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.
If someone could check these it would be heavily appreciated. Props to all the Jishka tutors who help out daily, you guys are awesome and appreciated.
To find the restoring force on a spring, you can use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position. The formula for Hooke's Law is F = -kx, where F is the restoring force, k is the spring constant, and x is the displacement.
For the given problem, the spring constant (k) is 16 N/m and the displacement (x) is 0.2 m. Plugging these values into the Hooke's Law formula, we get:
F = -16 * 0.2 = -3.2 N
So, the correct answer is B. -3.2N.
For the second problem, to find the mass of a box, you can use Newton's second law of motion, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration. The formula for Newton's second law is F = ma, where F is the force, m is the mass, and a is the acceleration.
In the given problem, the force (F) is 27 N and the acceleration (a) is 4.0 m/s². Plugging these values into the Newton's second law formula, we get:
27 = m * 4.0
Solving for m, we divide both sides of the equation by 4.0:
m = 27 / 4.0 = 6.75 kg
So, the correct answer is A. 6.8 kg.
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