A box is suspended by a string from the ceiling of an elevator. The string supports the box with a force of
17.0 N when the elevator is accelerating downwards at 1.70 m/s2. What force would the string exert if the elevator was moving upwards at a constant velocity
If the elevator is moving upwards at a constant velocity, that means it is not accelerating. Therefore, the net force acting on the box must be zero according to Newton's second law.
Since the box is still suspended by the string, the force exerted by the string must exactly balance the force due to gravity. The force due to gravity is given by the weight of the box, which is equal to its mass multiplied by the acceleration due to gravity (9.8 m/s^2).
To find the force exerted by the string, we first need to determine the mass of the box. We can use the equation:
Weight = mass * acceleration due to gravity
Given that the weight (force due to gravity) is 17.0 N and the acceleration due to gravity is 9.8 m/s^2, we can rearrange the equation to solve for the mass:
mass = Weight / acceleration due to gravity
mass = 17.0 N / 9.8 m/s^2
mass ≈ 1.73 kg
Now, since the elevator is moving upwards at a constant velocity, the net force must be zero. The force exerted by the string is equal in magnitude but opposite in direction to the force due to gravity.
Therefore, the force exerted by the string would be 17.0 N, pointing upwards.
To answer this question, we will use Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. In this case, we know the mass of the box is not given, but it cancels out when comparing the two situations, as the mass of the box remains the same.
1. When the elevator is accelerating downward:
The force exerted by the string is equal to the tension T in the string. We are given that T = 17.0 N and the acceleration of the elevator is a = 1.70 m/s^2.
Using Newton's second law, we have:
Net force = mass × acceleration
T - mg = ma
17.0 N - mg = m × 1.70 m/s^2
Here, the mass (m) cancels out, so we can solve for g (acceleration due to gravity):
17.0 N = 1.70 m/s^2 × g
Solving for g, we find:
g = 10.0 m/s^2
2. When the elevator is moving upward at a constant velocity:
In this case, the acceleration is zero (since constant velocity means no change in velocity). So, we need to find the force exerted by the string.
Using Newton's second law:
T - mg = ma
T - mg = 0
Since the acceleration is zero, the equation becomes:
T - mg = 0
Simplifying, we find:
T = mg
We already know the value of g from the previous calculations: g = 10.0 m/s^2.
Therefore, the force exerted by the string when the elevator is moving upwards at a constant velocity would be the weight of the box, given by:
T = mg = m × 10.0 m/s^2
However, without the mass of the box, we cannot determine the exact force exerted by the string.
tension=mass(g-a) going down
17=mass(9.8-1.70)
mass=17/(8.1)
going up
tension=mass(g+a) but a =0
tension=17/(8.1)*(9.8)