1) A concrete highway curve of radius 70 m and is banked at an angle of 30o. Imagine a car driving around the turn at a constant height. We want to find the maximum speed at which a 1100 kg rubber-tired car can go around this curve. Take the static coefficient of friction of rubber on concrete to be ?s = 1.0.

a) Calculate the maximum speed the car can go around the curve.

b) Discuss what is different from finding the maximum to finding the minimum speeds.

c) Calculate the minimum speed the car can go around the curve

2) On a rainy day, the concrete will be wet and reduce the coefficient of friction to ?s = 0.3

a) Calculate the maximum speed the car can go around the curve.

b) Calculate the minimum speed the car can go around the curve.

3) Freezing rain! The coefficient of friction is now zero! Can a car theoretically make it around this turn? If not, explain why not. If so, calculate the speed(s) at which they will be able to make it around the curve.

A small 0.11 kg metal ball is tied to a very light (essentially massless) string that is 0.9 m long. The string is attached to the ceiling so as to form a pendulum. The pendulum is set into motion by releasing it from rest at an angle of 60 ∘ with the vertical.

A) What is the speed of the ball when it reaches the bottom of the arc?

B)What is the centripetal acceleration of the ball at this point?

C)What is the tension in the string at this point?

A camera of weight 8 newtons is dropped from a drone at a height of 19.9 meters and enters free fall. Assuming no air resistance, what is the final velocity of the camera a moment before it shatters on the ground?

A straight, vertical wire carries a current of 1.25 Adownward in a region between the poles of a large superconducting electromagnet, where the magnetic field has a magnitude of B = 0.560 Tand is horizontal.

Part A

What is the magnitude of the magnetic force on a section of the wire with a length of 1.00 cm that is in this uniform magnetic field, if the magnetic field direction is east?

B

What is the direction of the magnetic force on a section of the wire with a length of 1.00  that is in this uniform magnetic field, if the magnetic field direction is east?

Part C

What is the magnitude of the magnetic force on a section of the wire with a length of 1.00 cm that is in this uniform magnetic field, if the magnetic field direction is south?

D

What is the direction of the magnetic force on a section of the wire with a length of 1.00 cm that is in this uniform magnetic field, if the magnetic field direction is south?

Part E

What is the magnitude of the magnetic force on a section of the wire with a length of 1.00 cm that is in this uniform magnetic field, if the magnetic field direction is30.0 ∘ south of west?

Part F

What angle will the magnetic force on this segment of wire make relative to the north, if the magnetic field direction is 30.0 ∘ south of west?

A 1.02 kg block is kept stationary on a 45 degree slope by applying a horizontal force F onto it. What is the minimum value of F if the coefficient of static friction is 0.5?

a) 3.33 N

b) 2.56 N

c) 4.25 N

d) 6.40 N

16. On a frictionless horizontal air table, puck A (with mass 0.255 kg ) is moving toward puck B (with mass 0.375 kg ), which is initially at rest. After the collision, puck A has velocity 0.125 m/s to the left, and puck B has velocity 0.649 m/s to the right.

Part A: What was the speed vAi of puck A before the collision?

Part B: Calculate ΔK, the change in the total kinetic energy of the system that occurs during the collision.

In its daily prowl of the neighborhood, a cat makes a displacement of 128m due north, followed by a 70m displacement due west.
a) Find the (a) magnitude and (b) direction of the displacement required for the cat to return home.
b) If, instead, the cat had first prowled 70m west and then 128m north, how would this affect the displacement needed to bring it home? Explain.

An energy plant produces an output potential of 2700 kV and serves a city 202 km away. A high-voltage transmission line carries 460 A to the city. The effective resistance of a transmission line [wire(s)] is 1.69 Ω/km times the distance from the plant to the city. 1) Assume the plant charges $ 0.105 /kW · hr for electric energy. At this rate, how much does it cost to transmit energy to the city (by the transmission line heating the atmosphere) each hour? Answer in units of dollars/hr. 2) Consider the money lost by the transmission line heating the atmosphere each hour. Assume the energy plant produces the same amount of power; however, the output electric potential of the energy plant is 20% greater. How much money per hour is saved by increasing the electric potential of the power plant? Answer in units of dollars/hr

Three children are riding on the edge of a merry‑go‑round that has a mass of 105 kg and a radius of 1.60 m . The merry‑go‑round is spinning at 16.0 rpm. The children have masses of 22.0, 28.0, and 33.0 kg. If the 28.0 kg child moves to the center of the merry‑go‑round, what is the new angular velocity in revolutions per minute? Ignore friction, and assume that the merry‑go‑round can be treated as a solid disk and the children as point masses.

During a solar eclipse, the moon, earth and sun all lie on the same line, with the moon between the earth and sun. Define your coordinates so that the earth and moon lie at greater x values than the sun. For each force, give the correct sign as well as the magnitude. (a) What force is exerted on the moon by the sun? (b) On the moon by the earth? (c) On the earth by the sun? (d) What total force is exerted on the sun? (e) On the moon? (f) On the earth?

A ball of mass 0.440 kg moving east ( + x direction) with a speed of 3.8 m/s collides head-on with a 0.220-kg ball at rest. If the collision is perfectly elastic, what will be the speed and direction of each ball after the collision?

Explain the phase shift in Lock in Amplifier

A hand-driven tire pump has a 2.00 cm diameter piston and a maximum stroke of 32.0 cm.

(a) How much work do you do in one stroke if the average gauge pressure is 2.40 ✕ 10⁵ N/m² (about 35 psi)? (You may consider this an isothermal process.)
J
(b) What average force do you exert on the piston, neglecting friction and gravity?
N

A 200 kg weather rocket is loaded with 100 kg of fuel and fired straight up. It accelerates upward at 35 m/s2 for 32 s, then runs out of fuel. Ignore any air resistance effects.

1. What is the rocket's maximum altitude?

2. How long is the rocket in the air before hitting the ground?

Using the alligator clip wires, attach the coil with more loops to the galvanometer. Look carefully at the direction that the wires are turned. The idea here is that you will be moving the pole of a magnet closer to the coil— increasing the magnetic field strength in the vicinity of the coil, which is one way to increase magnetic flux.

Experiment 2: , but move the magnet much faster. What happens to your current (as measured by the meter) as you move the magnet faster? Why? More current means more electrical energy. Where does this “extra” energy come from?