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levacccp [35]
3 years ago
13

The virtual image produced by a convex mirror is one third the size of the object.(a) If the object is 51 cm in front of the mir

ror, what is the image distance? (Include the sign of each answer.)cm(b) What is the focal length of this mirror?cm
Physics
1 answer:
Nimfa-mama [501]3 years ago
4 0

(a) -17 cm

Magnification equation:

\frac{h_i}{h_o}=-\frac{q}{p}

where

h_i is the size of the image

h_o is the size of the object

q is the distance of the image from the mirror

p is the distance of the object from the mirror

In this problem, we have:

p = 51 cm (the object is 51 cm in front of the mirror)

\frac{h_i}{h_o}=\frac{1}{3}

So, we can find q, the image distance:

q=-\frac{h_i}{h_o}p=-\frac{1}{3}(51 cm)=-17 cm

and the negative sign means the image is virtual.

(b) -25.5 cm

Mirror equation:

\frac{1}{f}=\frac{1}{p}+\frac{1}{q}

where

p = 51 cm

q = -17 cm

Substituting and re-arranging the equation, we find the focal length of the mirror:

\frac{1}{f}=\frac{1}{51 cm}-\frac{1}{17 cm}=-\frac{2}{51 cm}\\f=-\frac{51 cm}{2}=-25.5 cm

and the negative sign is due to the fact it is a convex mirror.

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Explanation:

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What is know:

Height (h) = 193 cm

Gravity (g) =  981 cm/s^{2}

Initial Velocity = 0

First, we can know how long it take to the drop to travel to the floor. It can be done with the following equation:

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Where:

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Vo is the Initial Velocity  which is zero

t is the time the time it takes the drop to travel from the shower to the floor

a is the aceleration, which in this case is the gravity.

With the Initial Velocity equals zero the equations simply:

193 cm = \frac{1}{2}gt^{2}

To search for the time:

t =\sqrt{\frac{2*193cm}{981cm/s^{2} } }

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This is the time it takes a drop to fall to the floor, with this time and knowing other 3 drops have driped from the shower by this time. We can calculate how much time it takes the shower to drip each drop.

Time for Drip = t/4

Time for Drip = 0.156

This time is the difference between each drop, using the same equation we can calculate where was each drop, because now it is know how much time had each drop after being drip from the shower.

Our first is already on the floor (193 cm) with 0.627 s, The second drops have been falling for (0.627s - 0.156) 0.471 s and our third drop for (0.627s - 0.156 - 0.156) 0.315 s

We can use (1) to know how far have each drop traveled on these times. We know the Initials Velocity are 0, know we need ot know the distances.

For the second drop:

x = \frac{1}{2} (981cm/s^{2})(0.471s)^{2}

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For the third drop:

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d.Both points have the same instantaneous angular velocity.

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Let's analyze each option one by one:

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\omega=\frac{\theta}{t}

where \theta is the angular displacement and t is the time taken. Therefore, all the points rotate by the same angle \theta in the same time t.

b.Both points have the same centripetal acceleration.  --> FALSE. The centripetal acceleration of a point along the disk is given by

a_c=\omega^2 r

where \omega is the angular velocity and r is the distance of the point from the axis of rotation. Here A is located farther away from the axis with respect to B, so it will have a greater centripetal acceleration.

c.Both points have the same tangential acceleration.  --> FALSE. The tangential acceleration is given by

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where \alpha is the angular acceleration. \alpha is the same for every point for a rigid body, but r is not (A is located farther away), so A and B do not have same tangential acceleration.

d.Both points have the same instantaneous angular velocity.  --> TRUE. This is true for what we said at point A).

e.Each second, point A turns through a greater angle than point B. --> FALSE. The two points cover the same angular displacement in the same time, since they have same angular velocity.

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Answer:

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c_{p} = specific heat of pallet = specific heat of iron

T_{pi} = Initial temperature of pellet = 200 C

m_{w} = mass of water = 50 g = 0.050 kg

c_{w} = specific heat of water

T_{wi} = Initial temperature of water = 20 C

T_{e} = Final equilibrium temperature

Also given that

c_{w} = 9 c_{p}

Using conservation of energy

Energy gained by water = Energy lost by pellet

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hence the correct choice is

a. closer to 20∘C

4 0
3 years ago
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