An object ob 2 kg mass is initially at rest on the ground. then, the object is pulled up by a 20N force in 4s before it is finally released. the maximum height that the one object can reach is ...
Remember that a weight force Mg = 19.6 N is also acting on the object in the opposite direction
While being pulled up, it accelerates at a rate
a = (F-M*g)/M = (20-19.6)/2 = 0.2 m/s^2
Its final velocity at release will be
a*t = 0.8 m/s.
From that release velocity, you can compute the height that it rises after release. It will acquire additional height (about 1.6 m) while being pulled
To determine the maximum height that the object can reach, we can use the principles of work, energy, and Newton's laws of motion.
First, let's calculate the work done on the object when it is pulled up by a 20N force.
The work done (W) is given by the formula:
W = Force × Distance × cos(θ)
Since the object is being pulled vertically upwards, the angle (θ) between the force and displacement is 0 degrees, and cos(0) = 1. Therefore, the work done can be calculated as:
W = 20N × Distance
Next, we can calculate the distance by using the formula for displacement:
Distance = Initial Velocity × Time + (1/2) × Acceleration × Time^2
Since the object is initially at rest, the initial velocity is 0 m/s. Also, the object is being pulled vertically upwards against the force of gravity, so the acceleration is equal to g, the acceleration due to gravity, which is approximately 9.8 m/s^2. Plugging in these values, the equation becomes:
Distance = (1/2) × 9.8 m/s^2 × (4s)^2
Simplifying:
Distance = 1/2 × 9.8 × 16
Distance = 78.4 meters
Now that we have the distance, we can calculate the work done:
W = 20N × 78.4m
W = 1568 Joules
The work done on the object represents the gain in potential energy. So, we can equate it to the change in gravitational potential energy:
W = mgh
where m is the mass of the object (2 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the maximum height the object reaches.
1568 Joules = 2kg × 9.8 m/s^2 × h
Simplifying:
h = 1568 J / (2 kg × 9.8 m/s^2)
h = 1568 J / 19.6 kg.m^2/s^2
h ≈ 80 meters
Therefore, the maximum height that the object can reach is approximately 80 meters.