Two people, one of mass 51.4KG and the other mass of 78.0 KG, sit a distance between of 2.3 metres apart on a low friction sleds with the same friction coefficients.

A)what is the strength of the gravitational force between them?
B) suppose the friction is slowly reduced until one of the people started moving.Which will accelerate first?
C) what would the coefficient of the static friction between the sleds and the ground have to be for gravity to pull the two together?

A) To calculate the strength of the gravitational force between the two people, we can use Newton's law of universal gravitation. The formula is:

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

Where F is the gravitational force between the two objects, G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2), m1 and m2 are the masses of the two people, and r is the distance between them.

Plugging in the values given:

F = (6.67430 × 10^-11) * (51.4 * 78.0) / (2.3^2)

Calculating this equation will give you the strength of the gravitational force between them.

B) To determine which person will accelerate first when the friction is slowly reduced, we can consider Newton's second law of motion. The formula is:

F = m * a

Where F is the force applied to an object, m is its mass, and a is the acceleration.

Since the two people are on low friction sleds with the same friction coefficients, the only force acting on them is the gravitational force between them. So, when the friction is reduced to a point where it is negligible, both people will accelerate equally due to the gravitational force between them.

C) To find the coefficient of static friction between the sleds and the ground for gravity to pull the two people together, we need to consider the balances of forces.

When the two people are pulled together by gravity, there must be an equal and opposite static frictional force acting on the sleds in the opposite direction to gravity. The force of static friction can be calculated using the formula:

F = μs * N

Where F is the force of static friction, μs is the coefficient of static friction, and N is the normal force between the sleds and the ground.

To achieve a net force of zero (so that the sleds do not slide), the static friction force should be equal to or greater than the gravitational force between the two people. Therefore, we have:

μs * N ≥ G * (m1 * m2) / r^2

By substituting the values given and solving for μs, you can determine the required coefficient of static friction.