Mechanics | Relativity Answers

A yo-yo is made of two solid cylindrical disks, each of mass 0.049 kg and diameter 0.070 m , joined by a (concentric) thin solid cylindrical hub of mass 0.0055 kg and diameter 0.012 m .
Part A
Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 0.90 m long string, if it is released from rest.
Express your answer using three significant figures and include the appropriate units.
Part B
What fraction of its kinetic energy is rotational?
Express your answer using two significant figures.

To get a flat, uniform cylindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in the figure (Figure 1). Suppose that the satellite has a mass of 4200 kg and a radius of 4.0 m, and that the rockets each add a mass of 250 kg.
What is the steady force required of each rocket if the satellite is to reach 49 rpm in 2.5 min, starting from rest?
Express your answer to two significant figures and include the appropriate units.

An Atwood machine consists of two masses, mA = 63 kg and mB = 72 kg , connected by a massless inelastic cord that passes over a pulley free to rotate (Figure 1). The pulley is a solid cylinder of radius R = 0.41 m and mass 5.0 kg . [Hint: The tensions FTA and FTB are not equal.]
Part A
Determine the acceleration of each mass.
Express your answer to two significant figures and include the appropriate units.
Part B
What % error would be made if the moment of inertia of the pulley is ignored?
Express your answer using two significant figures.

The bolts on the cylinder head of an engine require tightening to a torque of 94 m⋅N .
Part A
If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end?
Express your answer to two significant figures and include the appropriate units.
Part B
If the six-sided bolt head is 15 mm in diameter, estimate the force applied near each of the six points by a socket wrench.
Express your answer to two significant figures and include the appropriate units.

A 0.38-kg skeet (clay target) is fired at an angle of 28∘ to the horizon with a speed of 25 m/s. When it reaches the maximum height, h, it is hit from below by a 28-g pellet traveling vertically upward at a speed of 230 m/s. The pellet is embedded in the skeet.
How much higher, h′, did the skeet go up?
Express your answer to two significant figures and include the appropriate units.

If you stand on a bathroom scale, the spring inside the scale compresses 0.80 mm, and it tells you your weight is 700 N.
Now if you jump on the scale from a height of 1.8 m, what does the scale read at its peak?
Express your answer to two significant figures and include the appropriate units.

If a 1300 kg car can accelerate from 30 km/h to 65 km/h in 3.6 s , how long will it take to accelerate from 65 km/h to 90 km/h ? Assume the power stays the same, and neglect frictional losses.
Express your answer to two significant figures and include the appropriate units.

A 65-kg skier grips a moving rope that is powered by an engine and is pulled at constant speed to the top of a 23∘ hill. The skier is pulled a distance x = 330 m along the incline and it takes 2.0 min to reach the top of the hill.
If the coefficient of kinetic friction between the snow and skis is μk = 0.10, what horsepower engine is required if 30 such skiers (max) are on the rope at one time?
Express your answer using two significant figures.

Chris jumps off a bridge with a bungee cord (a heavy stretchable cord) tied around his ankle, (Figure 1). He falls for 15 m before the bungee cord begins to stretch. Chris's mass is 80 kg and we assume the cord obeys Hooke's law, F=−kx, with 54 N/m.
If we neglect air resistance, estimate what distance d below the bridge Chris's foot will be before coming to a stop. Ignore the mass of the cord (not realistic, however) and treat Chris as a particle.
Express your answer to two significant figures and include the appropriate units.

A spring with k = 58 N/m hangs vertically next to a ruler. The end of the spring is next to the 17-cm mark on the ruler.
If a 2.5-kg mass is now attached to the end of the spring, and the mass is allowed to fall, where will the end of the spring line up with the ruler marks when the mass is at its lowest position?
Express your answer to two significant figures and include the appropriate units.