Although the injuries tend to be less severe, heading a soccer ball carries many of the same dangers as getting hit by a blocker or tackler in a football game. Indeed, heading is now forbidden in many youth leagues. In a very simple model, calculate the impulse given to the skull and its average acceleration when struck by a soccer ball. Assume that a headed soccer ball undergoes an elastic collision lasting 0.7 ms in which it reverses direction. Consider two different heading techniques: (i) where the head effectively recoils on its own, independent of the body (ii) the head and body recoil together. Do calculations for both youth players and for adults.

                                                Youth              Adult

Soccer ball mass (kg)             0.375               0.425

Speed of kicked ball (m/s)      20                    35

Mass of skull (kg)                   3                      5

Mass of entire body (kg)        30                    60

why do the maximum and minimum momenta have opposite signs? like cart 1 hitting cart 2 why would cart one be positive and cart to be negative?

A spring has a Hooke's law spring constant of 3.4 N/m. If you load it with 1.3 kg, how far will it extend from its equilibrium length?

A spring 10 cm long extends 0.5 cm when a mass of 8 kg is hung from it. Suppose you made an similar spring of the same material, but twice as long. How much would it extend with the same mass?

If you apply a force {f} newtons on a spring, and it extends to some length 1.6 in meters, how far would it extend for another force 3.7 times that first one?

If you pull on a spring with a force F to extend it for some change in its length, what is the force that the spring pulls against you?

A gallon of water is about 3.785 liters, 3785 cm³ of volume, and 3.785 kg of mass. (Gasoline is somewhat less dense.) Suppose an empty tanker truck with a weight of 10,000 lbs (4545 kg mass) deflects a bridge by 1 cm (0.01 m) when it is in the middle of span. If a full truck could hold 8,000 gallons of water, how much would it deflect the bridge by if it were 36.1 percent full? Give your answer in cm, where 100 cm = 1 m or 2.54 cm = 1 in.

If you have a closed container containing gas at Earth's atmospheric pressure and at 20 °C , and you increase is temperature by 10 °C while leaving the container tightly closed, what happens to the pressure inside?

A very good vacuum on Earth is 10^-9 of Earth's atmospheric pressure at room temperature. How many atoms would be in a cubic meter of that vacuum?

Suppose you have plastic gallon milk bottle and you have removed all the water from it. In a microwave oven you boil a cup of water and while it is boiling pour it in, let the vapor fill the bottle and displace all the air inside, and then tightly cap the bottle. You wait for a minutes while the water inside cools and the vapor condenses, or you urge the process on by sitting the bottle outside on the snow. Since your bottle no longer contains air, how much force is being exerted on a side that is 0.25 by 0.2 meters?

Suppose we have a piston 0.5 cm in diameter pushing on a fluid, and that liquid is connected to a cylinder with another, larger, piston being used to lift up your car. If your car has a mass of 1500 kg, and without the apparatus you can lift at most 49.8 kg, what is the minimum diameter of the piston you will need to lift your car?

You have a choice of boats to make a trip across a lake with a 240 kg load of supplies for your vacation cabin. You and your friend both have masses of 80 kg. Since the smaller boats are less expensive to rent, and you want to keep it for several days, you chose the smallest one that will safely ferry your load. Allow a safety factor of 2x, such that the boat can support twice its weight and the load. Knowing the density of water is 1000 kg/m³, which one do you choose?

A circular loop of wire having a radius of 6.0 cm carries a current of 0.14 A. A unit vector parallel to the dipole moment of the loop is given by 0.40i -0.92j. If the loop is located in a magnetic field given by B = (0.40 T)i + (0.35 T)k,

A) find the magnitude of the magnetic dipole moment of the loop.

B) Find the i component of the torque on the loop.

C) Find the j component of the torque on the loop.

D) Find the k component of the torque on the loop.

E) Find the magnetic potential energy of the loop.

(1a)The car lift at your neighborhood garage is designed such that the radii of the input piston and output plunger are 7.70 10^-3 m and 0.120 m, respectively. The garage manager likes to use a hydraulic oil in the lift that has a density of 7.80 10² kg/m³. Compared to the weight of the output plunger, the weight of the input piston is negligible. Determine the force F_i needed at the input piston in order to support the 13,000-N combined weight of a car and the output plunger under the following conditions. (A) The bottom surfaces of the input piston and output plunger are at the same level. (B)The bottom surface of the input piston is 2.40 m below that of the output plunger.

(1b)The pressure at the bottom of a cylindrical container with a cross-sectional area of 48.0 cm² and holding a fluid of density 500 kg/m³ is 115 kPa. (A) Determine the depth of the fluid. (B)Determine the pressure at the bottom of the container if an additional 2.20 10^-3 m³ of this fluid is added to the container. (Give your answer to at least 3 significant figures.)

