A block is pushed with a force of 15 newtons and accelerates at a rate of 3.0 m/s2. How much force would be needed to accelerate the same block at a rate of 6.0 m/s2?
A.
7.5 N
B.
15 N
C.
30 N
D.
90 N
C. 30 N
To find the force needed to accelerate the same block at a rate of 6.0 m/s², we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration (F = m * a).
Given that the block's acceleration is 3.0 m/s² and the force applied is 15 Newtons, we can calculate the mass of the block using the equation F = m * a. Rearranging the equation gives m = F / a.
m = 15 N / 3.0 m/s²
m = 5 kg
Now, we can find the force needed to accelerate the block at a rate of 6.0 m/s² using the equation F = m * a.
F = 5 kg * 6.0 m/s²
F = 30 N
Therefore, the correct answer is C. 30 N.
To find the force needed to accelerate the block at a rate of 6.0 m/s^2, we can use Newton's second law of motion, which states that force (F) is equal to the mass (m) of the object multiplied by its acceleration (a).
Given:
Initial force (F1) = 15 N
Initial acceleration (a1) = 3.0 m/s^2
Final acceleration (a2) = 6.0 m/s^2
We can set up a proportion to solve for the unknown force (F2):
F1 / a1 = F2 / a2
Substituting the given values:
15 N / 3.0 m/s^2 = F2 / 6.0 m/s^2
Cross-multiplying:
15 N * 6.0 m/s^2 = F2 * 3.0 m/s^2
90 N = F2 * 3.0
Dividing both sides by 3.0:
90 N / 3.0 = F2
F2 = 30 N
Therefore, the force needed to accelerate the same block at a rate of 6.0 m/s^2 is 30 N.
The correct answer is C. 30 N.