A 1 kg object is located at a distance of 1.7 x 10^6 m fom center of a larger object whose mass is 7.4 x 10^22 kg.

a. What is the size of the force acting on the smalle object?

b. What is the size of the force acting on the larger object?

c. What is the acceleration of the smaller object when it is released?

d. What is the acceleration of the larger object when it is released?

I need help in solving the problems.

a,b the forces are the same (GM1M2/distance^2)

c. a=F/m
d. a=F/M

can you show me the math for a and b because I keep getting the answer 2.90 N.

Sure, I'd be happy to help! But before we get started, I have to warn you, my answers might be a little clowny. Now, let's dive in!

a. To find the size of the force acting on the smaller object, we can use the formula for gravitational force: F = (G * m1 * m2) / r^2. Here, m1 is the mass of the smaller object, m2 is the mass of the larger object, r is the distance between their centers, and G is the gravitational constant.

Plugging in the values, we have:
F = (6.67430 x 10^-11 N(m^2/kg^2) * 1 kg * 7.4 x 10^22 kg) / (1.7 x 10^6 m)^2

Now, I'll leave the actual calculation to you. But remember, you can always ask me for a little clownish nudge if you need it!

b. The size of the force acting on the larger object is the same as the force acting on the smaller object, as per Newton's third law! So the force would be the same as your calculated value in part a.

c. To find the acceleration of the smaller object when it is released, we can use Newton's second law: F = m * a. Here, F is the force, m is the mass of the smaller object, and a is the acceleration.

In this case, we already know the force from part a, and we can simply rearrange the formula to solve for acceleration:
a = F / m

Again, try plugging in the values and calculating this yourself, but if you need my comical assistance, just let me know!

d. The acceleration of the larger object when it is released would be negligible because of its significantly greater mass compared to the smaller object. The smaller object's mass is only 1 kg, while the larger object's mass is 7.4 x 10^22 kg. Therefore, the acceleration of the larger object would be so small that it can be considered as effectively zero.

And voila! I hope I didn't cause any comedic collisions while helping you out with these physics questions. Remember, physics can be fun if you sprinkle a little clown humor into it!

To solve these problems, we can use Newton's law of gravitation. According to the law, the force of gravity between two objects is given by:

F = G * (m1 * m2) / r^2

where:
F is the force of gravity,
G is the gravitational constant (approximately 6.674 × 10^-11 N m^2/kg^2),
m1 and m2 are the masses of the objects, and
r is the distance between their centers.

Let's solve each part of the problem step-by-step:

a. What is the size of the force acting on the smaller object?

Given:
Mass of the smaller object (m1) = 1 kg
Mass of the larger object (m2) = 7.4 x 10^22 kg
Distance between their centers (r) = 1.7 x 10^6 m

Using Newton's law of gravitation:
F = G * (m1 * m2) / r^2

Plugging in the values:
F = (6.674 × 10^-11 N m^2/kg^2) * (1 kg * 7.4 x 10^22 kg) / (1.7 x 10^6 m)^2

Calculating:
F ≈ 5.309 N

Therefore, the size of the force acting on the smaller object is approximately 5.309 N.

b. What is the size of the force acting on the larger object?

Since the force of gravity is mutual, the force acting on the larger object is equal in magnitude but opposite in direction to the force on the smaller object. Therefore, the size of the force acting on the larger object will also be approximately 5.309 N.

c. What is the acceleration of the smaller object when it is released?

We can use Newton's second law of motion to find the acceleration:

F = m * a

where:
F is the force acting on the object,
m is the mass of the object, and
a is the acceleration of the object.

Rearranging the formula:
a = F / m

Plugging in the values:
a = 5.309 N / 1 kg

Calculating:
a = 5.309 m/s^2

Therefore, the acceleration of the smaller object when it is released is 5.309 m/s^2.

d. What is the acceleration of the larger object when it is released?

Just like in part c, we can use Newton's second law of motion to find the acceleration:

F = m * a

Rearranging the formula:
a = F / m

Plugging in the values:
a = 5.309 N / (7.4 x 10^22 kg)

Calculating:
a ≈ 7.176 x 10^-23 m/s^2

Therefore, the acceleration of the larger object when it is released is approximately 7.176 x 10^-23 m/s^2.

Sure, I can help you solve these problems step by step.

a. To find the size of the force acting on the smaller object, we can use the formula for gravitational force:

F = (G * (m1 * m2)) / r^2

Where:
F is the force of gravity between the two objects,
G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^−1 s^−2),
m1 is the mass of the smaller object (1 kg),
m2 is the mass of the larger object (7.4 x 10^22 kg),
r is the distance between the centers of the two objects (1.7 x 10^6 m).

Plugging in the given values into the formula, we have:
F = (6.67430 × 10^-11) * ((1 kg) * (7.4 x 10^22 kg)) / (1.7 x 10^6 m)^2

Solving this equation will give us the size of the force acting on the smaller object.

b. To find the size of the force acting on the larger object, we can use the same formula for gravitational force. However, in this case, we need to consider that the force acts in the opposite direction. So the magnitude of the force will be the same, but the direction will be opposite.

c. To find the acceleration of the smaller object when it is released, we can use Newton's second law of motion:

F = m * a

Where:
F is the force acting on the smaller object (found in part a),
m is the mass of the smaller object (1 kg),
a is the acceleration of the smaller object (the value we need to find).

Rearranging the formula, we have:
a = F / m

Plugging in the values we found in part a, we can calculate the acceleration of the smaller object.

d. Similarly, to find the acceleration of the larger object when it is released, we can use the same formula as part c, but this time considering the force acting on the larger object (found in part b) and the mass of the larger object (7.4 x 10^22 kg).

Let me know if you need further assistance with the calculations.