if the force acting on an object stays the same, then the acceleration of the object is inversely proportional to its mass.If an object with an mass of 64 kilograms accelerates at a rate of 3 meters per second by a force, find the rate of acceleration of an object with an mass of 8 kilograms that is pulled by the same force.
a= 3m/s^2 * (64/8)
To find the rate of acceleration of an object with a mass of 8 kilograms that is pulled by the same force, we can use the principle that acceleration is inversely proportional to mass.
Here's how to do it step-by-step:
1. Start with the given information:
- Mass of the first object, m1 = 64 kilograms
- Acceleration of the first object, a1 = 3 meters per second
2. Use the formula for acceleration to find the force acting on the first object:
- Force, F = m1 * a1
- F = 64 kg * 3 m/s²
- F = 192 Newtons
3. Now, we want to find the rate of acceleration (a2) for an object with a mass of 8 kilograms.
4. Use the formula for force to find the rate of acceleration for the second object:
- F = m2 * a2
- F = 8 kg * a2
- Since the force acting on the object is the same, we know that F = 192 Newtons.
- Therefore, 8 kg * a2 = 192 N
5. Solve for a2 by dividing both sides of the equation by 8 kg:
- a2 = 192 N / 8 kg
- a2 = 24 meters per second squared
Therefore, the rate of acceleration for an object with a mass of 8 kilograms, pulled by the same force, is 24 meters per second squared.