An elevator cab is pulled upward by a cable. The cab and its single occupant have a combined mass of 1980 kg. When that occupant drops a coin, its acceleration relative to the cab is 7.30 m/s2 downward. What is the tension in the cable?
If it's accelerating upward the acceleration should be MORE than gravity.
T - mg = ma
To find the tension in the cable, we need to consider the forces acting on the elevator cab and its occupant.
There are two main forces at play here:
1. The force of gravity acting downwards on the cab and occupant, which is given by the formula F_gravity = m * g, where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s^2).
2. The tension force in the cable pulling the cab upwards.
Now let's break down the problem and solve it step by step:
Step 1: Calculate the force of gravity on the cab and occupant.
F_gravity = m * g
F_gravity = 1980 kg * 9.8 m/s^2
F_gravity = 19384 N
Step 2: Determine the net force acting on the coin when it is dropped relative to the cab.
The net force acting on the coin is the difference between the gravitational force acting on the coin and the acceleration it experiences relative to the cab.
Net force = F_gravity - (m_coin * a_coin)
Here, a_coin is the acceleration of the coin relative to the cab, which is given as -7.30 m/s^2 (negative because it is directed downward).
Step 3: Calculate the tension in the cable.
The tension in the cable is equal to the net force acting on the coin.
Tension = Net force
Tension = F_gravity - (m_coin * a_coin)
Tension = 19384 N - (m_coin * -7.30 m/s^2)
Notice that we are missing the mass of the coin (m_coin). Without that information, we cannot calculate the exact tension in the cable.