A constant net force of 406 N, up, is applied to a stone that weighs 33 N. The upward force is applied through a distance of 2.4 m, and the stone is then released. To what height, from the point of release, will the stone rise?
Thoughts: F = ma. Would the acceleration be g? You would divide the weight by g to get the mass of the stone, correct?
The acceleration a is given by
a = F/m = 12.30 m/s^2
The velocity when released is
V = sqrt (2aX) = 7.68 m/s
The height H that it reaches after that is given by
gH = V^2/2
H = V^2/(2g)
Yes, you are correct! To solve this problem, you can use the equation F = ma, where F represents the net force, m represents the mass, and a represents the acceleration.
In this case, the net force applied to the stone is 406 N, upward. Since the stone is not accelerating vertically, the net force must be equal to the gravitational force acting on the stone.
The weight of the stone can be calculated by multiplying the mass (m) of the stone by the acceleration due to gravity (g). So you can find the mass of the stone by dividing its weight by the acceleration due to gravity.
In this case, the weight of the stone is 33 N, and the acceleration due to gravity is approximately 9.8 m/s^2. So, the mass of the stone would be 33 N / 9.8 m/s^2.
Once you have the mass of the stone, you can use the work-energy principle to determine the height to which the stone will rise.
The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done on the stone is equal to the force applied (406 N) multiplied by the distance over which it is applied (2.4 m).
The work done on the stone is also equal to the change in its potential energy. Since the stone is released, its initial kinetic energy is zero. So, all the work done on the stone will be converted into potential energy.
The potential energy of an object is given by the formula PE = mgh, where PE represents the potential energy, m represents the mass, g represents the acceleration due to gravity, and h represents the height.
Now, you can find the height (h) to which the stone will rise by rearranging the formula for potential energy:
h = (work done) / (mass * gravity)
Plugging in the values, you can calculate the height to which the stone will rise.