An object is hung from a spring balance attached to the ceiling of an elevator cab. The balance reads 60 N when the elevator is standing still.
(a) What is the reading when the elevator is moving upward with a constant speed of 9.6 m/s?
N
(b) What is the reading when the elevator is moving upward with a speed of 9.6 m/s while decelerating at a rate of 1.9 m/s2?
N
a) F=ma+mg so if a is zero, ...
b)same formula.
3.4 N
i am afraid
To answer these questions, we need to consider the forces acting on the object in different situations. In both cases, we assume there is no air resistance.
Let's start with part (a) when the elevator is moving upward with a constant speed of 9.6 m/s. In this situation, the object experiences two forces: the gravitational force (weight) pulling it downward and the tension in the spring balance pulling it upward.
When the elevator is standing still, the object's weight is balanced by an equal and opposite force from the spring balance, resulting in a reading of 60 N. However, when the elevator is in motion, the object experiences an additional force due to its acceleration.
Since the elevator is moving upward with a constant velocity (constant speed), the net force on the object must be zero. This means that the tension in the spring balance should be equal to the object's weight.
To calculate this, we need to use Newton's second law of motion, which states that the net force on an object is equal to its mass multiplied by its acceleration. However, since the elevator is moving at a constant velocity, the net force must be zero, which means that the acceleration is also zero.
Therefore, the reading on the spring balance when the elevator is moving upward with a constant speed of 9.6 m/s is also 60 N. This is because the object's weight is still balanced by the spring tension, despite the elevator's motion.
Now let's move on to part (b) when the elevator is moving upward with a speed of 9.6 m/s while decelerating at a rate of 1.9 m/s². In this case, the object experiences three forces: the gravitational force (weight), the tension in the spring balance, and the force due to the elevator's deceleration.
The force due to deceleration acts in the opposite direction to the motion of the elevator, which means it acts downward. Therefore, the net force on the object will be the difference between the weight and the force due to deceleration.
To calculate the reading on the spring balance, we need to determine the acceleration of the object. The acceleration can be found using the equation of motion:
v² = u² + 2as
where:
v = final velocity (9.6 m/s)
u = initial velocity (0 m/s, as the object is initially at rest)
a = acceleration (-1.9 m/s², as it is decelerating)
s = distance covered (unknown)
Rearranging the equation, we get:
s = (v² - u²) / (2a)
s = (9.6² - 0) / (2 * (-1.9))
s = 92.16 / -3.8
s = -24.27368 m (- denotes downward direction)
Now that we have the distance covered, we can calculate the force due to the elevator's deceleration using the equation:
force = mass * acceleration
Since we don't have the mass of the object, we can cancel it out by comparing the ratio of the deceleration with the acceleration due to gravity (g = 9.8 m/s²). The ratio is:
-1.9 m/s² / 9.8 m/s² = -0.1939
The force due to deceleration is therefore:
force = weight * ratio
force = 60 N * 0.1939
force ≈ 11.63 N
Now we can calculate the net force on the object:
net force = weight - force due to deceleration
net force = 60 N - 11.63 N
net force ≈ 48.37 N
Therefore, the reading on the spring balance when the elevator is moving upward with a speed of 9.6 m/s while decelerating at a rate of 1.9 m/s² is approximately 48.37 N.