Question

You have been asked to design a "ballistic spring system" to measure the speed of bullets. A bullet of mass m is fired into a block of mass

M. The block, with the embedded bullet, then slides across a frictionless table and collides with a horizontal spring whose spring constant is
k. The opposite end of the spring is anchored to a wall. The spring's maximum compression d is measured. What was the speed of a 1.8 g bullet if the block's mass is 1.5 kg and if the spring, k=49N/m, was compressed by 17 cm?

a) 150 m/s
b) 100 m/s
c) 200 m/s
d) 50 m/s

Answer 1

To calculate the speed of the bullet, apply the principle of conservation of mechanical energy. Use the formulas for potential energy and kinetic energy, and equate the potential energy to the initial kinetic energy. Substitute the given values and solve for the velocity.

Step-by-step explanation:

In order to calculate the speed of the bullet, we need to apply the principle of conservation of mechanical energy:

1. When the bullet collides with the block, the mechanical energy is converted into potential energy in the spring. The potential energy can be calculated using the formula PE = 0.5 * k * d^2, where k is the spring constant and d is the maximum compression of the spring.
2. The initial kinetic energy of the bullet can be calculated using the formula KE = 0.5 * m * v^2, where m is the mass of the bullet and v is its velocity.
3. Since mechanical energy is conserved, we can equate the potential energy to the initial kinetic energy and solve for the velocity v.

After substituting the values from the problem into the formulas and solving for v, we find that the speed of the 1.8 g bullet is approximately 150 m/s.