Which of the following is a good thermal insulator?*<br> Iron<br> Styrofoam<br> Silver<br> Graphite

A 0.500-kg potato is fired at an angle of 80.0° above the horizontal from a PVC pipe used as a "potato gun" and reaches a height

lions [1.4K]

Answer:

(a) $47.15ms^{-1}$

(b) $2470.13ms^{-2}$

(c) 1235.06N and 252.05 as a ratio

Explanation:

From Newton's second law of motion

F=ma where m is mass, a is acceleration and F is net force

Also from kinetic equation of motion, velocity and displacement are related using equation

$v^{2}=u^{2}+2sa$

Where v is final velocity, u is initial velocity, a is acceleration and s is displacement

From the free body diagram attached, final velocity at maximum height is 0 and initial velocity is $usin80^{o}$

Also, the vertical component can be written as

$v_{y}^{2} }=u_{y}^{2} } -2gs$ The negative sign before 2gs means displacement is opposite the gravitational force

Where g is acceleration due to gravity, $u_{y}$ is vertical component of initial velocity and $v_{y}$ is vertical component of final velocity

Since $v_{y}$ is 0

$u_{y}^{2} } =2gs$

s=110 and g is taken as 9.8

$u_{y}=\sqrt{2*9.8*110}=46.43275$

$u_{y}=46.43ms^{-1}$

Also, it's evident that the vertical component of initial velocity is $u_{y}=u_{i}sin \theta$ where $\theta$ is angle of projection and $u_{i}$ is resultant velocity

Making $u_{i}$ the subject we obtain $u_{i}=\frac {u_{y}}{sin \theta}$

Since $u_{y}$ and $\theta$ are known as $46.43ms^{-1}$ and $80^{o}$ respectively, then $u_{i}=\frac {46.43ms^{-1}}{sin 80^{o}}=47.15ms^{-1}$

Therefore, the velocity of potato is $47.15ms^{-1}$

(b)

Displacement depends on length of tube hence s=0.450m hence going back to kinetic equation $v^{2}=u^{2}+2sa$

The final velocity v is answer in part a which is $47.15ms^{-1}$ , initial velocity u is $0ms^{-1}$ hence the equation is re-written as

$v^{2}=2sa$ and making a the subject we obtain

$a=\frac {v^{2}}{2s}$

$a=\frac {47.15^{2}}{2*0.450}=2470.13ms^{-2}$

Therefore, average acceleration is $2470.13ms^{-2}$

(c)

From Newton's second law of motion, F=ma where m=0.500kg and a is $2470.13ms^{-2}$

Therefore, the average force of potato is

F=0.5*2470.13=1235.06N

F=1235.06N

The weight, W of potato is given by W=mg

Taking R as ratio of average force and weight of potato

$R=\frac {F}{W}=\frac {F}{mg}$ and since F=1235.06, m=0.500kg and g=9.8

$R=\frac {1235.06}{0.500*9.8}$ =252.05

Therefore, ratio of average force to weight is 252.05

8 0

4 years ago

A 2 kg object being pulled across the floor with a speed of 10 m/sec is suddenly

zvonat [6]

Answer:

The frictional force producing this deceleration would have a magnitude of $4\; \rm N$ .

Explanation:

The velocity of this object changed by $\Delta v = (-10\; \rm m\cdot s^{-1})$ in $\Delta t = 5\; \rm s$ . The acceleration of this object would be:

$\begin{aligned}a &= \frac{\Delta v}{\Delta t} \\ &= \frac{-10\; \rm m\cdot s^{-1}}{5\; \rm s} = -2\; \rm m\cdot s^{-2}\end{aligned}$ .

Let $m$ denote the mass of this object. By Newton's Second Law of Motion, the net force on this object would be:

$\begin{aligned}F &= m \, a \\ &= 2\; \rm kg \times (-2\; \rm m\cdot s^{-2}) \\ &= -4\; \rm N\end{aligned}$ .

( $1\; {\rm kg \cdot m \cdot s^{-2} = 1\; {\rm N}$ .)

If the floor is level, friction would be the only unbalanced force on this object. Thus, the magnitude of the frictional force on this object would also be $4\; {\rm N}$ , same as the magnitude of the net force on this object.

5 0

3 years ago

A ball is moving at 3 m/s and has a momentum of 48 kg m/s. What is the ball's mass?

jonny [76]

$P = mv \\ m = \frac{P}{v} \\$

3 0

3 years ago

A nonconducting sphere is made of two layers. The innermost section has a radius of 6.0 cm and a uniform charge density of −5.0C

Leno4ka [110]

Answer:

a) E =0, b) E = 1,129 10¹⁰ N / C , c) E = 3.33 10¹⁰ N / C

Explanation:

To solve this exercise we can use Gauss's law

Ф = ∫ E. dA = $q_{int}$ / ε₀

Where we must define a Gaussian surface that is this case is a sphere; the electric field lines are radial and parallel to the radii of the spheres, so the scalar product is reduced to the algebraic product.

E A = $q_{int}$ /ε₀

The area of a sphere is

A = 4π r²

E = q_{int} / 4πε₀ r²

k = 1 / 4πε₀

E = k q_{int} / r²

To find the charge inside the surface we can use the concept of density

ρ = q_{int} / V ’

q_{int} = ρ V ’

V ’= 4/3 π r’³

Where V ’is the volume of the sphere inside the Gaussian surface

Let's apply this expression to our problem

a) The electric field in center r = 0

Since there is no charge inside, the field must be zero

E = 0

b) for the radius of r = 6.0 cm

In this case the charge inside corresponds to the inner sphere

q_{int} = 5.0 4/3 π 0.06³

q_{int} = 4.52 10⁻³ C

E = 8.99 10⁹ 4.52 10⁻³ / 0.06²

E = 1,129 10¹⁰ N / C

c) The electric field for r = 12 cm = 0.12 m

In this case the two spheres have the charge inside the Gaussian surface, for which we must calculate the net charge.

The charge of the inner sphere is q₁ = - 4.52 10⁻³ C

The charge for the outermost sphere is

q₂ = ρ 4/3 π r₂³

q₂ = 8.0 4/3 π 0.12³

q₂ = 5.79 10⁻² C

The net charge is

q_{int} = q₁ + q₂

q_{int} = -4.52 10⁻³ + 5.79 10⁻²

q_{int} = 0.05338 C

The electric field is

E = 8.99 10⁹ 0.05338 / 0.12²

E = 3.33 10¹⁰ N / C

8 0

3 years ago

Derive a general formula for projectile motion with the object launched at an angle

vagabundo [1.1K]

Answer:

y = x tan θ - (g / 2v₀² cos² θ) x²

Explanation:

An equation is called a general formula that relates the position on the x-axis and the height on the body's axis.

Let's write the position on each axis

X axis. No acceleration

x = v₀ₓ t

Y Axis. There is the acceleration of gravity

y = $v_{oy}$ t - ½ g t²

Let's clear the time in the first equation and substitute in the second

y = v₀ sin θ (x / v₀ₓ) - ½ g (x / v₀ₓ)²

y = v₀ sin θ / v₀ cos θ x - ½ g x² / v₀² cos² θ

y = x tan θ - (g / 2v₀² cos² θ) x²

This is the trajectory equation in projectile launching

6 0

3 years ago

Which of the following is a good thermal insulator?* Iron Styrofoam Silver Graphite