(1c)(a) Suppose a meter stick made of steel and one made of invar are the same length at 0°C. What is their difference in length at 48.0°C? The coefficient of thermal expansion is 12 ✕ 10⁻⁶/°C for steel and 0.9 ✕ 10⁻⁶/°C for invar. (B)Repeat the calculation for two 18.5-m-long surveyor's tapes.

After the Sun exhausts its nuclear fuel, its ultimate fate may be to collapse to a white dwarf state. In this state, it would have approximately the same mass as it has now, but its radius would be equal to the radius of the Earth. (a) Calculate the average density of the white dwarf.

(b) Calculate the surface free-fall acceleration

(c) Calculate the gravitational potential energy associated with a 2.04-kg object at the surface of the white dwarf.

A space station has a large ring-like component that rotates to simulate gravity for the crew. This ring has a mass M = 2.1×10^5 kg

and a radius of R= 86.0 m and can be modeled as a thin hoop. Before spinning up the ring section, crew members Dave and Frank

dock their ships, each with mass m= 3.5×10^4 kg on two docking ports located on opposite sides of the center of the ring. The docking

ports are located r = 31.0 m from the center of the ring. When the station’s computer begins to spin up the ring it has to spin both the

ring and the ships. The ships can be treated as point particles. Two identical thrusters on the edge of the ring are used to spin up the

ring with a constant angular acceleration. The ring-ship system takes 3 hours to reach the angular speed at which it simulates Earth’s

gravity for the crew on the edge of the ring. What constant force must each of the two thrusters apply to reach this rotational speed?

#1 A microwave oven has a power requirement of 1,261 W. A frozen dinner requires 4.1 min to heat on full power.

(a) How much electrical energy (in kWh) is used?
_________kWh

(b) If the cost of electricity is 13¢ per kWh, how much does it cost to heat the dinner? (Do not round your final answer. Fractional cent values are acceptable.)
______________¢

#2 - A student who weighs 556 N climbs a stairway (vertical height of 2.6 m) in 23 s.

(a) How much work is done?
__________J

(b) What is the power output of the student?
__________W

In a neutron scattering experiment, a neutron scatters off the stationary nucleus of an atom with an atomic mass of 61 amu in a 1 dimensional, elastic collision. After the collision, what percentage of the neutron's kinetic energy was transferred to the atom? In a second neutron absorbtion experiment, a neutron is absorbed into the nucleus of an atom with an atomic mass of 62 amu. After the collision, what percentage of the neutron's kinetic energy was remains?

Beryllium-8 is an unstable isotope and decays into two α particles, which are helium nuclei with mass 6.68×10−27kg. This decay process releases 1.5×10−14J of energy. For this problem, let's assume that the mass of the Beryllium-8 nucleus is just twice the mass of an α particle and that all the energy released in the decay becomes kinetic energy of the α particles.

a) If a Beryllium-8 nucleus is at rest when it decays, what is the speed of the  α particles after they are released?

b) If the Beryllium-8 nucleus is moving in the positive x-direction with a speed of 1.0×106 m/s when it decays, what is the speed of the slower-moving α particle after it is released? Assume that the α particles move entirely in the x-direction.

c) If the Beryllium-8 nucleus is moving in the positive x-direction with a speed of 1.0×106 m/s when it decays, what is the speed of the faster-moving α particle after it is released?  Assume that the α particles move entirely in the x-direction.

I have to do an experiment/ demonstration for my PHY251 class (Calculus based physics). I am only allowed to do it on one of the following topics: Vectors, Accelerated motion, Centripetal force, Free fall, projectile motion, Inertia, Equilibrium, Friction, Orbits, Tides. Does anyone have any ideas for a cool demonstration? Please provide instructions for the demonstration/experiment. Thank you in advance.

M, a solid cylinder (M=1.71 kg, R=0.133 m) pivots on a thin, fixed, frictionless bearing. A string wrapped around the cylinder pulls downward with a force F which equals the weight of a 0.690 kg mass, i.e., F = 6.769 N. Calculate the angular acceleration of the cylinder.

5.95×10¹ rad/s^2

If instead of the force F an actual mass m = 0.690 kg is hung from the string, find the angular acceleration of the cylinder.

How far does m travel downward between 0.730 s and 0.930 s after the motion begins?

The cylinder is changed to one with the same mass and radius, but a different moment of inertia. Starting from rest, the mass now moves a distance 0.379 m in a time of 0.470 s. Find I_cm of the new cylinder.

Write a 6-7 on how the ‘theory’ for projectile motion of the ‘stream of water’, (i.e., many small water particles), may useful to design a fountain.

Compare (take the ratio) the rate of heat conduction through a 20.0-cm-thick wall that has an area of 10.0 m2 and a thermal conductivity twice that of glass wool with the rate of heat conduction through a 0.750-cm-thick window that has an area of 2.00 m2, assuming the same temperature difference across each. Show a few steps. Qualitatively, explain how you can reduce heat conduction through a window in winter.