Answer:
The first part can be solved via conservation of energy.

For the second part,
the free body diagram of the car should be as follows:
- weight in the downwards direction
- normal force of the track to the car in the downwards direction
The total force should be equal to the centripetal force by Newton's Second Law.

where
because we are looking for the case where the car loses contact.

Now we know the minimum velocity that the car should have. Using the energy conservation found in the first part, we can calculate the minimum height.

Explanation:
The point that might confuse you in this question is the direction of the normal force at the top of the loop.
We usually use the normal force opposite to the weight. However, normal force is the force that the road exerts on us. Imagine that the car goes through the loop very very fast. Its tires will feel a great amount of normal force, if its velocity is quite high. By the same logic, if its velocity is too low, it might not feel a normal force at all, which means losing contact with the track.
Answer:

Explanation:
Torque is defined as the cross product between the position vector ( the lever arm vector connecting the origin to the point of force application) and the force vector.

Due to the definition of cross product, the magnitude of the torque is given by:

Where
is the angle between the force and lever arm vectors. So, the length of the lever arm (r) is minimun when
is equal to one, solving for r:

The object represented by this graph is moving toward the origin at constant velocity.
Option 3.
<u>Explanation:</u>
In the figure, x-axis is representing increase in the time and y-axis is presenting increase in the distance from bottom to up. But the line in the graph which is plotted is decreasing from high distance to small distance with increase in time. So this indicates that as the time is increasing, the distance is decreasing.
And the object is moving toward the origin as the distance of the object motion is found to decrease with increase of time as per the graph. But the slope of the graph is found to be almost constant, this indicates that the velocity of the object is constant. Thus, the object represented by this graph is moving toward the origin at constant velocity.
Answer:
A 3 feet radius snowball will melt in 54 hours.
Explanation:
As we can assume that the rate of snowball takes to melt is proportional to the surface area, then the rate for a 3 feet radius will be:
T= A(3 ft)/A(1 ft) * 6 hr
A is the area of the snowballs. For a spherical geometry is computing as:
A=4.pi.R^2
Then dividing the areas:
A(3 feet)/A(1 foot) = (4 pi (3 ft)^2)/(4 pi (1 ft)^2) = (36pi ft^2)/(4pi ft^2)= 9
Finally, the rate for the 3 feet radius snowball is:
T= 9 * 6 hr = 54 hr
<span>In an earthquake, a P wave is a longitudinal wave. It moves through soil and rock as a C. series of compressions and rarefactions.</span>