A stone weighs 34.0 N. What force must be applied to make it accelerate upward at 4.00 m/s2?
To determine the force needed to make the stone accelerate upward, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. The formula is:
F = m * a
Where:
F = Force (unknown)
m = Mass of the object (unknown)
a = Acceleration (given: 4.00 m/s²)
However, in this case, we are given the weight of the stone (34.0 N) instead of the mass. The weight of an object is the force acting on it due to gravity, and it can be calculated using the formula:
W = m * g
Where:
W = Weight (given: 34.0 N)
m = Mass of the object (unknown)
g = Acceleration due to gravity (approximately 9.8 m/s²)
By rearranging this formula, we can solve for the mass:
m = W / g
Substituting the given values:
m = 34.0 N / 9.8 m/s²
m ≈ 3.47 kg
Now that we know the mass, we can substitute it into Newton's second law and solve for the force needed:
F = m * a
F = 3.47 kg * 4.00 m/s²
F ≈ 13.9 N
Therefore, a force of approximately 13.9 N must be applied to the stone in order to make it accelerate upward at 4.00 m/s².