2D Car Collision

Car Collision in 2D (c7p50) A 900- kg car collides with a 1400- kg car that was initially at rest at the origin of an x-y coordinate system. After the collision, the lighter car moves at 10.0 km/h in a direction of 35 degrees with respect to the positive x axis. The heavier car moves at 13 km/h at -41 degrees with respect to the positive x axis.

A) What was the initial speed of the lighter car (in km/h)? ____Tries 0/7

B) What was the initial direction (as measured counterclockwise from the x-axis)? ___Tries 0/7

At t=0 a grinding wheel has an angular velocity of 27.0 rad/s . It has a constant angular acceleration of 25.0 rad/s2 until a circuit breaker trips at time t = 2.00 s . From then on, it turns through an angle 430 rad as it coasts to a stop at constant angular acceleration.

Through what total angle did the wheel turn between t=0 and the time it stopped?At what time did it stopWhat was its acceleration as it slowed down?

1) A ball is kickedfrom the top of a bridge at a height of 50 m (measured from the surface of the water below) with an initial speed of 30 [m/s] at 22 degrees with respect to the x-axis.

a) Determine the time it takes for the ball to reach its maximum height.

b) Determine the maximum height of the ball (measured from the water below)

c) Determine the speed of the ball at its heighest point on its trajectory

d) Determine the time at which the ball lands/.

e) Where does the ball land? [i.e. Calculate its range]

f) Calculate the velocity of the ball just before it lands[both magnitude and direction]

What is the difference between ultraviolet and visible radiation?

a nonconducting thin spherical shell of radius 6.00 cm has a uniform density of 9.00 nC/m^2.
a. what is the total charge on the shell
b. what is the electric field at a distance of 2.00 cm from the center of the shell?
c. what is the electric field a distance 10.0 cm from the center of the shell.

For each statement, select the phrase that makes the statement true (e.g., if the answer to the first is A and to the others B, enter ABBBB):

1. 
   
2. Two identical shallow containers are placed on identical scales. A live duck is put in one container. Both containers are then filled with water to their brims; it is observed that the duck is standing on the bottom of its container. The reading on the scale under the container with the duck is ____ the reading on the other scale.
3. A boat containing a cement block floats in a swimming pool. The water level in the pool ____ when the cement block is thrown to the shore.
4. A block of wood floats in a pail of water in a stationary elevator. The level of water in the pail ____ when the elevator accelerates upward.
5. Two balloons of the same volume are filled with helium and hydrogen, respectively. The buoyant force on the helium-filled balloon is ____ the buoyant force on the hydrogen-filled balloon.
6. A glass containing an ice cube is filled with enough water to float the ice cube. The water level in the glass ____ when the ice cube melts.

1. Circular motion
   1. If 1 metric ton elevator is accelerating upwards at 7.0 m/s², Calculate the force of tension in the cable.
   2. If the elevator is accelerating downwards at 7.0 m/s² calculate the force of tension in the cable.
   3. Describe the acceleration that is most likely to break the elevator cable.
   4. Now imagine the elevator is in Willy Wonka’s chocolate factor and it can move in any direction. If the elevator is moving at a speed of 3.5 m/s around a curve with a radius of 18 ft, what will the centripetal acceleration of the elevator be?
   5. What will the centripetal force of the elevator be?
   6. If the radius of the curve and the speed of the elevator both double, what will happen to the centripetal force?

A 34.8-kg child starting from rest slides down a water slide with a vertical height of 16.0 m. (Neglect friction.)

(a) What is the child's speed halfway down the slide's vertical distance?

m/s

(b) What is the child's speed three-fourths of the way down?

m/s

Gauss's Law

A spherical shell of radius R has charge Q spread uniformly over its surface.
Find the electric field inside and outside the shell.

Imagine that you have just purchased a coffee in a cup, with a lid. You place your coffee cup on a table and it starts to cool down. We are going to model this cooling process. Choose whatever type of coffee cup you are most familiar with.

2. Do a Ninja Physics estimate of how long it will take for the sides of the cup to warm up.

The specific heat capacity of water (and coffee) is around 4200 J Kg-1 K-1. Cardboard has a thermal conductivity of around k ~ 0.025 W m-2 K-1 , a density of around 700 kg m-3 and a specific heat capacity of around 1400 J kg-1 K-1. Glass has a thermal conductivity of around k ~ 1 W m-2 K-1, a density of around 2500 kg m-3 and a specific heat capacity of around 700 J kg-1 K-1. Styrofoam (foamed plastic) has a thermal conductivity similar to air and a density of around 50 kg m-3, while hard plastics have thermal conductivities of k ~ 0.025 W m-2 K-1 and densities similar to water: both have specific heat capacities of around 1500 J Kg-1 K-1.

A 420-N uniform rectangular sign 4.00 m wide and 3.00 m high is suspended from a horizontal, 6.00-m-long, uniform, 130-N rod as indicated in the figure below. The left end of the rod is supported by a hinge and the right end is supported by a thin cable making a 30.0

A thin spool with a mass of 2.0kg and a radius of 15cm is hung in a fixed position so that it is free to rotate. A massless string is wrapped around it with a 0.80kg mass tied at the end. When the mass is released, the spool begins to unwind.

What is the rotational inertia of the spool? (You can treat it as a thin disk.)

What is the kinetic energy and angular momentum of the spool 2.0s after the

hanging mass is released?

What is the kinetic energy and angular momentum of the spool after 3 full

rotations?

An object is placed 10 m before a convex lens with focal length 5 . 9 m . Another convex ens is placed 9 . 39 m behind the first lens with a focal length 3 . 8 m (see the figure below). Note: Make a ray diagram sketch in order to check your numerical answer a)At what distance is the first image from the first lens? Answer in units of m
b)What is the magnification of the first image?
c)At what distance is the second image from the second lens? Answer in units of m
d)What is the magnification of the final image, when compared to the initial object?

2(a) A typical metallic particle has a rest mass (i.e. mass when the particle is not moving) of 0.5x10-24Kg and an energy of 10 eV (Electron Volt). (i) What would be the wavelength and momentum of the associated wave for this particle? -- (5) (ii) Assuming the uncertainty principle and a spherical particle, estimate the diameter of this particle? Is it a nanoparticle ? ----------------------------------------- (5) (iii) This particle passes through an inter-lattice spacing of 1nm along the x axis. What would be the spread of the particle in the y-axis, 10microns from this interlattice spacing ------- (5) 2. (b) The primitive translation vectors of the hexagonal space lattice may be taken as z ccy a xaby a xaa     ; ) 2 () 4 3 (;) 2 () 4 3 ( (a) Calculate the volume of the primitive unit cell ------ (5) (b) What is its atomic packing fraction ? ----- (5)

A child is playing with a ball at the base of a hill. She rolls the ball up the hill with a speed of 8 m/s. After 23s, the ball comes back to her and has the same speed as when she rolled it but it's moving in the opposite direction. Assume that the ball's acceleration was constant as it rolled up and down the hill, and take the positive direction to point up the hill.

What was the ball's acceleration while rolling up and down the hill?