A constant force is applied to an object, causing the object to accelerate at 6.00 m/s^2. What will the acceleration be if:
a.The force and the object's mass are both doubled?
b.The force is doubled and the object's mass is halved?
F = ma,
a = f/m,
a. a = 2f/2m = f/m = no change = 6.00
m/s^2.
b. a = 2f/0.5m = 4 + f/m =4 * 6 = 24
m/s^2.
To solve these problems, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration (F = ma). Let's break down each scenario step by step.
a. If the force and the object's mass are both doubled:
1. Let's assume the initial force is F1 and the initial mass is m1.
2. The initial acceleration can be calculated using Newton's second law: F1 = m1 * a1.
3. Since we are doubling both the force and the mass, the new force is 2F1 and the new mass is 2m1.
4. The new acceleration (a2) can be calculated using the new force and mass: 2F1 = (2m1) * a2.
5. Solving for a2, we get a2 = (2F1) / (2m1) = F1 / m1 = a1.
6. Therefore, the acceleration remains the same, and in this case, it will still be 6.00 m/s^2.
b. If the force is doubled and the object's mass is halved:
1. Let's assume the initial force is F1 and the initial mass is m1.
2. The initial acceleration can be calculated using Newton's second law: F1 = m1 * a1.
3. Since the force is doubled, the new force is 2F1. Since the mass is halved, the new mass is m1 / 2.
4. The new acceleration (a2) can be calculated using the new force and mass: 2F1 = (m1 / 2) * a2.
5. Solving for a2, we get a2 = (2F1) / (m1 / 2) = 4F1 / m1.
6. Therefore, the new acceleration (a2) will be four times the initial acceleration (a1), which is 4 * 6.00 m/s^2 = 24.00 m/s^2.
So, the answers are:
a. The acceleration will remain the same, and it will be 6.00 m/s^2.
b. The acceleration will be 24.00 m/s^2.
To find the acceleration in each case, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
a. If the force and the object's mass are both doubled:
According to Newton's second law, we can write the equation:
Force = mass × acceleration
Let's say the initial force is F and the initial mass is m. The initial acceleration is given as 6.00 m/s^2. So we have:
F = m × 6.00
If we double both the force and the mass, the equation becomes:
(2F) = (2m) × acceleration
Substituting the initial values, we get:
2F = (2m) × acceleration = 2(m × 6.00)
Since we doubled both the force and the mass, the acceleration remains the same at 6.00 m/s^2.
b. If the force is doubled and the object's mass is halved:
Using the same equation as before, we have:
(2F) = (0.5m) × acceleration
Substituting the initial values, we get:
2F = (0.5m) × acceleration = (m × 6.00)
To solve for the new acceleration, we need to isolate it in the equation:
2 × 6.00 = 0.5 × acceleration
12 = 0.5 × acceleration
Dividing both sides by 0.5 gives us:
acceleration = 12 / 0.5 = 24 m/s^2
Therefore, if the force is doubled and the object's mass is halved, the acceleration will be 24.00 m/s^2.