Alice ((7.500x10^1) kg) and Bob ((8.5x10^1) kg) are standing at rest on friction free ice. Alice pushes Bob causing Bob to accelerate at (2.300x10^0) m/s^2. What is the magnitude of Alice’s acceleration?
Ma*Va=-MbVb
Valice= - Mb/Ma * Vb for magnitude, ignore the negative sign (direction)
To find the magnitude of Alice's acceleration, we can use Newton's third law of motion, which states that the force exerted on one object is equal in magnitude and opposite in direction to the force exerted on the other object.
In this case, when Alice pushes Bob, an equal and opposite force is applied to Alice. The force applied on Bob causes him to accelerate, so we need to find the force first.
We can use Newton's second law of motion, which states that the force (F) applied on an object is equal to the mass (m) of the object multiplied by its acceleration (a). Mathematically, F = m * a.
Given that Bob's mass is (8.5x10^1) kg and his acceleration is (2.300x10^0) m/s^2, we can calculate the force applied on Bob as follows:
F = (8.5x10^1) kg * (2.300x10^0) m/s^2.
Multiply the numbers:
F = 195.5 N
Since Alice exerts an equal and opposite force on herself, her acceleration will be in the opposite direction to Bob's acceleration.
Thus, the magnitude of Alice's acceleration is 2.300 m/s^2 in the opposite direction.