While an elevator of mass 2681 kg moves upward, the tension in the cable is 29.4 kN.
(a) What is the acceleration of the elevator?
(b) If at some point in the motion the velocity of the elevator is 1.04 m/s upward, what is the elevator's velocity 3.96 s later?
To answer part (a), we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In this case, the net force is the tension in the cable.
Step 1: Convert the tension from kilonewtons to newtons.
To convert 29.4 kN to N, we multiply by 1000:
29.4 kN x 1000 N/kN = 29,400 N
Step 2: Calculate the acceleration.
Using Newton's second law, we have:
Tension = mass x acceleration
29,400 N = 2681 kg x acceleration
Now we can solve for the acceleration:
acceleration = 29,400 N / 2681 kg
acceleration ≈ 10.96 m/s²
So, the acceleration of the elevator is approximately 10.96 m/s².
To answer part (b), we can use the equation of motion:
velocity = initial velocity + acceleration x time
Step 1: Determine the initial velocity.
The initial velocity is given as 1.04 m/s upward.
Step 2: Calculate the final velocity.
Using the equation of motion, we have:
velocity = 1.04 m/s + 10.96 m/s² x 3.96 s
Now we can solve for the final velocity:
velocity ≈ 1.04 m/s + 43.38 m/s
velocity ≈ 44.42 m/s
Therefore, the elevator's velocity 3.96 s later is approximately 44.42 m/s.