An empty 160 kg elevator accelerates upward
at 1.2 m/s
2
.
The acceleration of gravity is 9.8 m/s
2
.
What is the tension in the cable that lifts
the elevator cab?
Answer in units of N
1760N
(160kg)(9.8m/s^2) = 1568
T-1568 = (160kg)(1.2m/s^2)
T = 1760N
To find the tension in the cable that lifts the elevator cab, we'll need to calculate the net force acting on the elevator.
The net force is given by the equation:
net force = mass x acceleration
The mass of the elevator is 160 kg and the acceleration is 1.2 m/s^2.
So, the net force is:
net force = 160 kg x 1.2 m/s^2 = 192 N
Since the elevator is accelerating upward, the tension in the cable must be greater than the force due to gravity.
The force due to gravity is given by the equation:
force due to gravity = mass x acceleration due to gravity
The acceleration due to gravity is 9.8 m/s^2.
So, the force due to gravity is:
force due to gravity = 160 kg x 9.8 m/s^2 = 1568 N
Therefore, the tension in the cable that lifts the elevator cab is:
tension = net force + force due to gravity
= 192 N + 1568 N
= 1760 N
The tension in the cable that lifts the elevator cab is 1760 N.
To find the tension in the cable that lifts the elevator cab, we can use Newton's second law of motion.
The formula for Newton's second law is:
F = m * a
Where F represents the force, m represents the mass, and a represents the acceleration.
In this case, the elevator is accelerating upwards, so the force that we need to find is the tension in the cable. The mass of the elevator is given as 160 kg, and the acceleration is given as 1.2 m/s^2.
So, using Newton's second law, we can calculate the tension in the cable:
Tension = m * a
Tension = 160 kg * 1.2 m/s^2
Tension = 192 N
Therefore, the tension in the cable that lifts the elevator cab is 192 N.