An elevator starts from rest with a constant
upward acceleration and moves 1m in the first
1.9 s. A passenger in the elevator is holding a
5.3 kg bundle at the end of a vertical cord.
The acceleration of gravity is 9.8 m/s2 .
What is the tension in the cord as the elevator accelerates?
Answer in units of N.
Well, it certainly seems like this elevator is going up in the world! Let's clown around with some physics.
To find the tension in the cord, we can start by finding the net force acting on the bundle. This force can be calculated using Newton's second law, F = ma, where F is the force, m is the mass, and a is the acceleration.
The force acting on the bundle is the tension in the cord, which we're trying to find. So, we'll rewrite Newton's second law as T = ma, where T is the tension, m is the mass of the bundle (5.3 kg), and a is the acceleration.
Now, we need to find the acceleration of the elevator. We can use the kinematic equation s = ut + (1/2)at^2, where s is the displacement, u is the initial velocity, t is the time, and a is the acceleration.
Given that the elevator moves 1m in the first 1.9s and starts from rest, the initial velocity can be assumed to be zero. Plugging in these values, we get 1 = (1/2)a(1.9)^2. Solving for a, we find the acceleration of the elevator to be approximately 0.557 m/s^2.
Now, we can substitute this value of acceleration into our equation for tension. T = (5.3 kg)(0.557 m/s^2). Crunching the numbers gives us a tension of around 2.95 N (rounded to two decimal places).
So, the tension in the cord as the elevator accelerates is approximately 2.95 N. There you have it! Keep in mind, though, that I might have twisted this answer into a laughable state. So it's always good to double-check!
To find the tension in the cord, we need to consider the forces acting on the bundle.
The only two forces acting on the bundle are the tension in the cord and the force of gravity. Since the elevator is moving upward with acceleration, we know that the net force acting on the bundle must be upward.
First, let's calculate the force of gravity acting on the bundle. The force of gravity can be calculated using the equation F = m * g, where F is the force, m is the mass, and g is the acceleration due to gravity.
F_gravity = (mass of the bundle) * (acceleration due to gravity)
= 5.3 kg * 9.8 m/s^2
= 51.94 N
Next, let's calculate the net force acting on the bundle using Newton's second law of motion, which states that the net force equals the mass times the acceleration.
net force = (mass of the bundle) * (acceleration of the elevator)
To find the acceleration of the elevator, we can use the equation for uniformly accelerated motion, which relates displacement (d), initial velocity (u), final velocity (v), and time (t):
d = ut + (1/2) * a * t^2
Rearranging the equation, we can solve for the acceleration (a):
a = 2(d - ut) / t^2
Given that the displacement (d) is 1m and the time (t) is 1.9s, and assuming the elevator starts from rest (u = 0), we can calculate the acceleration of the elevator.
a = 2(1m - 0 * 1.9s) / (1.9s)^2
= 2m / (3.61s^2)
= 0.554 m/s^2
Now, we can calculate the net force:
net force = (mass of the bundle) * (acceleration of the elevator)
= 5.3 kg * 0.554 m/s^2
= 2.93 N
Since the net force is upward, the tension in the cord must also be upward and equal to the net force:
Tension in the cord = net force = 2.93 N
Therefore, the tension in the cord as the elevator accelerates is 2.93 N.
69.96
Use the fact that it goes 1 m in 1.9 s to get the acceleration, a.
(1/20 a t^2 = (1/2)a*(1s)^2 = 1.7 m
a = 3.4 m/s^2
The tension T in the cord minus the weight equals ma.
T = m (g + a)
m = 5.3 kg and g = 9.8 m/s^2
Do the numbers.