A 5.0 kg particle and a 2.7 kg particle have a gravitational attraction with a magnitude of 2.2 10-12 N. What is the gravitational potential energy of the two-particle system?

a) A 5.0 kg particle and a 2.7 kg particle have a gravitational attraction with a magnitude of 2.2 10-12 N. What is the gravitational potential energy of the two-particle system?
(I got a) which is -4.451E-11 J)

b) If you triple the separation between the particles, how much work is done by the gravitational force between the particles?

c) How much work is done by you?

Well, the force depends on the inverese of distance squared, the energy is INT f*dx

The integral is constnt/r. The constant is Gm1M2. So, GPE must be Gm2m2/r, but

F=GM1M2/r^2 or r = sqrt GM2M1/F, so put that in, and you have E.

If you triple the distance, F is down to 1/9 of before.

Work done by you is the beginning energy at r and the final energy at 3r

I don't understand what you mean about the work I have done, is it the same as the magnitude as b)? different signs?

If you triple the distance, F is down by 1/9, so you have a new F to put in the formula...

GPE must be Gm2m2/r, but

F=GM1M2/r^2 or r = sqrt GM2M1/F, so put that in, and you have E.

Thank you, I GOT IT!

A diver descends from a salvage ship to the ocean floor at a depth of 35 m below the surface. The density of ocean water is 1.025x10^3 kg/m^3.

a) Calculate the guage pressure on the diver on the ocean floor.

b) Calculate the absolute pressure on the diver on the ocean floor.

The diver finda a rectangular aluminum plate having dimensions
1.0m x 2.0m x 0.03m. A hoisting cable is lowered from the ship and the diver connects it to the plate. The density of aluminum is 2.7x10^3 kg/m^3. Ignore the effects of viscosity.

c) Calculate the tension in the cable if it lifts the plate upward at a slow, constant velocity.

d) Will the tension in the hoisting cable increase, decrease, or remain the same if the plate accelerates upward at 0.05m/s^2? Justify your answer.

a. Pguage=pgh=1.025E3(9.8)(35)=351575n/m2

b. Pabsolute=Po+Pguage=452575
c. gives you density and volume so convert to kg as the mass. T=mg=1587.6 N
d. Increase F=ma, so when it is accelerating there is a greater force pushing down on it

a) To calculate the gauge pressure on the diver on the ocean floor, you can use the formula:

P_gauge = ρgh

Where ρ is the density of water, g is the acceleration due to gravity, and h is the depth below the surface.

Given:
ρ = 1.025x10^3 kg/m^3
g = 9.8 m/s^2
h = 35 m

Using these values in the formula, we can calculate:

P_gauge = (1.025x10^3 kg/m^3)(9.8 m/s^2)(35 m)
P_gauge = 3.41x10^5 Pa

b) To calculate the absolute pressure on the diver on the ocean floor, you need to add the atmospheric pressure to the gauge pressure. The atmospheric pressure is typically around 101,325 Pa.

So, the absolute pressure on the diver on the ocean floor is:

P_absolute = P_gauge + P_atmospheric
P_absolute = 3.41x10^5 Pa + 101,325 Pa
P_absolute = 4.52x10^5 Pa

c) To calculate the tension in the cable when it lifts the plate upward at a slow, constant velocity, you need to consider the forces acting on the plate. There are two forces: the gravitational force and the buoyant force.

The gravitational force can be calculated using the formula:

F_gravity = m*g

Where m is the mass of the plate and g is the acceleration due to gravity.

Given:
m = (1.0m)(2.0m)(0.03m)(2.7x10^3 kg/m^3) = 16.2 kg
g = 9.8 m/s^2

Using these values, we can calculate:

F_gravity = (16.2 kg)(9.8 m/s^2)
F_gravity = 158.76 N

The buoyant force can be calculated using the formula:

F_buoyant = ρ_fluid * V * g

Where ρ_fluid is the density of the fluid displaced by the plate, V is the volume of the plate, and g is the acceleration due to gravity.

Given:
ρ_fluid = 1.025x10^3 kg/m^3
V = (1.0m)(2.0m)(0.03m) = 0.06 m^3
g = 9.8 m/s^2

Using these values, we can calculate:

F_buoyant = (1.025x10^3 kg/m^3)(0.06 m^3)(9.8 m/s^2)
F_buoyant = 603.9 N

Since the plate is lifted upward at a slow, constant velocity, the tension in the cable must be equal to the sum of the gravitational force and the buoyant force:

Tension in the cable = F_gravity + F_buoyant
Tension in the cable = 158.76 N + 603.9 N
Tension in the cable = 762.66 N

d) If the plate accelerates upward at 0.05 m/s^2, the tension in the hoisting cable will increase. This is because the net force acting on the plate will be greater than just the sum of the gravitational force and the buoyant force.

The net force can be calculated using the formula:

Net force = mass * acceleration

Given:
mass = 16.2 kg
acceleration = 0.05 m/s^2

Using these values, we can calculate:

Net force = (16.2 kg)(0.05 m/s^2)
Net force = 0.81 N

Since the net force is nonzero, there must be an additional force acting on the plate to cause the acceleration. This additional force will increase the tension in the hoisting cable.

a) To calculate the gauge pressure on the diver on the ocean floor, we can use the formula P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height or depth.

Given:
Density of ocean water (ρ) = 1.025x10^3 kg/m^3
Depth of the ocean floor (h) = 35 m

Using the formula, we can calculate the gauge pressure as follows:
P = (1.025x10^3 kg/m^3) * (9.8 m/s^2) * (35 m)
P = 1.23925x10^6 Pa

b) The absolute pressure is the sum of the gauge pressure and the atmospheric pressure. Assuming the atmospheric pressure is approximately 1 atm or 101,325 Pa, we can calculate the absolute pressure as follows:
Absolute Pressure = Gauge Pressure + Atmospheric Pressure
Absolute Pressure = 1.23925x10^6 Pa + 101,325 Pa
Absolute Pressure = 1.34058x10^6 Pa

c) To calculate the tension in the cable if it lifts the plate upward at a slow, constant velocity, we need to consider the forces acting on the plate. The tension in the cable must match the weight of the plate to keep it at a constant velocity.

Given:
Dimensions of the aluminum plate:
Length (L) = 1.0 m
Width (W) = 2.0 m
Height (H) = 0.03 m
Density of aluminum (ρ) = 2.7x10^3 kg/m^3

Weight of the plate (W) = m * g, where m is the mass of the plate and g is the acceleration due to gravity.
The mass of the plate (m) = density * volume = ρ * L * W * H

Substituting the given values:
Mass of the plate (m) = (2.7x10^3 kg/m^3) * (1.0 m) * (2.0 m) * (0.03 m)
Mass of the plate (m) = 16.2 kg

Tension in the cable (T) should equal the weight:
T = W = m * g

Substituting the values:
T = (16.2 kg) * (9.8 m/s^2)
T = 158.76 N

d) If the plate accelerates upward at 0.05 m/s^2, the tension in the hoisting cable will increase. This is because the acceleration creates an additional force that needs to be counteracted by the tension in the cable. The equation for the net force on the plate is given by:

Net Force = T - m * a,

where T is the tension in the cable, m is the mass of the plate, and a is the acceleration. If the plate is accelerating upward, then the net force must be positive, meaning T > m * a. Therefore, the tension in the hoisting cable will increase.