Answer:
The value of d is 183.51 m.
Explanation:
Given that,
Speed of car = 34.0 m/s
Suppose The car race in the circle parallel to the ground surface is at an angle 40°
The radius of circular path 
Normal force acting on the car = N
We need to calculate the value of d
Using component of normal force
The horizontal component of normal force is equal to the gravitational force.
....(I)
The vertical component of normal force is equal to the centripetal force
.....(II)
Divided equation (I) by equation (II)
Put the value of g
Put the value into the formula
Hence, The value of d is 183.51 m.
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Answer: The gravitational force Fg exerted on the orbit by the planet is Fg = G 4/3πr3rhom/ (R1 + d+ R2)^2
Explanation:
Gravitational Force Fg = GMm/r2----1
Where G is gravitational constant
M Mass of the planet, m mass of the orbit and r is the distance between the masses.
Since the circular orbit move around the planet, it means they do not touch each other.
The distance between two points on the circumference of the two massesb is given by d, while the distance from the radius of each mass to the circumferences are R1 and R2 from the question.
Total distance r= (R1 + d + R2)^2---2
Recall, density rho =
Mass M/Volume V
Hence, mass of planet = rho × V
But volume of a sphere is 4/3πr3
Therefore,
Mass M of planet = rho × 4/3πr3
=4/3πr3rho in kg
From equation 1 and 2
Fg = G 4/3πr3rhom/ (R1 + d+ R2)^2
Answer:
3.76 m/s
Explanation:
Instantaneous velocity: This can be defined as the velocity of an object in a non uniform motion. The S.I unit is m/s.
v' = dx(t)/dt..................... Equation 1
Where v' = instantaneous velocity, x = distance, t = time.
Given the expression,
x(t) = 28.0 m + (12.4 m/s)t - (0.0450 m/s³)t³
x(t) = 28 + 12.4t - 0.0450t³
Differentiating x(t) with respect to t.
dx(t)/dt = 12.4 - 0.135t²
dx(t)/dt = 12.4 - 0.135t²
When t = 8.00 s.
dx(t)/dt = 12.4 - 0.135(8)²
dx(t)/dt = 12.4 - 8.64
dx(t)/dt = 3.76 m/s.
Therefore,
v' = 3.76 m/s.
Hence, the instantaneous velocity = 3.76 m/s
In a collision, there is a force on both objects that causes an acceleration of both objects; the forces are equal in magnitude and opposite in direction. For collisions between equal-mass objects, each object experiences the same acceleration.
