Classical Mechanics Answers

A two point system consists of two masses, m and 2m, separated by a distance d. If mass m is replaced by a mass 3m and is kept at a distance d/2, what are the ratios of the gravitational potential energy of the two systems?

A car has a drag coefficient C_{d} = 0.30

Cd

​=0.30, a frontal area of A=1.9 m

2

and a mass 1.2 tonnes. The density of air is 1.2 kg.m^{-3}

−3

.

i) What is the drag force when it is traveling at v=110 kph 

in a straight line? F_{drag} =

Fdrag

​= _____  N 

.

Hint: Retain accurate values until the final calculation, but remember significant figures.

A rubber band has mass m=0.30 g 

and a spring constant k=15 N.m

−1

. I stretch it by 5.0 cm 

(which in this case doubles its length). Assume the rubber band behaves as a Hooke's law spring. Assume that, when you launch the rubber band, all of the stored potential energy is converted into kinetic energy. How fast is it at the launch?

v =

v= _____  m.s

−1

.

I drag a mass m=21 kg 

in a straight line, along a horizontal surface, a distance D=23 m 

. I drag it at constant speed v=0.90 m.s in a straight line using a horizontal force. The coefficients of friction are \mu_{s} = 1.2 μs​=1.2 and μk ​=1.1. How much work do I do? W =

W= _____  J 

.

estimate the hall voltages generated in each case across a 5mm width of sample of thickness 1mm when a current 100mA is passed along it and the perpendicular field is given as 100mT

In the figure below, a spring with k = 170 N/m is at the top of a frictionless incline of angle θ = 370. The lower end of the incline is distance D = 1.00 m from the end of the spring, which is at its relaxed length. A 2.00 kg canister is pushed against the spring until the spring is compressed 0.200 m and released from rest. (a) What is the speed of the canister at the instant the spring returns to its relaxed length (which is when the canister loses contact with the spring)? (b) What is the speed of the canister when it reaches the lower end of the incline?

A rectangular block of ice with dimensions 2 m by 2 m by 0.3 m floats on water. A person weighing 835 N wants to stand on the ice. Would the ice sink below the surface of the water?

1. A room on the lower level of a cruise ship has a 40-cm-diameter circular window. If the midpoint of the window is 2 m below the water surface, determine the hydrostatic force acting on the window, and the pressure center. Take the specific gravity of seawater to be 1.025.

2. The water side of the wall of a 70-m-long dam is a quarter circle with a radius of 7 m. Determine the hydrostatic force on the dam and its line of action when the dam is filled to the rim.

1. Consider an 8-m-long, 8-m-wide, and 2-m-high aboveground swimming pool that is filled with water to the rim.

(a) Determine the hydrostatic force on each wall and the distance of the line of action of this force from the ground.

(b) If the height of the walls of the pool is doubled and the pool is filled, will the hydrostatic force on each wall double or quadruple? Why?

2. Consider a heavy car submerged in water in a lake with a flat bottom. The driver's side door of the car is 1.1 m high and 0.9 m wide, and the top edge of the door is 10 m below the water surface. Determine the net force acting on the door (normal to its surface) and the location of the pressure center if (a) the car is well-sealed, and it contains air at atmospheric pressure and (b) the car is filled with water.

1. The variation of pressure P in gas with density p is given by P = Cpⁿ where C and n and are constants with P = P_o and p = p₀, at elevation z = 0. Obtain a relation for the variation of P with elevation in terms of z. g. n. P_o and p_o.

2. A manometer containing oil (p₀ = 850 kg/m³) is attached to a tank filled with air. If the oil-level difference between the two columns is I50 cm and the atmospheric pressure is 98 kPa, determine the absolute pressure of the air in the tank.