An elevator weighing 400kg is to be lifted up at a constant velocity of 0.6m/s for this purpose a motor of required horse power is used. (g=9.8m/s).(a)What is the acceleration of motor in case of upward motion? (b)What is power of motor?
constant velocity no acceleration so F = m g
Tension in cable = 400 * 9.80 = 3920 Newtons
power = force * speed = 3020 * 0.6 m/s
= 2352 Newton meters/sec or Watts
(a) To find the acceleration of the motor in the upward motion, we need to use Newton's second law of motion, which states that the force exerted on an object is equal to its mass multiplied by its acceleration.
In this case, the force exerted by the motor is equal to the weight of the elevator:
Force = Weight = mass * gravity
Given:
Mass of elevator (m) = 400 kg
Acceleration due to gravity (g) = 9.8 m/s²
Using the formula:
Force = m * g
Substituting the given values:
Force = 400 kg * 9.8 m/s²
Therefore, the force exerted by the motor is equal to 3,920 Newtons (N).
Since the elevator is moving up at a constant velocity, the net force on the elevator is zero. The force downward due to gravity is balanced by the force upwards by the motor. Therefore, the acceleration of the motor in the upward motion is zero.
(b) Power is defined as the rate at which work is done or energy is transferred. In this case, the power of the motor can be calculated using the formula:
Power = Force * Velocity
Given:
Force (F) = 3,920 N
Velocity (v) = 0.6 m/s
Using the formula:
Power = 3,920 N * 0.6 m/s
Therefore, the power of the motor is equal to 2,352 Watts (W).
To find the answers, we need to use some basic principles of physics.
(a) What is the acceleration of the motor in case of upward motion?
We can find the acceleration using Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration.
The force acting on the elevator can be calculated using the formula:
Force = Mass * Acceleration
In this case, the force is the weight of the elevator, which can be found using the formula:
Weight = Mass * Gravitational Acceleration
Since the elevator is being lifted up at a constant velocity, the acceleration of the motor will be equal to the gravitational acceleration. Therefore, the acceleration of the motor is 9.8 m/s^2.
(b) What is the power of the motor?
Power is the rate at which work is done or energy is transferred. In this case, the motor is doing work by lifting the elevator.
The power can be calculated using the formula:
Power = Work / Time
To find the work done by the motor, we need to calculate the force exerted by the motor and the distance over which the force is exerted. Since the elevator is lifted at a constant velocity, the net force acting on the elevator is zero (since the acceleration is zero).
The force exerted by the motor is equal to the weight of the elevator: Force = Weight
The work done by the motor can be calculated using the formula:
Work = Force * Distance
Since the elevator is lifted up at a constant velocity, the distance traveled by the elevator can be calculated using the formula:
Distance = Velocity * Time
Given that the velocity of the elevator is 0.6 m/s, we can substitute the values into the equation:
Distance = 0.6 m/s * Time
Substituting the value of distance into the equation for work, and substituting the values of force and work into the equation for power, we can calculate the power of the motor.
Power = (Force * Distance) / Time
Power = (Weight * (0.6 m/s * Time)) / Time
Since the weight of the elevator can be calculated using the formula:
Weight = Mass * Gravitational Acceleration
and substituting the value of weight into the equation for power:
Power = (Mass * Gravitational Acceleration * (0.6 m/s * Time)) / Time
Given that the mass of the elevator is 400 kg, and the gravitational acceleration is 9.8 m/s^2, we can substitute the values into the equation to find the power of the motor.
Power = (400 kg * 9.8 m/s^2 * (0.6 m/s * Time)) / Time
Please provide the value of time in order to calculate the power of the motor.