An elevator is being lifted up an elevator shaft at a constant speed by a steel cable. All fricional effects are negligible. In this situation,forces on the elevator are such that?:
A.the upward force by the cable is greater than the downward force of gravity
B. the upward force by the cable is smaller than the downward force of gravity
C.None of these: the elevator goes up because the cable is being shortened,not because an upward force is exerted on the elevator by the cable
D. the upward force of the cable is greater than the sum of the downward force of gravity and downward force due to the air
E. the upward force of the cable is equal to the downward force of gravity
Would it be choice A or C?
There is no acceleration up or down
F = m a
so
Net force is zero
m g down = cable tension up
so
E
To determine the correct answer, we need to analyze the forces acting on the elevator.
In this situation, the elevator is being lifted up at a constant speed, which implies it is in equilibrium - the net force acting on the elevator is zero.
There are two main forces acting on the elevator:
1. The downward force of gravity: This force is exerted on the elevator due to the Earth's gravitational pull acting on its mass. The magnitude of this force can be calculated using the formula F = mg, where m is the mass of the elevator and g is the acceleration due to gravity.
2. The upward force exerted by the cable: This force is responsible for lifting the elevator.
Since the elevator is in equilibrium and moving at a constant speed, it means that the magnitudes of the downward force of gravity and the upward force exerted by the cable are equal. Hence, the correct answer is E.
Choice A is incorrect because it suggests that the upward force by the cable is greater than the downward force of gravity, which would result in an acceleration upwards. However, the question specifically states that the elevator is moving at a constant speed, indicating that there is no net force acting on it.
Choice C is also incorrect because it implies that the elevator goes up solely due to the cable being shortened, not because an upward force is exerted by the cable. However, the cable is responsible for exerting the upward force that counteracts the downward force of gravity, allowing the elevator to move upwards.
Hmm, let me see if I can lift your spirits with an answer! The correct choice here is actually C. None of these. The elevator goes up because the cable is being shortened, not because an upward force is exerted on the elevator by the cable. So, no need to pull your hair out over this one!
The correct answer is A. The upward force exerted by the cable is greater than the downward force of gravity. This is because in order for the elevator to move upwards at a constant speed, the net force acting on it must be zero.
Since all frictional effects are negligible, the only forces acting on the elevator are the upward force exerted by the cable and the downward force of gravity. In order for the elevator to maintain a constant speed, the magnitude of the upward force must be equal to the magnitude of the downward force.
Therefore, the upward force by the cable is greater than the downward force of gravity. Choice C suggests that the elevator goes up because the cable is being shortened, but this is not accurate in a scenario where the elevator is being lifted at a constant speed.