A catapult used to hold a stone of mass 500g is extended by 20cm with an applied force.If the stone leaves with a velocity of 4om/s,what is the value of force?
To solve this problem, we can use the principles of work and energy. The work done on an object is equal to the force applied multiplied by the distance over which the force is applied. The work done on the stone will be equal to the kinetic energy gained by the stone.
First, let's convert the mass of the stone from grams to kilograms.
Mass of the stone = 500g = 0.5kg
Next, let's calculate the work done on the stone.
Work done = Force x distance
Distance = 20cm = 0.2m
Since the force is applied in extending the catapult, the distance over which the force is applied will be the distance by which the catapult is extended.
Work done = Force x 0.2m
The work done is equal to the kinetic energy gained by the stone. So we can write:
Force x 0.2m = 0.5kg x (40m/s)^2 / 2
40m/s is the final velocity of the stone, and we divide it by 2 because we are calculating the kinetic energy.
Now, let's rearrange the equation to solve for Force:
Force = (0.5kg x (40m/s)^2 / 2) / 0.2m
Calculating this expression will give us the value of the force applied on the stone.