an adult elephant has an average shoulder height of 350 cm and average mass of 5,7000 kg. If an elephant initially at rest was to be lifted by a cable to a height of 20 m (a) What is the tension in the cable if the elephant is accelerating upwards at rate of 1.5 m/s²? (b) How long will it take for the elephant to travel distance
Bobo
To answer both part (a) and (b) of the question, we need to analyze the forces acting on the elephant.
(a) The tension in the cable is the force that lifts the elephant upwards. We can use Newton's second law of motion to calculate this tension.
Newton's second law states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = m * a). In this case, the acceleration is given as 1.5 m/s² and the mass of the elephant is 5,7000 kg.
Therefore, the tension in the cable can be calculated as:
Tension = mass * acceleration
Tension = 5,7000 kg * 1.5 m/s²
Tension = 85,500 N
So, the tension in the cable is 85,500 Newtons.
(b) To calculate the time it takes for the elephant to travel a certain distance, we need to use the equation of motion that relates distance, initial velocity, time, and acceleration.
The equation is:
Distance = (initial velocity * time) + (0.5 * acceleration * time^2)
In this case, the initial velocity of the elephant is 0 m/s, as it starts from rest. The distance travelled is given as 20 m, and the acceleration is 1.5 m/s².
Plugging in the values into the equation, we get:
20 m = (0 * t) + (0.5 * 1.5 m/s² * t^2)
Simplifying the equation, we have:
20 m = 0.75 m/s² * t^2
Rearranging the equation, we get:
t^2 = 20 m / 0.75 m/s²
t^2 = 26.67 s²
Taking the square root of both sides, we get:
t = sqrt(26.67 s²)
t ≈ 5.16 s
So, it will take approximately 5.16 seconds for the elephant to travel a distance of 20 meters.