Hi, I'm just confused as to what steps to take in order to solve these problems.
If you could please show your steps and method on how to approach these questions to get the answer that would be great. I have the answers to these too, if needed. I want to know how to solve them though.
1) An elevator (mass 4850kg) is to be designed so that the maximum acceleration is 0.0680g. What are the maximum and minimum forces the motor should exert on the supporting cable?
2) A person stands on a bathroom scale in a still (motionless) elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person's regular weight. Calculate the acceleration of the elevator and find the direction of acceleration.
3) a)What is the acceleration of two falling sky divers (mass 132kg) when the upward force of air resistance is equal to one-fourth of their weight?
b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the sky divers and their parachute?
Thank you for your time!
Sure, I'd be happy to explain how to approach each of these problems step by step. Let's go through them one by one:
1) An elevator (mass 4850 kg) is to be designed so that the maximum acceleration is 0.0680g. What are the maximum and minimum forces the motor should exert on the supporting cable?
To solve this problem, we need to use Newton's second law, which states that the force acting on an object is equal to its mass multiplied by its acceleration (F = m * a). In this case, the force exerted by the elevator motor will be the maximum and minimum forces.
The maximum acceleration is given as 0.0680g, where g represents the acceleration due to gravity (approximately 9.8 m/s^2). So we can calculate the maximum force as follows:
Maximum force = mass * maximum acceleration
Maximum force = 4850 kg * (0.0680 * 9.8 m/s^2)
The minimum force would be the negative value of the maximum force, since the elevator could be decelerating. So the minimum force is:
Minimum force = - Maximum force
By plugging in the values and performing the calculations, you can find both the maximum and minimum forces the motor should exert on the supporting cable.
2) A person stands on a bathroom scale in a still (motionless) elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person's regular weight. Calculate the acceleration of the elevator and find the direction of acceleration.
Let's denote the person's regular weight as W. According to the problem, when the elevator begins to move, the scale reads only 0.75W. This means that the normal force acting on the person (which is equal to the reading on the scale) is 0.75W.
Now, we know that the normal force equation is given by:
Normal force = mass * acceleration
Since the person is standing still (motionless) in the elevator, the net force acting on the person should be zero. The person's weight (mg) acts downwards while the normal force acts upwards. So we have:
mg - Normal force = 0
Substituting the given values, we get:
mg - 0.75W = 0
Solving this equation for acceleration, we find:
Acceleration = (0.25W) / m
The direction of the acceleration can be determined from the fact that the person feels lighter, which means the acceleration is upward (opposite to gravity).
3) a) What is the acceleration of two falling skydivers (mass 132 kg) when the upward force of air resistance is equal to one-fourth of their weight?
When the upward force of air resistance is equal to one-fourth of their weight, we can set up the following equation:
mg - (1/4)mg = ma
Here, m represents the mass of each skydiver and a is the acceleration we want to find.
Simplifying the equation:
(3/4)mg = ma
Dividing both sides of the equation by m, we get:
(3/4)g = a
So, the acceleration of the skydivers is (3/4) times the acceleration due to gravity.
b) After popping open the parachute, the divers descend leisurely to the ground at constant speed. What now is the force of air resistance on the skydivers and their parachute?
When the skydivers are descending at a constant speed, their acceleration is zero, meaning the net force acting on them is zero.
The force of air resistance is equal to the force of gravity since there is no net force acting on the skydivers. So, the force of air resistance on the skydivers and their parachute would be equal to their combined weight.
I hope this explanation helps you understand the steps involved in solving these problems! If you have any further questions or need clarification, feel free to ask.
Sure, I can help you solve these problems step-by-step. Let's start with problem 1.
1) An elevator (mass 4850kg) is to be designed so that the maximum acceleration is 0.0680g. What are the maximum and minimum forces the motor should exert on the supporting cable?
Step 1: Calculate the maximum force:
To calculate the maximum force, we need to use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a). In this case, the acceleration is given as 0.0680g, where g is the acceleration due to gravity (9.8 m/s^2).
F = m * a
F = 4850 kg * 0.0680 * 9.8 m/s^2
Calculating the maximum force will give you the answer.
Step 2: Calculate the minimum force:
The minimum force occurs when the elevator is at rest or moving at a constant velocity. In this case, the acceleration is 0, so the force is equal to zero.
The minimum force is 0.
Now let's move on to problem 2.
2) A person stands on a bathroom scale in a still (motionless) elevator. When the elevator begins to move, the scale briefly reads only 0.75 of the person's regular weight. Calculate the acceleration of the elevator and find the direction of acceleration.
Step 1: Understand the problem:
The person's weight is the force exerted by the person due to gravity. It is given that the scale reads only 0.75 (3/4) of the person's regular weight. This means the normal force exerted by the scale is 0.75 times the person's weight.
Step 2: Calculate the acceleration:
The net force acting on the person in the elevator is the difference between the force of gravity downward and the normal force exerted by the scale upward. Using Newton's second law of motion, we can relate this net force to the mass of the person (m) and the acceleration (a) of the elevator.
Net Force = m * a
In this case, the net force is the difference between the person's weight (m * g) and the scale's normal force (0.75 * m * g).
m * g - 0.75 * m * g = m * a
Simplifying the equation will give you the acceleration.
Step 3: Find the direction of acceleration:
The direction of acceleration can be determined based on the net force acting on the person. If the net force is positive (greater than zero), the acceleration is upward (opposite to the force of gravity). If the net force is negative (less than zero), the acceleration is downward (in the same direction as the force of gravity).
Now let's move on to problem 3.
3) a) What is the acceleration of two falling skydivers (mass 132kg) when the upward force of air resistance is equal to one-fourth of their weight?
Step 1: Understand the problem:
The weight of each skydiver is the force exerted by them due to gravity. In this case, it is given that the upward force of air resistance is equal to one-fourth of their weight. This means the force of air resistance is one-fourth (1/4) of the force of gravity acting on the skydivers.
Step 2: Calculate the acceleration:
Similar to problem 2, the net force acting on the skydivers is the difference between the force of gravity downward and the force of air resistance upward.
Net Force = m * a
In this case, the net force is the difference between the force of gravity (m * g) and the force of air resistance (1/4 * m * g).
m * g - 1/4 * m * g = m * a
Simplifying the equation will give you the acceleration.
b) After opening the parachute, the divers descend leisurely to the ground at a constant speed. What is the force of air resistance on the skydivers and their parachute?
When the skydivers are descending at a constant speed, the force of air resistance equals the force of gravity acting on them (since the net force is zero).
Force of air resistance = Force of gravity = m * g
Therefore, the force of air resistance on the skydivers and their parachute is equal to their weight.
Net force on mass = mass * acceleration
1)
accelerating up
T - 4850*9.8 = 4850 *.068
accelerating down
T - 4850*9.8 = -4850*.068
2) define up as +
- m g + .75 m g = m a
so
a = -.25 g
accelerating down
3)a) 132 *9.8 - .25*132*9.8 = 132 a
b) 132*9.8 -air resistance = 132*0