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# Questions by Ben B. from Los Angeles, CA

You are on an amusement park ride with your back against the wall of a spinning vertical cylinder. The floor falls away and you are held up by static friction. Assume your mass is 72 kg. (a) Draw...

You plan to fly a model airplane of mass 0.550 kg that is attached to a horizontal string. The plane will travel in a horizontal circle of radius 5.10 m. (Assume the weight of the plane is balanced...

Your moving company is to load a crate of books on a truck with the help of some planks that slope upward 33°. The mass of the crate is 98.0 kg, and the coefficient of sliding friction between it...

A curve of radius 138 m is banked at an angle of 11°. An 762-kg car negotiates the curve at 82 km/h without skidding. Neglect the effects of air drag and rolling friction. Find the following. (a)...

The radius of curvature of a loop-the-loop for a roller coaster is 14.0 m. At the top of the loop, the force that the seat exerts on a passenger of mass m is 0.35mg. Find the speed of the roller coaster...

Suppose you ride a bicycle in a 21.6-m-radius circle on a horizontal surface. The resultant force exerted by the surface on the bicycle (normal force plus frictional force) makes an angle of 13.8°...

A 0.70 kg stone attached to a string is whirled in a horizontal circle of radius 28 cm as in the figure below. The string makes an angle of 30° with the vertical. (a) Find the speed of the stone...

A block of mass m1 is attached to a cord of length L1, which is fixed at one end. The block moves in a horizontal circle on a frictionless tabletop. A second block of mass m2 is attached to the first...

A 0.30 kg stone attached to a 0.8 m long string is rotated in a horizontal plane. The string makes an angle of 15° with the horizontal. Determine the speed of the stone.

A 74.4-kg airplane pilot pulls out of a dive by following, at a constant speed of 184 km/h, the arc of a circle whose radius is 282.0 m. (a) At the bottom of the circle, what are the direction...

A sky diver of mass 66 kg can slow herself to a constant speed of 99 km/h by orienting her body horizontally, looking straight down with arms and legs extended. In this position, she presents the...

The coefficient of static friction between a rubber tire and the road surface is 0.85. What is the maximum acceleration of a 1042-kg four-wheel-drive truck if the road makes an angle of 12.7° with...

An automobile is going up a grade of 15° at a speed of 25.5 m/s. The coefficient of static friction between the tires and the road is 0.70. (a) What minimum distance does it take to stop the car...

A rear-wheel-drive car supports 48% of its weight on its two drive wheels and has a coefficient of static friction of 0.60. (a) What is the vehicle's maximum acceleration? (b) What is the...

In the figure below, m1 = 3.2 kg, m2 = 5.8 kg, and the coefficient of kinetic friction between the inclined plane and the 3.2-kg block is μk = 0.25. Find the magnitude of the acceleration of the masses...

You are racing in a rally on a snowy day when the temperature is near the freezing point. The coefficient of static friction between a car's tires and an icy road is 0.170. Your crew boss is concerned...

A 15000-kg helicopter is lowering a 4300-kg truck by a cable of fixed length. The truck, helicopter, and cable are descending at 17.0 m/s and must be slowed to 5.00 m/s in the next 56.0 m of descent...

A block of mass M = 16 kg with a pulley attached slides along a frictionless ledge. It is connected by a massless string to a block of mass m = 5.2 kg. (a) Find the acceleration of each block...

Both sides of wire start out with 5 washers with the total mass of 5m.  When N washers are transferred from the left side to the right side, the right side descends 70.56 cm in 0.60 s. Find N.

A block of mass m slides across a frictionless floor and then up a frictionless ramp. The angle of the ramp is θ and the speed of the block before it starts up the ramp is v0. The block will slide...

A 32.8-kg traffic light is supported by two wires. T1 is of the right wire which connects to the vertical pole at 30 degrees below horizontal. T2 is of the left wire which connects to the...

# 2 dimensional motion problem

A woman throws a ball at a vertical wall d = 3.8 m away. The ball is h = 1.9 m above ground when it leaves the woman's hand with an initial velocity of 20 m/s at 45°. When the ball hits the wall,...

# 2 dimensional motion problem

Starting from rest at point A, you ride your motorcycle north (the direction) to point B 90.0 m away, increasing speed at a steady rate of 1.55 m/s2. You then gradually turn toward the east (the direction)...

# 2 dimensional motion problem

(a) What are the period and speed of a person on a carousel if the person has an acceleration with a magnitude of 0.86 m/s2 when she is standing 3.6 m from the axis? (b) What are her...

# 2 dimensional motion problem

Earth rotates on its axis once every 24 hours, so that objects on its surface execute uniform circular motion about the axis with a period of 24 hours. Consider only the effect of this rotation on...

# 2 dimensional motion problem

The range of a cannonball fired horizontally from a cliff is equal to the height of the cliff. What is the direction of the velocity vector of the projectile as it strikes the ground? (Ignore any...

# 2 dimensional motion problem

A ball launched from ground level lands 2.9 s later on a level field 42 m away from the launch point. Find the magnitude of the initial velocity vector and the angle it is above the horizontal. (Ignore...

# 2 dimensional motion problem

A small steel ball is projected horizontally off the top of a long flight of stairs. The initial speed of the ball is 3.4 m/s. Each step is 0.19 m high and 0.29 m wide. Which step does the ball strike...

A train pulls away from a station with a constant acceleration of 0.37 m/s2. A passenger arrives at a point next to the track 6.1 s after the end of the train has passed the very same point. What...

A rock dropped from a cliff covers one-third of its total distance to the ground in the last second of its fall. Air resistance is negligible. How high is the cliff?

Bats use echolocation to determine their distance from objects they cannot easily see in the dark. The time between the emission of a high-frequency sound pulse (a click) and the detection of its...

The cheetah can run as fast as 113 km/h, the falcon can fly as fast as 161 km/h, and the sailfish can swim as fast as 105 km/h. The three of them run a relay with each covering a distance L at maximum...

# Summation Convergency tests by 3-condition test

For each of the following series, tell whether or not you can apply the 3-condition test (i.e. the alternating series test). If you can apply this test, enter D if the series diverges, or C if the...

# Summation of a?n from n=1 to infinity=1-1/10+1/100-1/1000.......

For the following alternating series, Σ an = 1-1/10+1/100-1/1000+1/10000 ....... ^(from n=1 to infinity) how many terms do you have to go for your approximation (your partial sum) to be...

# summation of ((8^n)(x^n)(n+1))/(n+2) from n=1 to infinity

Find all the values of x such that the given series would converge. The Above Equation The series is convergent from = ? , left end included (enter Y or N): ? to = ? , right end included...

# how can you simplify (n^10)/((n+1)^10)?

This is coming from the original question of : Find all the values of x such that the given series would converge. summation of ((11x)^n)/(n^10) from n=1 to infinity The series is convergent from...