It takes the elevator in a skyscraper 3.6 s to reach its cruising speed of 10 m/s. A 69 kg passenger gets aboard on the ground floor.
1.What is the passenger's weight before the elevator starts moving?
2.What is the passenger's weight while the elevator is speeding up?
3.What is the passenger's weight after the elevator reaches its cruising speed?
the passenger's weight is ALWAYS mass x acceleration.
Can you work out the acceleration at all 3 stages?
The mass of the person is the same for all 3.
How do i find the acceleration?Is it 9.8m/s^2?
and do i need to convert kg into g?
1. The passenger's weight before the elevator starts moving is the same as their mass times the acceleration due to gravity. The acceleration due to gravity is approximately 9.8 m/s². Therefore, the passenger's weight before the elevator starts moving is 69 kg × 9.8 m/s² = 676.2 N.
2. While the elevator is speeding up, the passenger will experience a greater force due to the upward acceleration of the elevator. This force is equal to mass times acceleration (F = ma). The acceleration can be calculated using the equation v = u + at, where v = final velocity, u = initial velocity, a = acceleration, and t = time taken. Rearranging the equation, we have a = (v - u) / t. Plugging in the given values, v = 10 m/s (cruising speed), u = 0 m/s (initial speed), and t = 3.6 s (time taken to reach cruising speed), we find that the acceleration of the elevator is a = (10 m/s - 0 m/s) / 3.6 s ≈ 2.78 m/s². Therefore, the force experienced by the passenger while the elevator is speeding up is 69 kg × 2.78 m/s² = 191.82 N.
3. Once the elevator reaches its cruising speed, it continues to move at a constant velocity. This means that the passenger is no longer experiencing any upward acceleration or deceleration. Therefore, the passenger's weight after the elevator reaches its cruising speed is the same as their weight before the elevator starts moving, which is 676.2 N.
To answer these questions, we need to understand the concepts of weight and acceleration.
1. The passenger's weight before the elevator starts moving is the same as their weight on the ground floor. Weight is the force exerted on an object due to gravity, and it is given by the formula: weight = mass × acceleration due to gravity. The acceleration due to gravity on Earth is approximately 9.8 m/s^2. Therefore, the passenger's weight before the elevator starts moving is 69 kg × 9.8 m/s^2.
2. When the elevator is speeding up, the passenger will experience two forces: gravity and the upward force due to acceleration. The net force acting on the passenger is the difference between these two forces. By Newton's second law, force = mass × acceleration. The acceleration in this case is the elevator's acceleration. To find the upward force, we first need to determine the acceleration. The elevator reaches its cruising speed in 3.6 seconds, and its speed increases from 0 to 10 m/s. Using the formula: acceleration = change in velocity / time taken, we can find the elevator's acceleration. The change in velocity is 10 m/s, and the time taken is 3.6 seconds. Once we have the acceleration, we can calculate the upward force on the passenger using force = mass × acceleration. The passenger's weight while the elevator is speeding up is their normal weight (as calculated in question 1) plus the upward force.
3. Once the elevator reaches its cruising speed, it no longer accelerates. Therefore, the passenger will only experience their normal weight due to gravity.
To summarize:
1. The passenger's weight before the elevator starts moving = 69 kg × 9.8 m/s^2.
2. Calculate the elevator's acceleration using acceleration = change in velocity / time taken. Then, calculate the upward force on the passenger using force = mass × acceleration. The passenger's weight while the elevator is speeding up = their normal weight + the upward force.
3. The passenger's weight after the elevator reaches its cruising speed = their normal weight.