What average force is needed to accelerate a 6.00-gram pellet from rest to 110 over a distance of 0.800 along the barrel of a rifle?
To find the average force needed to accelerate the pellet, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) times acceleration (a).
First, let's convert the mass of the pellet from grams to kilograms:
1 gram = 0.001 kilograms
Therefore, the mass of the pellet (m) is:
m = 6.00 grams * 0.001 kilograms/gram = 0.006 kilograms
The final velocity of the pellet (v) is given as 110 m/s, the initial velocity (u) is 0 m/s (as it starts from rest), and the distance (s) is 0.800 m.
The average acceleration (a) can be found using the equation of motion:
v^2 = u^2 + 2as
Substituting the given values, we have:
(110 m/s)^2 = (0 m/s)^2 + 2a * 0.800 m
12100 m^2/s^2 = 2a * 0.800 m
12100 m^2/s^2 = 1.6a m
Simplifying, we find:
a = 12100 m^2/s^2 / 1.6 m = 7562.5 m/s^2
Now, we can calculate the average force (F) using Newton's second law equation:
F = m * a
F = 0.006 kg * 7562.5 m/s^2 = 45.375 N
Therefore, the average force needed to accelerate the pellet is 45.375 Newtons.
To find the average force needed to accelerate the pellet, we can use Newton's second law of motion. The formula is:
F = m * a
Where:
F = force
m = mass
a = acceleration
Given:
m = 6.00 grams = 0.00600 kg (since 1 gram = 0.001 kg)
v = 110 m/s (final velocity)
d = 0.800 m (distance)
To find the acceleration, we can use the equation for constant acceleration:
v^2 = u^2 + 2 * a * d
Where:
v = final velocity
u = initial velocity (which is 0 since the pellet is at rest)
a = acceleration
d = distance
Rearranging the equation, we have:
a = (v^2 - u^2) / (2 * d)
By substituting the given values, we get:
a = (110^2 - 0^2) / (2 * 0.800)
a = 15190 / 1.6
a = 9493.75 m/s^2
Now we can calculate the force using Newton's second law:
F = m * a
F = 0.00600 kg * 9493.75 m/s^2
F = 56.96 N
Therefore, the average force needed to accelerate the pellet is approximately 56.96 Newtons.