A man in an elevator is 79kg. The elevator itself is 860kg. As the elevator begins to move down, a scale the man is standing on reads 437N. How do I determine the acceleration of the elevator? (I tried dividing the force of the man by his mass, it was incorrect)
To determine the acceleration of the elevator, we need to consider the forces acting on the man and the elevator. Since the elevator is moving down, the acceleration can be determined by considering the net force acting on the man.
Step 1: Calculate the weight of the man
The weight of an object is given by the formula W = mg, where W is the weight, m is the mass of the object, and g is the acceleration due to gravity. In this case, the mass of the man is given as 79 kg. Therefore, the weight of the man can be calculated as follows:
Weight of the man = 79 kg x 9.8 m/s^2 = 774.2 N
Step 2: Calculate the weight of the elevator
Similar to the previous step, we can calculate the weight of the elevator using its mass. Given that the mass of the elevator is 860 kg, the weight of the elevator can be determined as follows:
Weight of the elevator = 860 kg x 9.8 m/s^2 = 8432 N
Step 3: Determine the net force
The net force acting on the man can be obtained by subtracting the weight of the man from the reading on the scale. In this case, the scale reading is 437 N, and the weight of the man is 774.2 N. Therefore, the net force can be calculated as follows:
Net force = 437 N - 774.2 N = -337.2 N
Step 4: Apply Newton's second law of motion
According to Newton's second law of motion, the net force acting on an object is equal to the mass of the object multiplied by its acceleration. Therefore, we can rearrange the formula to calculate the acceleration:
Acceleration = Net force / Total mass
Total mass is the sum of the masses of the man and the elevator:
Total mass = Mass of the man + Mass of the elevator = 79 kg + 860 kg = 939 kg
Now, we can calculate the acceleration:
Acceleration = -337.2 N / 939 kg = -0.359 m/s^2
The negative sign indicates that the elevator is moving down, which aligns with the problem statement. Therefore, the acceleration of the elevator is approximately -0.359 m/s^2.
To determine the acceleration of the elevator, you need to consider the forces acting on the man and the elevator. In this case, the force due to the weight of the man and the elevator is acting downwards, and the force reading on the scale is also acting downwards. The net force is the difference between these two forces.
Step 1: Calculate the weight of the man and the elevator individually.
The weight of the man can be calculated using the equation: Weight = mass * gravity.
Weight of the man = 79 kg * 9.8 m/s^2 = 774.2 N
The weight of the elevator can be calculated using the same equation:
Weight of the elevator = 860 kg * 9.8 m/s^2 = 8,428 N
Step 2: Calculate the net force.
The net force is the difference between the weight of the man and the elevator (acting downwards) and the force reading on the scale (also acting downwards).
Net force = (Weight of the man + Weight of the elevator) - Force reading on scale
Net force = (774.2 N + 8,428 N) - 437 N
Net force = 8,765.2 N - 437 N
Net force = 8,328.2 N
Step 3: Use Newton's second law of motion.
Newton's second law of motion states that force = mass * acceleration.
Net force = (mass of the man + mass of the elevator) * acceleration
8,328.2 N = (79 kg + 860 kg) * acceleration
8,328.2 N = 939 kg * acceleration
Step 4: Solve for acceleration.
Divide both sides of the equation by the mass of the elevator and the man:
acceleration = 8,328.2 N / 939 kg
acceleration ≈ 8.868 m/s^2
Therefore, the acceleration of the elevator is approximately 8.868 m/s^2.