One of the predicted problems due to global warming is that ice in the polar ice caps will melt and raise sea level everywhere i
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A) When the plane is flying straight down, there are three forces acting on it:
- the centripetal force
, directed toward the center of the circle (so, horizontally)
- the weight of the plane:
, downward, so vertically
- a third force, given by the propulsion of the plane, which is accelerating it towards the ground (because the problem says that the plane has an acceleration of a=12 m/s^2 towards the ground)
The radius of the circle is
, so the centripetal force acting on the plane is
On the vertical axis, we have two forces: the weight
and the other force F given by the propulsion. Since we know that their sum should generate an acceleration equal to
, we can find the magnitude of this other force F by using Newton's second law:
So, the net force acting on the plane will be the resultant of the centripetal force (acting in the horizontal direction) and the two forces W and F (acting in the vertical direction):
(b) The tangent of the angle with respect to the horizontal is the ratio between the sum of the forces in the vertical direction (taken with negative sign, since they are directed downward) and the forces acting in the horizontal direction, so:
And so, the angle is
- the centripetal force
- the weight of the plane:
- a third force, given by the propulsion of the plane, which is accelerating it towards the ground (because the problem says that the plane has an acceleration of a=12 m/s^2 towards the ground)
The radius of the circle is
On the vertical axis, we have two forces: the weight
and the other force F given by the propulsion. Since we know that their sum should generate an acceleration equal to
So, the net force acting on the plane will be the resultant of the centripetal force (acting in the horizontal direction) and the two forces W and F (acting in the vertical direction):
(b) The tangent of the angle with respect to the horizontal is the ratio between the sum of the forces in the vertical direction (taken with negative sign, since they are directed downward) and the forces acting in the horizontal direction, so:
And so, the angle is
Answer:
a
The radial acceleration is
b
The horizontal Tension is
The vertical Tension is
Explanation:
The diagram illustrating this is shown on the first uploaded
From the question we are told that
The length of the string is
The mass of the bob is
The angle made by the string is
The centripetal force acting on the bob is mathematically represented as
Now From the diagram we see that this force is equivalent to
where T is the tension on the rope and v is the linear velocity
So
Now the downward normal force acting on the bob is mathematically represented as
So
=>
=>
The centripetal acceleration which the same as the radial acceleration of the bob is mathematically represented as
=>
substituting values
The horizontal component is mathematically represented as
substituting value
The vertical component of tension is
substituting value
The vector representation of the T in term is of the tension on the horizontal and the tension on the vertical is
substituting value
Answer:
The speed of the large cart after collision is 0.301 m/s.
Explanation:
Given that,
Mass of the cart,
Initial speed of the cart,
Mass of the larger cart,
Initial speed of the larger cart,
After the collision,
Final speed of the smaller cart, (as its recolis)
To find,
The speed of the large cart after collision.
Solution,
Let is the speed of the large cart after collision. It can be calculated using conservation of momentum as :
So, the speed of the large cart after collision is 0.301 m/s.