In 2005, the space probe Deep Impact launched a 370 kg projectile into Comet Temple 1. Observing the collision helped scientists learn about the comet’s characteristics. The comet is estimated to have a mass of about 9.0 x 10^13 kg.a. Assuming the estimated mass of the comet at that time was correct, at what distance from the comet’s centre was the gravitational force between the comet and the projectile 32 N?

b. Deep Impact also released a probe to fly by the comet and record images of the collision. Determine the strength of the comet’s gravitational field at the probe’s distance of 5.0 x 103 km from the comet.

Answers

Answer 1

Answer: Parta a.

Equation: F = G*m1*m2/d^2

Where
F = 32 N
G = 6.67*10^-11 N.m^2/kg^2
m1 = 9.0*10^13kg
m2 =370 kg
d = distance that separate the center of the two objects.

d^2 = G*m1*m2 / F = 6.67*10^-11 N.m^2/kg^2 * 9.0*10^13 kg *370 kg / 32N = 69,409.69 m^2

d = √69,409.69m^2 = 263.5 m

Part B.

The gravitational field of the comet is g = G*m1/d^2

Notice that it does not depend on the mass of other objects.

Notice also that I will use a distance of 5.0 * 10^3 km, because I think that that is the number that you intended to write in the part b. If that is not the number you can put the right number instead because the solution is written step by step.

g = (6.67*10^-11 N*m^2/kg^2)*(9.0*10^13kg)/(5.0*10^3*10^3m)^2 = 2.4*10^-4 N/kg = 2.4*10^-4 m/s^2

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On a highway curve with radius 30 m, the maximum force of static friction (centripetal force) that can act on a 1,423-kg car going around the curve is 8,127 n. what speed limit should be posted for the curve so that cars can negotiate it safely?

Answers

To determine the speed limit for the curve, we can use the centripetal force equation. The centripetal force (Fc) is given by the equation Fc = (m * v^2) / r, where m is the mass of the car, v is the velocity, and r is the radius of the curve.

In this case, the maximum force of static friction acting as the centripetal force is given as 8,127 N, the mass of the car is 1,423 kg, and the radius of the curve is 30 m.

We can rearrange the equation to solve for the velocity (v):

v = sqrt((Fc * r) / m)

Now, let's substitute the given values into the equation:

v = sqrt((8,127 N * 30 m) / 1,423 kg)

v ≈ 13.57 m/s

Therefore, to ensure that cars can negotiate the curve safely, the speed limit should be posted at approximately 13.57 m/s (or about 49 km/h). It's important to note that this is only a rough estimate, and other factors such as road conditions and driver behavior should also be taken into consideration when setting speed limits.

Final answer:

The speed at which a car can safely navigate a given curve is determined by the equation for centripetal force and the maximum static friction that prevents the car from slipping. Calculating this speed using the given force of static friction (8,127 N), mass of the car (1,423 kg) and the radius of the curve (30 m), we get a result of roughly 22.6 m/s or 81.4 km/h.

Explanation:

The problem involves finding the speed at which a car can safely navigate a highway curve without slipping, given a set radius and maximum force of static friction. This is a physics scenario involving centripetal force and friction. Centripetal force is the net force causing circular motion and static friction is the friction that acts to prevent the car from slipping off the road.

In this scenario, the maximum static friction matches the required centripetal force for a safe curve negotiation. Hence, the equation for centripetal force, Fc = mv²/r, applies here. In this expression, Fc is the centripetal force, m is the mass of the car, v is the velocity or speed, and r is the radius of the curve. Given that Fc = 8,127N, m = 1,423 kg, and r = 30 m, we can rearrange the formula to find v = √(Fc ∗ r / m).

Running the calculation, v = √((8,127 N * 30m) / 1,423 kg), results in a speed limit of roughly 22.6 m/s. However, as speed limits are not posted in meters per second, it is appropriate to convert the speed to kilometers per hour. Multiply the result by (3600 s/h / 1000 m/km) to convert it into km/h which gives a speed limit of about 81.4 km/h.

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The indicators that a chemical reaction is occurring include:

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Signs that show that chemical reaction is occurring

Formation of Bubbles (Gas Evolution): The production of gas bubbles can signify a chemical reaction. This often happens when reactants combine to release a gaseous product, such as in the reaction of an acid with a carbonate, producing carbon dioxide.

Change in Color: A noticeable change in color can indicate a chemical reaction. It suggests that the arrangement of atoms in the molecules has changed, leading to the absorption or emission of specific wavelengths of light.

Formation of a Precipitate: A precipitate is an insoluble solid formed when two solutions are mixed. It suggests that a chemical reaction has occurred because the reactants have combined to create an insoluble product.

The indicators that a chemical reaction is occurring include all the following

the formation of bubbles, a change in color, the formation of a liquid and the formation of a precipitate

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Hi there! When a chemical Reaction happens, the tell tale signs are as listed:
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Which describes the relationship between potential and kinetic energy of a ball thrown up in the air as it falls back to the ground? A.
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The ball originally contains potential energy and no kinetic energy, therefore we can use the theory of conservation of mechanical energy. Its total energy, which is made up of the KE and PE, is constant and equal to its starting PE as it falls. Thus, option C is correct.

What potential and kinetic energy of a ball thrown up?

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As it rises, the ball's speed slows until the very apex of its motion, where it briefly pauses. At the peak, it accelerates at -9.8 m/s2.

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The answer is c, because ball is falling so its gravitationl potential energy decreases, but it kinetic energy increases. Energy is always conserved.

You are twice as likely to become good friends with the person who is in the dorm room next to you than the person two doors down. This is due to:A. Proximity.
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Answers

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The correct answer is A

Potential and kinetic energy 1. An apple falling from a tree
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Here's how potential and kinetic energy relate to the scenarios you've mentioned:

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2. A stationary ball on the ground: No kinetic energy (it's not moving), but it has potential energy due to its position above the ground.

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5. A car traveling on the road: The car has both kinetic energy (due to its motion) and potential energy (due to its position above the road).

6. A stretched rubber band: The stretched rubber band has potential energy stored in its stretched configuration.

7. A basketball being thrown: The basketball has both kinetic energy (while it's in motion) and potential energy (when it's at the highest point of its trajectory).

8. A girl biking at the park: Similar to the boy running, the girl on the bike has both kinetic and potential energy.

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In general, potential energy is associated with an object's position or state, while kinetic energy is associated with its motion.

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