Suppose that a sled is accelerating at a rate of 2 m/s2. If the net force is tripled and the mass is doubled, then what is the new acceleration of the sled?
a = F/m = 2 m/s^2.
a = 3F/2m = 1.5(F/m).
Replace F/m with 2:
a = 1.5 * 2 = 3.0 m/s^2.
My name is walter heisenburg
To find the new acceleration of the sled, you can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass.
The formula for Newton's second law is:
F = m * a
where F is the net force, m is the mass, and a is the acceleration.
In the given scenario, the sled's initial acceleration is 2 m/s^2. We need to find the new acceleration when the net force is tripled and the mass is doubled.
Let's denote the new net force as F', and the new mass as m' (which is twice the initial mass).
According to the question, the new net force (F') is three times the initial net force (F), and the new mass (m') is twice the initial mass (m).
Mathematically, we can write:
F' = 3 * F
m' = 2 * m
Now, using Newton's second law (F = m * a), we can substitute the new values into the equation to find the new acceleration (a').
F' = m' * a'
Substituting the given values:
3 * F = 2 * m * a'
Dividing both sides of the equation by 2 * m:
a' = (3 * F) / (2 * m)
But we know that F = m * a (from Newton's second law). Substituting this into the equation:
a' = (3 * m * a) / (2 * m)
The m on the numerator cancels with the m on the denominator:
a' = (3 * a) / 2
Therefore, the new acceleration of the sled, given the tripled net force and doubled mass, is (3 * a) / 2.
In this case, since the initial acceleration (a) is 2 m/s^2, the new acceleration (a') would be:
a' = (3 * 2) / 2
a' = 3 m/s^2
Hence, the new acceleration of the sled is 3 m/s^2.