Suppose that you let the masses m1 and m2 slide (without adding the third mass).
a) What is the acceleration of the mass 25g? Hint: identify the force that produces the motion and the one that opposses and write the equation for the net force.
b) What is the change in momemtum of the 25g mass after 2 seconds of motion?
c) What distance would the mass fall?
not I need help
To answer these questions, we need to use Newton's second law of motion and apply it to each part separately. Let's break it down step by step:
a) To determine the acceleration of the mass of 25g, we need to find the net force acting on it. The force that produces the motion is the force of gravity acting on the mass, which is given by the equation F = mg, where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s^2).
The force that opposes the motion is the force of friction. Assuming there is no friction mentioned in the question, we can neglect this opposing force.
Therefore, the net force acting on the mass is equal to the force of gravity. Applying Newton's second law, F = ma, we can rearrange the equation to solve for acceleration (a):
F = ma
mg = ma
Plugging in the values, we have:
0.025 kg * 9.8 m/s^2 = 0.025 kg * a
Simplifying the equation, we find:
a = 9.8 m/s^2
So, the acceleration of the mass of 25g is 9.8 m/s^2.
b) To find the change in momentum of the 25g mass after 2 seconds of motion, we need to use the formula for momentum, which is given by the equation p = mv, where p is momentum, m is mass, and v is velocity.
The change in momentum is given by the difference in momentum before and after the motion. Initially, the mass was at rest, so the initial momentum is zero. After 2 seconds, the mass has accelerated to a certain velocity.
To find the final velocity, we can use the equation of motion, v = u + at, where u is the initial velocity, a is acceleration, and t is time.
Since the mass started from rest, the initial velocity (u) is zero. Plugging in the values, we have:
v = 0 + 9.8 m/s^2 * 2 s
Simplifying the equation, we find:
v = 19.6 m/s
Now, we can calculate the change in momentum:
Δp = m * (vf - vi)
Δp = 0.025 kg * (19.6 m/s - 0 m/s)
Simplifying the equation, we find:
Δp = 0.49 kg·m/s
So, the change in momentum of the 25g mass after 2 seconds of motion is 0.49 kg·m/s.
c) To determine the distance the mass would fall, we can use the equation of motion, s = ut + (1/2) a t^2, where s is the distance, u is the initial velocity, a is the acceleration, and t is the time.
Since the mass started from rest, the initial velocity (u) is zero. Plugging in the values, we have:
s = 0 + 0.5 * 9.8 m/s^2 * (2 s)^2
Simplifying the equation, we find:
s = 19.6 m
So, the distance the mass would fall is 19.6 meters.