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Mechanics | Relativity

.There is a node, starting at (0, 0, 0), and it's moving 10 per second on the X axis, 6 per second on the Y axis, and 8 per second on the Z axis. Please answer the follow questions.

(1) What is the motion equation of this node?

(2) what is the position of this node after 5 seconds?

Mechanics | Relativity

Spiderman uses his spider webs to save a runaway train (see the figure). His web stretches a few city blocks before the 1.0×104 kgkg train comes to a stop.Part A Assuming the web acts like a spring, estimate the spring constant. Assume the train is moving 30 m/sm/s , and that the distance of "a few city blocks" is perhaps about 600 meters.

Mechanics | Relativity

Iodine-131 has a half-life of about 8.0 days. When consumed in food, it localizes in the thyroid. Suppose 7.0 percent of the 131I localizes in the thyroid and that 20 percent of its disintegrations are detected by counting the emitted gamma rays. How much 131I must be ingested to yield a thyroid count rate of 50 counts per second?

Mechanics | Relativity

What is the de Broglie wavelength for a particle moving with

speed 2.0 × 106 m/s if the particle is (*a*) an electron, (*b*) a proton,

and (*c*) a 0.20-kg ball?

Mechanics | Relativity

Two narrow, horizontal, parallel slits (a distance *a *= 0.60 mm

apart) are illuminated by a beam of 500-nm light. Light that is diffracted at certain angles *θ *reinforces; at others, it cancels. Find the three smallest values for *θ *at which (*a*)

reinforcement occurs and (*b*) cancellation occurs.

Mechanics | Relativity

In a plane electromagnetic wave, the electric field (in V/m) is given by equation

*Ez*= 6.0 sin [2π(2· 10^{10} *t *+ 500 *x*)] where *x *is in metre and *t *in second.

(a) What is the direction of propagation of the wave?

(b) What is the rms value of electric field?

(c) Find the wavelength and frequency of the wave.

(d) Write the expression for the magnetic field.

Mechanics | Relativity

A mass m=2kg hangs from a spring of spring constant 400 N/m. The spring is stretched 0.25m from its equilibrium position and then released. Use the Lagrangian to determine the vertical velocity of the block at t = 5s.

Mechanics | Relativity

A potter’s wheel—a thick stone disk of radius 0.500 m and mass 100 kg—is freely rotating at 50.0 revs/min. The potter can stop the wheel in 6.00 s by pressing a wet rag against the rim and exerting a radially inward force of 70.0 N. Find the effective coefficient of kinetic friction between wheel and rag.

Mechanics | Relativity

The diagram depicts a trajectory consisting of two segments: The first segment, AB, is a quarter of a particle circle with a radius of R = 45. Point B is on the circular trajectory. A second section, BD, is a non-smooth sloping slope whose angle is a = 30 degrees. Release from rest from point A a 2kg weight box stopping on the inclined plane at point D, which is 50m away from point B.

1. Calculate the speed of the box at point B. Show in the drawing the direction of the speed at point. necrosis.

2. Given that beta = 60 degrees. Draw a diagram depicting the forces acting on the box at point K and calculate the normal force acting on the body at this point.

3. Calculate the frictional force acting on the box during its movement.

4. Calculate the kinetic coefficient of friction between the slope and the box.

5. Where during the movement of the box will the magnitude of the normal force acting on it be maximum? Necrosis.

6. What will be the work of the normal force on the box during its movement from the point you found in section 5 to its stopping? Necrosis.

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Mechanics | Relativity

A pulley rotating in the counterclockwise directions is attached to a mass suspended from a string. The mass causes the pulley's angular velocity to decrease with a constant angular acceleration, α = -2.10 rad/s^2. (a) if the pulley's initial angular velocity is ω = 5.40 rad/s, how long does it take for the pulley to come to rest? (b) Through what angle does the pulley turn during this time? (c) if the radius of the pulley is 5.0 cm, through what distance is the mass lifted? *