A spring with a spring constant of 16 N-m is compressed 0.2 m. What is the restoring force on the spring?
A. -1.25N
B. -3.2N
C. -15.8N
D. -80N
My answer is D.
What is the mass of a box that requires a force of 27 N to be accelerated to 4.0 m/s²?
A. 6.8 kg
B. 2.3 kg
C. 31 kg
D. 108 kg
My answer is A.
To calculate the restoring force on the spring, we can use Hooke's Law, which states that the restoring force (F) exerted by a spring is directly proportional to the displacement (x) from its equilibrium position and the spring constant (k).
The formula for Hooke's Law is:
F = k * x
Given that the spring constant (k) is 16 N/m and the displacement (x) is 0.2 m, we can substitute these values into the formula to calculate the restoring force (F):
F = 16 N/m * 0.2 m = 3.2 N
So, the restoring force on the spring is 3.2 N.
Therefore, the correct answer to the first question is B. -3.2N.
To calculate the mass of the box in the second question, we can use Newton's second law of motion, which states that the force applied to an object is equal to the mass (m) of the object multiplied by its acceleration (a).
The formula for Newton's second law is:
F = m * a
Given that the force applied (F) is 27 N and the acceleration (a) is 4.0 m/s², we can substitute these values into the formula to calculate the mass (m):
27 N = m * 4.0 m/s²
To solve for the mass (m), we divide both sides of the equation by 4.0 m/s²:
m = 27 N / 4.0 m/s² = 6.75 kg
So, the mass of the box is 6.75 kg.
However, none of the answer choices provided match this exact value. The closest option is A. 6.8 kg, which is rounded to one decimal place. Therefore, A. 6.8 kg is the closest approximate answer.
Therefore, the correct answer to the second question is A. 6.8 kg.