It's time for Santa to deliver his presents. Assuming he delivers presents all over the world, he has to travel about 75,000,000
1 answer:
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Answer:
a) v = 1.01 m/s
b) a = 5.6 m/s²
Explanation:
a)
- If the disk is initially at rest, and it is applied a constant force tangential to the rim, we can apply the following expression (that resembles Newton's 2nd law, applying to rigid bodies instead of point masses) as follows:
- Where τ is the external torque applied to the body, I is the rotational inertia of the body regarding the axis of rotation, and α is the angular acceleration as a consequence of the torque.
- Since the force is applied tangentially to the rim of the disk, it's perpendicular to the radius, so the torque can be calculated simply as follows:
- τ = F*r (2)
- For a solid uniform disk, the rotational inertia regarding an axle passing through its center is just I = m*r²/2 (3).
- Replacing (2) and (3) in (1), we can solve for α, as follows:
- Since the angular acceleration is constant, we can use the following kinematic equation:
- Prior to solve it, we need to convert the angle rotated from revs to radians, as follows:
- Replacing (6) in (5), taking into account that ω₀ = 0 (due to the disk starts from rest), we can solve for ωf, as follows:
- Now, we know that there exists a fixed relationship the tangential speed and the angular speed, as follows:
- where r is the radius of the circular movement. If we want to know the tangential speed of a point located on the rim of the disk, r becomes the radius of the disk, 0.200 m.
- Replacing this value and (7) in (8), we get:
b)
- There exists a fixed relationship between the tangential and the angular acceleration in a circular movement, as follows:
- where r is the radius of the circular movement. In this case the point is located on the rim of the disk, so r becomes the radius of the disk.
- Replacing this value and (4), in (9), we get:
- Now, the resultant acceleration of a point of the rim, in magnitude, is the vector sum of the tangential acceleration and the radial acceleration.
- The radial acceleration is just the centripetal acceleration, that can be expressed as follows:
- Since we are asked to get the acceleration after the disk has rotated 0.2 rev, and we have just got the value of the angular speed after rotating this same angle, we can replace (7) in (11).
- Since the point is located on the rim of the disk, r becomes simply the radius of the disk,, 0.200 m.
- Replacing this value and (7) in (11) we get:
- The magnitude of the resultant acceleration will be simply the vector sum of the tangential and the radial acceleration.
- Since both are perpendicular each other, we can find the resultant acceleration applying the Pythagorean Theorem to both perpendicular components, as follows:
Answer:
part (a) towards north east direction.
part (b) s = 46.60 m
Explanation:
Given,
- velocity of the river due to east =
- velocity of the boat due to the north =
part (a)
River is flowing due to east and the boat is moving in the north, therefore both the velocities are perpendicular to each other and,
Hence the resultant velocity i,e, the velocity of the boat relative to the shore is in the North east direction. velocities are the vector quantities, Hence the resultant velocity is the vector addition of these two velocities and the angle between both the velocities are
Let 'v' be the velocity of the boat relative to the shore.
Let be the angle of the velocity of the boat relative to the shore with the horizontal axis.
Direction of the velocity of the boat relative to the shore.
part (b)
- Width of the shore = w = 300m
total distance traveled in the north direction by the boat is equal to the product of the velocity of the boat in north direction and total time taken
Let 't' be the total time taken by the boat to cross the width of the river.
Therefore the total distance traveled in the direction of downstream by the boat is equal to the product of the total time taken and the velocity of the river
Answer:
Explanation:
Given that,
The mass of the paperclip, m = 1.8 g = 0.0018 kg
We need to find the energy obtained. The relation between mass and energy is given by :
Where
c is the speed of light
So,
So, the energy obtained is .