What average force is needed to accelerate a 8.00-gram pellet from rest to 135 m/s over a distance of 0.800 m along the barrel of a rifle?
To determine the average force needed to accelerate the pellet, we can use Newton's second law of motion, which states that the force acting on an object is equal to its mass multiplied by its acceleration. In this case, we need to find the acceleration first.
Step 1: Find the mass of the pellet
The question states that the pellet's mass is 8.00 grams. However, it is often easier to work with mass in kilograms for scientific calculations. So, let's convert grams to kilograms.
Mass = 8.00 grams × (1 kilogram / 1000 grams) = 0.00800 kg
Step 2: Find the final velocity of the pellet
The question indicates that the pellet accelerates from rest to a final velocity of 135 m/s. Since the initial velocity is zero, the change in velocity, Δv, is equal to the final velocity.
Δv = 135 m/s
Step 3: Find the acceleration of the pellet
We can use the equation of motion: v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity, a is the acceleration, and s is the displacement.
Since the pellet starts from rest (u = 0), the equation simplifies to: v^2 = 2as
135^2 = 2a(0.800)
a = (135^2) / (2 × 0.800) = 11259.375 m/s^2
Now, we have the acceleration of the pellet.
Step 4: Calculate the average force needed
Using Newton's second law of motion (F = ma), we can calculate the average force needed.
F = 0.00800 kg × 11259.375 m/s^2
F ≈ 90.074 N
Therefore, an average force of approximately 90.074 Newtons is needed to accelerate the 8.00-gram pellet from rest to 135 m/s over a distance of 0.800 m along the barrel of the rifle.