The position of a 0.30-kg object attached to a spring is described by

x = (0.22 m) cos(0.3?t)

(a) Find the amplitude of the motion.
m

(b) Find the spring constant.
N/m

(c) Find the position of the object at t = 0.26 s.
m

(d) Find the object's speed at t = 0.26 s.
m/s

A blue car with mass m_c = 497 kg is moving east with a speed of v_c = 16 m/s and collides with a purple truck with mass m_t = 1336 kg that is moving south with an unknown speed. The two collide and lock together after the collision moving at an angle of θ = 51° South of East

1)

What is the magnitude of the initial momentum of the car?

kg-m/s

2)

What is the magnitude of the initial momentum of the truck?

kg-m/s

3)

What is the speed of the truck before the collision?

m/s

4)

What is the magnitude of the momentum of the car-truck combination immediately after the collision?

kg-m/s

5)

What is the speed of the car-truck combination immediately after the collision?

m/s

6)

Compare the magnitude of the TOTAL momentum of the system before and after the collision:

A man stands on the roof of a building of height 13.4 m and throws a rock with a velocity of magnitude 27.5 m/s at an angle of 32.8 ∘ above the horizontal. You can ignore air resistance.

1. Calculate the maximum height above the roof reached by the rock.

2. Calculate the magnitude of the velocity of the rock just before it strikes the ground.

3. Calculate the horizontal distance from the base of the building to the point where the rock strikes the ground.

1) Imagine an object moving horizontally with uniform (that is, constant) velocity. Sketch the position time and velocity-time graphs for this motion.

2) Imagine tossing an object straight up into the air, then catching it. Sketch the position-time and velocity-time graphs for this motion, from the moment it leaves your hand to the moment just before it lands in your hand.

3) Imagine tossing a ball slightly upwards and towards another person. Consider the motion from the moment the ball leaves your hand to the moment just before it lands in the other person’s hands. Draw the trajectory for the ball. In how many dimensions is the object moving?

Steam at 100°C is added to ice at 0°C.

(a) Find the amount of ice melted and the final temperature when the mass of steam is 13 g and the mass of ice is 48 g.

(b) Repeat with steam of mass 2.1 g and ice of mass 48 g.

1)Discuss how energy conservation applies to a swinging pendulum. (PLEASE EXPLAIN YOUR ANSWERS, WITHOUT ANY EXPLANATION YOU WILL NOT RECEIVE FULL CREDIT) Where is the potential energy the greatest? The least? Where is the kinetic energy the most? The least? Where is the pendulum moving the fastest? The slowest?

2)Why does the force of gravity do no work on a bowling ball rolling along a bowling alley?

Your cousin’s voice sound different over the telephone than it does in person. This is because telephones

     do not transmit frequencies over about 3000 Hz. Since 3000 Hz is well above the normal frequency of

     speech, why does eliminating these high frequencies change the sound of your cousin’s voice? Carefully

     provide the reasoning behind your answer.

A horizontal pipe of diameter 0.768 m has a smooth constriction to a section of diameter 0.4608 m. The density of oil flowing in the pipe is 821 kg/m3 . If the pressure in the pipe is 7120 N/m2 and in the constricted section is 5340 N/m2 , what is the rate at which oil is flowing? Answer in units of m3/s.

1. When determining the amount of work needed to pump something what would cause the final work to be negative?  

2. What is the purpose behind integration in determining fluid force on vertical surfaces?

Starting from rest, a 4.20-kg block slides 2.30 m down a rough 30.0° incline. The coefficient of kinetic friction between the block and the incline is μ_k = 0.436.

(a) Determine the work done by the force of gravity.
J

(b) Determine the work done by the friction force between block and incline.
J

(c) Determine the work done by the normal force.
J

(d) Qualitatively, how would the answers change if a shorter ramp at a steeper angle were used to span the same vertical height?

Sarah leaves her house and walks 11 miles to the west and then 6 miles at an angle 30 degrees west of north. How far and in what direction does Sarah need to walk to get home?

A picture and detailed show of work would be appreciated!

Suppose you want to determine the electric field in a certain region of space. You have a small object of known charge and an instrument that measures the magnitude and direction of the force exerted on the object by the electric field.

(a) The object has a charge of +12.0

1- what is the relation between the terminal voltage drop and the resistor voltage drops?

2- how are the absolute potentials related to the voltage drop?

3- how are the resistor voltage drops related to the terminal voltage drop?

4- how are the resistor voltage drops related to the resistances.

5- how are the resistor currents related to the circuit current?

6- How are the resistor currents and resistances related?

7- how are the currents in the wires related to the currents in the resistors ?

8- what can you conclude about Currents in a series circuit? Is the circuit current the same as it was in the parallels circuit?why?

Three capacitors, all initially without any dielectrics inserted, of C1 = 4 micro-farads, C2 = 10 micro-farads, and C3 = 10 micro-farads, are connected purely in series to a battery and the total stored energy of all three capacitors is 248 micro-joules. Then, the plates of C1 are brought closer by a factor of 3 and a dielectric with a dielectric constant of 1.9 is inserted into C2 while still connected in series to the same battery. (C3 does not change at all.) How much does the total stored energy of all three capacitors increase in micro-joules after the capacitors are changed? Not the factor change... how much does the stored energy go up in value. step by step please and thank you!

You have a parallel-plate 6.33 × 10-6 F capacitor that is charged to 0.00861 C. While the capacitor is isolated, you change the plate separation so that the capacitance becomes 2.41 × 10-6 F. How much work do you perform in this process?