Final answer:
To find the tension in the cord, combine the gravitational force (weight) of the mass with the force required for the upward acceleration. Tension equals the sum of weight and force from acceleration.
Step-by-step explanation:
The student has asked how to calculate the tension in a cord from which a 2.0 kg block is hanging while it accelerates upward at 4.0 m/s2. To solve this, we need to apply Newton's second law of motion, which states that the force is equal to mass times acceleration (F=ma). In this case, the tension in the cord must counteract both the gravitational force (weight of the block) and provide the upward acceleration.
- First, calculate the gravitational force (weight) using Fg = m * g, where m is the mass (2.0 kg) and g is the acceleration due to gravity (9.8 m/s2).
- Then, calculate the total force needed for the upward acceleration using Fa = m * a, where a is the given acceleration (4.0 m/s2).
- Add the gravitational force and the force for acceleration to get the total tension in the rope.
Calculating the gravitational force: Fg = 2.0 kg * 9.8 m/s2 = 19.6 N.
Calculating the force needed for acceleration: Fa = 2.0 kg * 4.0 m/s2 = 8 N.
Add both forces to get the tension: Tension = Fg + Fa = 19.6 N + 8 N = 27.6 N.