A force acts on a 2kg mass and gives it an acceleration of 3 m/s^2. what acceleration is produced by the same force when acting on a mass of
(1) 1kg? (2) 4kg? (3) how large is the force?
(3) F = m a
so
F = 2 * 3 = 6 Newtons
(2) 6 = 1 * a
so a = 6 m/s^2
(1) 6=4 * a
a = 1.5 m/s^2
The Answer's of this question are as follows-
(1)1.5m/s^2
(2)6m/s^2
(3)6N
To find the acceleration produced by the same force when acting on different masses, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by the acceleration produced.
Given:
Mass of the first object (m1) = 2 kg
Acceleration of the first object (a1) = 3 m/s²
We can calculate the force (F) using the formula:
F = m * a
1) For a mass of 1 kg:
m2 = 1 kg
Using the formula, F = m * a
F = 1 kg * 3 m/s²
F = 3 N
Therefore, the same force will produce an acceleration of 3 m/s² when acting on a 1 kg mass.
2) For a mass of 4 kg:
m3 = 4 kg
Using the formula, F = m * a
F = 4 kg * 3 m/s²
F = 12 N
Therefore, the same force will produce an acceleration of 3 m/s² when acting on a 4 kg mass.
3) To determine the magnitude of the force:
We can use the value of the mass (m1) and the acceleration (a1) given initially.
F = m * a
F = 2 kg * 3 m/s²
F = 6 N
Therefore, the magnitude of the force is 6 N.
To find the acceleration produced by the same force when acting on different masses, we can use Newton's second law of motion. According to Newton's second law, the force (F) acting on an object is equal to the mass (m) multiplied by the acceleration (a), or F = ma.
Let's answer each part of the question step by step:
(1) For a mass of 1kg:
We already know that the force applied is causing a 2kg mass to accelerate at 3 m/s^2. To find the acceleration when acting on 1kg, we can use the same formula, F = ma, and rearrange it to solve for acceleration (a). So we have: a = F/m.
Since the force (F) remains the same, we can substitute the known values as follows:
a = (2kg * 3 m/s^2) / 1kg
a = 6 m/s^2
Therefore, when the same force acts on a 1kg mass, the acceleration produced is 6 m/s^2.
(2) For a mass of 4kg:
Again, we can use the same formula, F = ma, and rearrange it to solve for acceleration (a):
a = F/m.
Since the force (F) remains the same, we can substitute the known values as follows:
a = (2kg * 3 m/s^2) / 4kg
a = 1.5 m/s^2
Therefore, when the same force acts on a 4kg mass, the acceleration produced is 1.5 m/s^2.
(3) To determine the force (F):
Given that the force is acting on a 2kg mass and producing an acceleration of 3 m/s^2, we can rearrange the formula F = ma to solve for force (F).
F = m * a
F = 2kg * 3 m/s^2
F = 6 N
Therefore, the force acting on the 2kg mass is 6 Newtons.