A sled is accelerating down a hill at a rate of 1 m/s2
. If the mass of the sled is suddenly cut in half and the net force on the sled is doubled, what is the acceleration of the sled?
4 times original acceleration
To find the acceleration of the sled, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The equation can be written as:
F = ma
Where:
F is the net force,
m is the mass of the sled, and
a is the acceleration of the sled.
Given that the sled's acceleration is initially 1 m/s² and the mass of the sled is cut in half while the net force is doubled, we can express the changes in terms of ratios:
Initial mass: Final mass = 1 : 1/2 = 2 : 1
Net force: Doubled
Let's assume the initial mass of the sled is represented by "m". Therefore, the final mass would be "m/2" (half of the initial mass), and the net force would be "2F" (double the initial force).
Now we can set up the equation for the final acceleration:
2F = (m/2) * a'
We need to solve for "a'" which represents the final acceleration.
Simplifying the equation, we can rewrite it as:
2F = (m * a') / 2
Multiplying both sides by 2 and dividing both sides by m, we have:
2F * 2 / m = a'
4F / m = a'
Therefore, the acceleration of the sled after cutting its mass in half and doubling the net force is 4 times its initial value. So, the sled's final acceleration is 4 m/s².
To find the acceleration of the sled after the changes in mass and net force, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
First, let's assign variables to the given values:
Initial acceleration (before the changes): a1 = 1 m/s^2
Initial mass (before the changes): m1
Final mass (after the changes, cut in half): m2 = m1/2
Initial net force (before the changes): F1
Final net force (after the changes, doubled): F2 = 2 * F1
According to Newton's second law, we have the following equation relating acceleration, net force, and mass:
a1 = F1 / m1
Now, let's find the new acceleration (a2) after the changes:
a2 = F2 / m2
= (2 * F1) / (m1/2)
= (2 * F1) * (2/m1)
= (4 * F1) / m1
Therefore, the acceleration of the sled after the changes in mass and net force is (4 * F1) / m1.
net force=mass*acceleration
so doubling net force doubles acceleration, and cutting mass in half, doubles it again.
Answer: 4 time original acceleration.