A stone weighs 34.0 N. What force must be applied to make it accelerate upward at 4.00 m/s2?
To find the force required to make the stone accelerate upward at 4.00 m/s², we can use Newton's second law of motion.
Newton's second law states that the force on an object is equal to the mass of the object multiplied by its acceleration. The formula for this law is:
F = m * a
Where F is the force, m is the mass, and a is the acceleration.
In this case, we are given the weight of the stone, which is 34.0 N. Weight is the force of gravity acting on an object and is equal to the mass of the object multiplied by the acceleration due to gravity (g). The formula for weight is:
W = m * g
Where W is the weight, m is the mass, and g is the acceleration due to gravity.
To find the mass of the stone, we can rearrange the weight formula:
m = W / g
Now we can substitute the weight of the stone, 34.0 N, and the acceleration due to gravity, which is approximately 9.8 m/s²:
m = 34.0 N / 9.8 m/s²
m ≈ 3.47 kg
Now that we have the mass of the stone, we can use Newton's second law to find the force required to accelerate the stone:
F = m * a
F = 3.47 kg * 4.00 m/s²
F ≈ 13.9 N
Therefore, a force of approximately 13.9 Newtons must be applied to the stone to make it accelerate upward at 4.00 m/s².