The gravitation force is quartered when two objects' masses are halved without changing their distance.
Gravitational law states that the force of attraction and repulsion between two objects is directly proportional to the product of their masses and inversely proportional to the square of their distance apart.
F=(KM1 M2)/r^2
K= Gravitation force constant
M1M2 = masses of the object
r = distance between objects
When M1 and M2 are halved, it becomes M1/2 and M2/2
F=(K M1/2 x M2/2)/r^2
F=(K (M1 x M2)/4)/r^2
F=(KM1 x M2)/(4r^2 )
Recall
F=(KM1 x M2)/r^2
Therefore
F=F/4
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Answers:
a) 5400000 J
b) 45.92 m
Explanation:
a) The kinetic energy of an object is given by:
Where:
is the mass of the train
is the speed of the train
Solving the equation:
This is the train's kinetic energy at its top speed
b) Now, according to the Conservation of Energy Law, the total initial energy is equal to the total final energy:
Where:
is the train's initial kinetic energy
is the train's initial potential energy
is the train's final kinetic energy
is the train's final potential energy, where is the acceleration due gravity and is the height.
Rewriting the equation with the given values:
Finding :
Answer:
a. 8.96 m/s b. 1.81 m
Explanation:
Here is the complete question.
a) A long jumper leaves the ground at 45° above the horizontal and lands 8.2 m away.
What is her "takeoff" speed v
0
?
b) Now she is out on a hike and comes to the left bank of a river. There is no bridge and the right bank is 10.0 m away horizontally and 2.5 m, vertically below.
If she long jumps from the edge of the left bank at 45° with the speed calculated in part a), how long, or short, of the opposite bank will she land?
a. Since she lands 8.2 m away and leaves at an angle of 45 above the horizontal, this is a case of projectile motion. We calculate the takeoff speed v₀ from R = v₀²sin2θ/g. where R = range = 8.2 m.
So, v₀ = √gR/sin2θ = √9.8 × 8.2/sin(2×45) = √80.36/sin90 = √80.36 = 8.96 m/s.
b. We use R = v₀²sin2θ/g to calculate how long or short of the opposite bank she will land. With v₀ = 8.96 m/s and θ = 45
R = 8.96²sin(2 × 45)/9.8 = 80.2816/9.8 = 8.192 m.
So she land 8.192 m away from her bank. The distance away from the opposite bank she lands is 10 - 8.192 m = 1.808 m ≅ 1.81 m
Velocity means [ (speed) and (direction) ].
If you're traveling around a curve, then your direction is
always changing. So your velocity is always changing,
even if your speed isn't.