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marta [7]
4 years ago
14

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.
Physics
1 answer:
Ilya [14]4 years ago
3 0
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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hot-air balloon is ascending at the rate of 14 m/s and is 84 m above the ground when a package is dropped over the side. (a) How
timurjin [86]

Answer:

a) t = 4.14 s

b) Speed with which it hits the ground = 40.58 m/s

Explanation:

Using the equations of motion,

g = 9.8 m/s², y = H = 84 m,

Initial velocity, u = 0 m/s,

final velocity, v = ?

Total Time of fall, t = ?

a) y = ut + gt²/2

84 = 0 + 9.8t²/2

4.9t² = 84

t² = 84/4.9

t = 4.14 s

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v = 0 + (9.8 × 4.14)

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4 years ago
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Find an expression for the kinetic energy of the car at the top of the loop.Express the kinetic energy in terms of m, g, h, and
lyudmila [28]

Answer:

K.E₂ = mg(h - 2R)

Explanation:

The diagram of the car at the top of the loop is given below. Considering the initial position of the car and the final position as the top of the loop. We apply law of conservation of energy:

K.E₁ + P.E₁ = K.E₂ + P.E₂

where,

K.E₁ = Initial Kinetic Energy = (1/2)mv² = (1/2)m(0 m/s)² = 0 (car initially at rest)

P.E₁ = Initial Potential Energy = mgh

K.E₂ = Final Kinetic Energy at the top of the loop = ?

P.E₂ = Final Potential Energy = mg(2R) (since, the height at top of loop is 2R)

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4 years ago
The titanium shell of an SR-71 airplane would expand when flying at a speed exceeding 3 times the speed of sound. If the skin of
Fed [463]

Answer:

The 10-meter long rod of an SR-71 airplane expands 0.02 meters (2 centimeters) when plane flies at 3 times the speed of sound.

Explanation:

From Physics we get that expansion of the rod portion is found by this formula:

\Delta l = \alpha\cdot l_{o}\cdot (T_{f}-T_{o}) (Eq. 1)

Where:

\Delta l - Expansion of the rod portion, measured in meters.

\alpha - Linear coefficient of expansion for titanium, measured in \frac{1}{^{\circ}C}.

l_{o} - Initial length of the rod portion, measured in meters.

T_{o} - Initial temperature of the rod portion, measured in Celsius.

T_{f} - Final temperature of the rod portion, measured in Celsius.

If we know that \alpha = 5\times 10^{-6}\,\frac{1}{^{\circ}C}, l_{o} = 10\,m, T_{o} = 0\,^{\circ}C and T_{f} = 400\,^{\circ}C, the expansion experimented by the rod portion is:

\Delta l = \left(5\times 10^{-6}\,\frac{1}{^{\circ}C} \right)\cdot (10\,m)\cdot (400\,^{\circ}C-0\,^{\circ}C)

\Delta l = 0.02\,m

The 10-meter long rod of an SR-71 airplane expands 0.02 meters (2 centimeters) when plane flies at 3 times the speed of sound.

4 0
3 years ago
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