An elevator and its load have a combined mass of 1650 kg. Find the tension in the supporting cable when the elevator, originally
moving downward at 11 m/s, is brought to rest with constant acceleration in a distance of 41 m.
1 answer:
Answer:
Tension in the supporting cable is = 4,866 N ≅4.9 KN
Explanation:
First of all, we need to understand that tension is a force, so the motion law
F = Ma applies perfectly.
From Newtons third law of motion, action and reaction are equal and opposite. This means that the force experienced by the elevator, is equal to the tension experienced by the spring.
Parameters given:
Mass of load = 1650 kg
Acceleration of load = ?
The acceleration of the load can be obtained by diving the change in velocity by the time taken. But we need to know the time taken for the motion to 41 m.
Time taken = distance covered / velocity
= = 3.73 seconds
∴Acceleration = ( initial velocity - final velocity )/ time taken
Note: Final velocity is = 0 since the body came to a rest.
Acceleration = = 2.95m/
Force acting on the cable = mass of elevator × acceleration of elevator
= 1650 × 2.95 = 4869.5 kg ≅ 4.9 KN
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Before we solve this, we should know this fact:
According to Newton's Law of Gravitation, the force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The force acts along the line joining the centres of the two objects. It can be shown by this:
Now, let us check all the options.
A. As we move to higher altitudes, the force of gravity on us decreases.
<em>This </em><em>statement </em><em>is </em><em>true.</em>
The force of gravity is inversely proportional to the square of distance from the centre of the earth. If, we go up the surface of the earth, the distance from the centre of the earth increases and hence the value of force of gravity decrease. So, force of gravity decreases with altitude.
B. As we move to higher altitudes, the force of gravity on us increases.
<em>This </em><em>statement</em><em> </em><em>is </em><em>false.</em>
We have already got the result in option A. that the force of gravity decreases with altitude. It never increases with altitude.
C. As we gain mass, the force of gravity on us decreases.
<em>This </em><em>statement</em><em> </em><em>is </em><em>false.</em>
The force of gravity is directly proportional to the product of the masses. So, if increase our mass, then the force of gravity will also increase and if we decrease our mass, then the force of gravity decreases.
D. As we gain mass, the force of gravity on us increases.
<em>This </em><em>statement</em><em> is</em><em> </em><em>true.</em>
As mentioned earlier in option C., the force of gravity is directly proportional to the product of the masses of the earth and another object. So, as we gain mass, the force of gravity on us increases.
E. As we move faster, the force of gravity on us increases.
<em>This </em><em>statement</em><em> is</em><em> </em><em>true</em><em>.</em>
Here, we have to consider a different formula. According to Newton's Second Law,
F = ma, where F is the force, m is the mass and a is the acceleration.
In other words,
F ∝ a, i.e., force is directly proportional to acceleration.
We know, acceleration is the rate of change of velocity of an body within a time period.
So, if speed is increased, then acceleration will also be greater, which results in the increase of force. So, as we move faster, the force of gravity on us increases.
<u>Answers:</u>
A: As we move to higher altitudes, the force of gravity on us decreases.
D: As we gain mass, the force of gravity on us increases.
E: As we move faster, the force of gravity on us increases.
Hope you could understand.
If you have any query, feel free to ask.