Question 1.

Darts is a popular game where we can calculate at what speeds the arrow must be thrown to
frame specific fields on the dartboard, which are shown on the left. Above right is shown
the standard suspension of the dartboard (center is in height hc = 1.73 m) and the distance where thrownexecuted from, L = 2.73 m. We assume that the thrower’s hand is in the distance L when the arrow is released and in height 1.63 m. The dart is thrown with the speed 𝑣𝑣0 and at an angle 𝛼𝛼0.
How long does it take the arrow to reach the dartboard if there is no air resistance?

Question 2.
[Continuation of previous question]
In darts you can finish by either hitting a double (eg 2 x 20 points, in the outer ring) or in bulls eye (50 points). Between the bulls eye (in the center of the disc) and 2 x 20 points there is 166 mm (see character).
If 𝛼0 is 15 °, at what speed must the arrow be thrown to hit the 2 x 20 point field?

Question 3.
Both Earth and Mars exert a gravitational pull on you. If you are traveling on a straight line between Earth and Mars, how far do you have to travel from the center of the Earth to the gravitational attraction from Earth and Mars are equal? The distance between the centers of Earth and Mars is changing over time, but assume in this task that the distance is 220 million km. The mass of Mars is 6.4 ×1023 kg and the mass of the Earth is 6.0 × 1024 kg.

Question 4.
Two identical springs with equilibrium lengths of 25 cm and spring constants of 300 N / m are connected to a box and stretched to a length of 𝐿 = 36 cm (see figure). A horizontal, external force 𝐹 (𝑥) now pulls the box a distance 𝐷 = 2.0 cm to the right, after which the box is held by the force. How big one work performs the force 𝐹 (𝑥) during the pull?

Question 5.
A body with a mass of 2.0 kg moves along the x-axis. The potential energy as a function of position is shown in the figure below. The body starts with a kinetic energy of 12 J. The system is conservative.
What is the kinetic energy of the body when the body reaches 2.0 m on the x-axis?

Question 6.
What is the speed of the body when the body reaches 6.0 m on the x-axis?

Question 7.
You are a DJ at a party and you have a special turntable that is both massless and can rotate freely without friction. On the turntable is a vinyl record that has a mass of 120 g and a diameter of 30.0 cm. The turntable rotates at 33.3 rpm (revolutions per minute). Someone places a can
with soda having the mass 400 g and diameter 7.00 cm, in the middle of the turntable.
How many revolutions per minute will the record player with vinyl record and can now perform?

Question 8.

We consider a buoy at sea which is oriented as shown in the figure to
right. It has a green broom at the top, which can be ignored in this
assignment.
The buoy is shaped like a cylinder with length L = 1.5 m and radius R
= 0.3 m, with a hemispherical bottom with the same radius. The buoy
density is constant. The buoy weighs 170 kg. The density of seawater is
1027 kg / m3.
How high is the part of the buoy that protrudes above the water, h?
Hint: The volume of a sphere with radius 𝑟𝑟 is given by 4/3
𝜋𝑟^3 and volume of a cylinder with height ℎ and radius 𝑟 is given by 𝜋𝑟^2ℎ.

Question 9.

A large open water tank with height h is used to
provide a water pressure. To get more speed on the water
we put a propeller in the pipe at the bottom of the tank.
The cross-sectional area of the open part of the tank is
much larger than the cross-sectional area of the pipe.
The flow can be assumed to be laminar and
frictionless. The density of water is 1000 kg / m3.

However, it is such that water boils spontaneously if
the pressure falls below 2.3 kPa. This is called cavitation.

What is the maximum speed that our propeller can accelerate the water to before it starts to
boil after the propeller if the height of the water tank, h, is 1.7 m?

Question 10.
A 50 g bullet flies at a speed of 100 m / s and hits a block with a mass of 5.0 kg. The block is connected to a spring with a spring constant of 10 N / m. The table on which the block stands is smooth. How long time it will take the block to compress the spring and return to the original position. (Assume that the spring is long enough for the amplitude to be no longer than the compressed distance of the spring.)

Question 11.

An electron and two spherically symmetrical charge distributions are arranged on a line as shown on the figure. The two spherically symmetrical charge distributions are maintained while the electron is free.
What must the value of q2 be for the electron to be in static equilibrium?

Question 12.

A plate capacitor with a capacitance 𝐶𝐶 = 4.0 μF is charged with an electrostatic energy of 0.50 J.
A water molecule with a dipole moment of 6.13 ∙ 10-30 C ∙ m is located between the plates as shown in the figure. The distance between the plates is 300 μm.
What work must be done on the water molecule to turn its dipole moment 180 degrees?

Question 13.
In a ‘synchrotron’, protons with a kinetic energy of 2.0 ∙ 106 eV are held in a circular orbit with a
radius of 50 cm using a magnetic field perpendicular to the circle.
What is the required magnetic field strength?

Question 14.
Two particles perform a smooth circular motion about the same center. The acceleration of particle A is 8 times greater than the acceleration of particle B, while the period of particle B is 2 times longer than the period of particle A.
What is the ratio of the radius of the circle for particle A to the radius of the circle for particle B?