A force of 20 N gives an object an acceleration of 5m/s^2. (a) What force would be needed to give the same object an acceleration of 1m/s^2? (b) What force be needed to give it an acceleration of 10m/s^2?
To answer both questions, we need to use Newton's second law of motion, which states that the force applied to an object is equal to the mass of the object multiplied by its acceleration.
The formula to calculate the force (F) is given by:
F = m * a
where F is the force, m is the mass of the object, and a is the acceleration.
However, in this scenario, we are assuming the mass of the object remains constant. Therefore, we can compare the forces needed to achieve different accelerations without explicitly considering the mass.
Let's calculate the forces required for each acceleration:
(a) To find the force needed to give the object an acceleration of 1 m/s^2:
Using the formula F = m * a, we substitute the given acceleration, a = 1 m/s^2:
F = m * 1 (Since the mass is constant)
F = m N
So, the force required to give the object an acceleration of 1 m/s^2 would be 1 m/s^2.
(b) To find the force needed to give the object an acceleration of 10 m/s^2:
Using the same formula, F = m * a, we substitute the given acceleration, a = 10 m/s^2:
F = m * 10 (Since the mass is constant)
F = 10m N
So, the force required to give the object an acceleration of 10 m/s^2 would be 10 times the force required for an acceleration of 1 m/s^2, which means it would be 10 N.
In summary:
(a) The force needed to give the object an acceleration of 1 m/s^2 is 1 N.
(b) The force needed to give the object an acceleration of 10 m/s^2 is 10 N.