select the correct image. each pair of clay balls represents two planetesimals. if each planetesimal is composed of the same material and is separated by the same distance, which pair experiences the greatest gravitational attraction?
Options:
A.) Top Right
B.) Top Left
C.) Bottom right
D.) Bottom left
Answer:
A.) Top Right
Explanation:
The pair in the top right corner is the one which experiences the greatest gravitational attraction.
From the picture, of all the pairs of clay balls that represent two planetesimals, the one on the top right will experience the greatest gravitational attraction.
The gravitational force is given by:
F = GmM / r^2 (1)
Where:
- G is the gravitational constant = 6.67x10⁻¹¹ N*m²*kg⁻²
- m and M are the masses of the first and second balls
- r is the distance between the planetesimals
From equation (1), we can see that the gravitational force is directly proportional to the masses of the planetesimals and inversely proportional to the distance. The pair of planetesimals with bigger balls (more mass) will have the greatest gravitational attraction since the distance is the same for each of them.
In the picture, of all the planetesimals, the second one (top right) will have the greatest gravitational attraction since its pair of balls are the largest (bigger product m*M). On the contrary, the pair of balls on the down left will have the lowest gravitational attraction (they are the smallest).
Therefore, the pair of balls on the top right will experience the greatest gravitational attraction.
In order to determine which pair of clay balls experiences the greatest gravitational attraction, we need to consider a few factors.
First, it's important to understand that gravitational attraction depends on two main factors: the mass of the objects involved and the distance between them. The greater the mass of an object, the stronger its gravitational pull. And the closer two objects are to each other, the stronger their gravitational attraction.
Looking at the given information, it states that each planetesimal is composed of the same material. This means that the mass of each clay ball is the same in each pair.
Now, let's analyze the distance factor. It is mentioned that each planetesimal is separated by the same distance in each pair. This means that the distance between the clay balls is the same for all pairs.
Based on this information, we can conclude that the gravitational attraction will be the same for all pairs of clay balls. Since the mass and distance are constant across all pairs, the gravitational attraction will be equal.
Therefore, none of the pairs will experience greater gravitational attraction than the others.
Explanation:
The weight of the two blocks acts downwards.
Let the weight of the two blocks be W. Solving for T₁ and T₂:
w = T₁/cos 60° -----(1);
w = T₂/cos 30° ----(2);
equating (1) and (2)
T₁/cos 60° = T₂/cos 30°;
T₁ cos 30° = T₂ cos 60°;
T₂/T₁ = cos 30°/cos 60°;
T₂/T₁ =1.73.
Therefore, option a is false since T₂ > T₁.
Option B is true since T₁ cos 30° = T₂ cos 60°.
Option C is true because the T₃ is due to the weight of the two blocks while T₄ is only due to one block.
Option D is wrong because T₁ + T₂ > T₃ by simple summation of the two forces, except by vector addition.
D. Heat each cube to the same temperature, place each cube into different containers with 500 grams of water at the same temperature, and measure the temperature of the water.
Explanation:
First find the distance it takes to stop
s = [v^2-u^2]/2a = 0^2 - 8.7^2/2[-2.4] = 8.7^2/4.8
Next find the time it takes to go that distance , s = ut +[1/2] at^2
8.7^2/4.8 = 8.7t +[1/2] [ -2.4]t^2 , rearrange and
t^2 -[8.7/1.2]+ 8.7^2/[(1.2)(4.8)]=0 complete the square
[t - (8.7/2.4)]^2=0
t = 8.7/2.4 = 3.625 secs
At this stage the deceleration will push the object back in the direction it came from for another 3.625 secs when it will be 8.7 m/s again
Total time , T =2t = 7.25 secs.
Note:
The term differential is used in calculus to refer to an infinitesimal (infinitely small) change in some varying quantity. For example, if x is a variable, then a change in the value of x is often denoted Δx (pronounced delta x). The differential dx represents an infinitely small change in the variable x.
First sum applied the Newton's second law motion: F = ma
Force = mass* acceleration
This motion define force as the product of mass times Acceleration (vs.Velocity). Since acceleration is the change in velocity divided by time,
force=(mass*velocity)/time
such that, (mass*velocity)/time=momentum/time
Therefore we get mass*velocity=momentum
Momentum=mass*velocity
Elephant mass=6300 kg; velocity=0.11 m/s
Momentum=6300*0.11
P=693 kg (m/s)
Dolphin mass=50 kg; velocity=10.4 m/s
Momentum=50*10.4
P=520 kg (m/s)
The elephant has more momentum(P) because it is large.
Weight of barbell (m) = 100 kg
Uplifted to height (h) = 2m
Time taken= 1.5 s
Work done by Jordan = potential energy stored in barbell = mgh
= 100×2×9.8
= 1960J
Power = energy/time
= 1960/1.5
1306.67watts
Weight of jasmine (m) = 400 N
Height climbed on wall (h) = 5m
Total time taken in climbing = 5 sec
Work done in climbing the wall = rise in potential energy = mgh
= 400×9.8×51
= 19600J
Power generated by Jasmine = potential energy / time
= 19600/5
= 3920Watts
The horizontal and vertical motions of balloons are independent from each other.
Let vertical component of initial velocity U' horizontal component of initial velocity U"
Time of landing (t) is found with the help of vertical motion.
Since vertical component of initial velocity of balloon is zero(U' = 0)
From equation h = U't + 1/2gt^2
h = 1/2gt^2
t = √(2h/g)
t = √( 2×150/9.8)
t = 5.53 sec
Horizontal velocity = 50m/s
Horizontal range of balloon, R = U"t
= 50× 5.53
= 27.65m
So the balloon will go 27.65 metre away from the bridge
72
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