A bullet of mass 1.8 X 10-3 kg is moving at +500. m/s when it impacts a tree stump. It penetrates into the stump 6.00 centimeters before coming to rest.
1. Assuming the acceleration to be constant, calculate the force (including direction) exerted by the stump on the bullet.
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To calculate the force exerted by the stump on the bullet, you need to apply Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a). In this case, the acceleration is the deceleration of the bullet as it comes to rest inside the stump.
First, let's calculate the initial velocity of the bullet in meters per second (m/s). The given velocity is +500. m/s, which means the bullet is moving in the positive direction. Therefore, the initial velocity is +500. m/s.
Next, let's calculate the final velocity of the bullet. The bullet comes to rest inside the stump, so the final velocity is 0 m/s.
We can use the kinematic equation:
vf^2 = vi^2 + 2ad
Here, vf is the final velocity (0 m/s), vi is the initial velocity (+500. m/s), a is the acceleration, and d is the displacement (penetration into the stump). Rearranging the equation, we get:
a = (vf^2 - vi^2) / (2d)
Calculating the acceleration:
a = (0^2 - 500.^2) / (2 * 0.06)
Now, we have the acceleration. To calculate the force exerted by the stump, we need to know the mass of the bullet, which is given as 1.8 X 10^-3 kg.
Finally, we can calculate the force:
F = m * a
Substituting the values:
F = (1.8 X 10^-3) * (0^2 - 500.^2) / (2 * 0.06)
Calculate the above expression to find the force exerted by the stump on the bullet. The force will have a negative sign indicating that it is opposite to the initial velocity direction.