Which property is expressed in distance units?

he adventurous robot M.A.N.D.I. is orbiting Saturn’s moon Dione. She wants to cause an impact with themoon to kick up some of th

GuDViN [60]

Answer:

v = 2.928 10³ m / s

Explanation:

For this exercise we use Newton's second law where the force is the gravitational pull force

F = ma

a = F / m

Acceleration is

a = dv / dt

a = dv / dr dr / dt

a = dv / dr v

v dv = a dr

We substitute

v dv = a dr

∫ v dv = 1 / m G m M ∫ 1 / r² dr

We integrate

½ v² = G M (-1 / r)

We evaluate from the lower limit v = 0 for r = R m to the upper limit v = v for r = R + 2.73 10³, where R is the radius of Saturn's moon

v² = 2G M (- 1 / R +2.73 10³+ 1 / R)

We calculate

v² = 2 6,674 10⁻¹¹ 1.10 10²¹ (10⁻³ / 5.61 - 10⁻³ /(5.61 + 2.73))

v² = 14.6828 10⁷ (0.1783 -0.1199)

v = √8.5748 10⁶

v = 2.928 10³ m / s

5 0

3 years ago

Two people stand facing each other at roller skating rink then push off each other

9966 [12]

a) 0 kg m/s

b) 0 kg m/s

c) +3 m/s

d) 60 N

Explanation:

a)

The momentum of an object is a vector quantity given by:

$p=mv$

where

m is the mass of the object

v is the velocity of the object

In this problem, we have a system of two people, so the total momentum will be the sum of the individual momenta of the two people:

$p=p_1 + p_2$

Which can be rewritten as

$p=m_1 u_1 + m_2 u_2$

where $m_1,m_2$ are the masses of the two people and $u_1,u_2$ their initial velocities.

However, the two people are initially at rest, so

$u_1 = 0\\u_2 = 0$

Therefore the total momentum is

$p=0+0=0$

b)

The principle of conservation of momentum states that when there are no external forces acting on a system, the total momentum of the system is conserved, so we can write:

$p_i = p_f$

where

$p_i$ is the total momentum of the system before

$p_f$ is the total momentum of the system after

In this problem,

$p_i = 0$

As we calculated in part a: this is because the total momentum of the two people before they push off each other is zero.

Therefore, according to the law of conservation of momentum,

$p_f = p_i = 0$

So the total momentum is zero also after they push off each other.

c)

The total momentum of the girl and the boy after they push off each other can be written as:

$p_f = m_1 v_1 + m_2 v_2$ (1)

where:

$m_1 = 30 kg$ is the mass of the girl

$v_1 = -5 m/s$ is her velocity (she moves backward, so the negative sign)

$m_2 = 50 kg$ is the mass of the boy

$v_2$ is the velocity of the boy

As calculated in part b), we also know that the total momentum of the girl and the boy is

$p_f = 0$ (2)

By combining eq(1) and eq(2) we get

$0=m_1 v_1 + m_2 v_2$

And solving for v2 we find the velocity of the boy:

$v_2=-\frac{m_1 v_1}{m_2}=-\frac{(30)(-5)}{50}=+3 m/s$

and the positive sign means he is moving forward.

d)

We can solve this part by applying the impulse theorem, which states that the change in momentum of an object is equal to the product between the force applied on it and the duration of the collision:

$\Delta p = F\Delta t$

where

$\Delta p$ is the change in momentum

F is the force

$\Delta t$ is the time during which the force is applied

In this problem:

$\Delta t = 2.5 s$

For the boy, the change in momentum is:

$\Delta p = m_2 (v_2 - u_2)$

And since

$m_2 = 50 kg\\u_2 = 0 m/s\\v_2 = 3 m/s$

We have

$\Delta p = (50)(3-0)=150 kg m/s$

So, the force exerted between the boy and the girl is:

$F=\frac{\Delta p}{\Delta t}=\frac{150}{2.5}=60 N$

8 0

3 years ago

You and your friends find a rope that hangs down 19m from a high tree branch right at the edge of a river. You find that you can

tangare [24]

Answer:

Explanation:

Given

length of rope $L=19\ m$

velocity while running $v=2\ m/s$

when the person jumps off the bank and hang on the rope then we can treat the person as pendulum with Time period T which is given by

$T=2\pi \sqrt{\frac{L}{g}}$

$T=2\pi \sqrt{\frac{19}{9.8}}$

$T=2\pi \times 1.392$

$T=8.74\ m/s$

Greatest Possible distance will be covered when person reaches the other extreme end of assumed pendulum (velocity=zero)

therefore he must hang on for 0.5 T time

$time=0.5\times 8.74=4.37\ s$

5 0

3 years ago

2. How is frequency described in mathematical terms?

alexdok [17]

Answer:

Explanation:

Frequency refers to the number of occurrences of a periodic event per time and is measured in cycles/second. In this case, there is 1 cycle per 2 seconds. So the frequency is 1 cycles/2 s = 0.5 Hz.

4 0

3 years ago

Read 2 more answers

Um corpo de massa 50g recebe 300 calorias e sua temperatura sobe de -10°C até 20°C. Determine a capacidade térmica do corpo e o

kykrilka [37]

The specific heat capacity of the substance is $0.963 J/g^{\circ}C$