KE_initial = (1/2) * 0.005 kg * (0 m/s)^2 = 0 J.

Next, we calculate the final kinetic energy. The final velocity is given as 1000 m/s. Therefore, the final kinetic energy is KE_final = (1/2) * 0.005 kg * (1000 m/s)^2. Plugging in the numbers, we get KE_final = 2.5 kg·m^2/s^2, which is equivalent to 2.5 Joules (J).

Finally, we can find the work done to accelerate the bullet by subtracting the initial kinetic energy from the final kinetic energy: Work = KE_final - KE_initial = 2.5 J - 0 J = 2.5 J.

Therefore, the work necessary to accelerate a bullet with a mass of 5.0 g to a velocity of 1000 m/s is 2.5 Joules.