An old street car rounds a flat corner of radius 10 . 5 m at 16 km h - 1 . What angle with the vertical will be made by the loosely hanging hand straps?

Given, Radius of circular motion, R = 10 . 5 m . Speed of car, v = 16 km h - 1 = 16 × 5 18 m s - 1 = 4 . 44 m s - 1 . Let, T be tension in hanging hand straps and θ be and angle with vertical. From above figure, T sin θ will provide centripetal force. T sin θ = m v 2 R … 1 T cos θ = m g … 2 From equations 1 and 2 , we get, tan θ = v 2 R g ⇒ θ = tan - 1 v 2 R g … 3 Putting values of v , R and g = 9 . 8 m s - 2 in equation 3 , we get, θ = tan - 1 4 . 4 2 10 . 5 × 9 . 8 θ = 12 ° .

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A roller-coaster car has a mass of $1300 kg$ When fully loaded with passengers. As the car passes over the top of a circular hill of radius $20 m$ , its speed is not changing. At the top of the hill, what are the (a) magnitude $F_{N}$ and (b) direction (up or down) of the normal force on the car from the track if the car's speed is $v = 11 m / s ?$ What are (c) $F_{N}$ and (d) the direction if $v = 14 m / s ?$

Important Questions on Force and Motion-II

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Principles Of Physics International Student Version>Chapter 6 - Force and Motion-II>Problems>Q 49

In the figure shown below, a car is driven at constant speed over a circular hill and then into a circular valley with the same radius. At the top of the hill, the normal force on the driver from the car seat is $0$ . The driver's mass is $80.0 kg$ . What is the magnitude of the normal force on the driver from the seat when the car passes through the bottom of the valley?

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Principles Of Physics International Student Version>Chapter 6 - Force and Motion-II>Problems>Q 50

An $85.0 kg$ passenger is made to move along a circular path of radius $r = 3.50 m$ in uniform circular motion. (a) Figure (a) is a plot of the required magnitude $F$ of the net centripetal force for a range of possible values of the passenger's speed $v$ . What is the plot's slope at $v = 8.30 m s^{- 1}$ ? (b) Figure (b) is a plot of $F$ for a range of possible values of $T$ , the period of the motion. What is the plot's slope at $T = 2.50 s$ ?

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Principles Of Physics International Student Version>Chapter 6 - Force and Motion-II>Problems>Q 51

An airplane is flying in a horizontal circle at a speed of $600 km h^{- 1}$ (shown in figure). If its wings are tilted at angle $θ = 40 °$ to the horizontal, what is the radius of the circle in which the plane is flying? Assume that, the required force is provided entirely by an "aerodynamic lift" that is perpendicular to the wing surface.

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Principles Of Physics International Student Version>Chapter 6 - Force and Motion-II>Problems>Q 52

An amusement park ride consists of a car moving in a vertical circle on the end of a rigid boom of negligible mass. The combined weight of the car and riders is

6.0 kN

and the circle's radius is

10 m

. At the top of the circle, what are the (a) magnitude

F_{B}

and (b) direction (up or down) of the force on the car from the boom if the car's speed is

v = 5.0 m s^{- 1}

? What are (c)

F_{B}

and (d) the direction if

v = 12 m s^{- 1}

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Principles Of Physics International Student Version>Chapter 6 - Force and Motion-II>Problems>Q 53

An old street car rounds a flat corner of radius

10.5 m

16 km h^{- 1} .

What angle with the vertical will be made by the loosely hanging hand straps?

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Principles Of Physics International Student Version>Chapter 6 - Force and Motion-II>Problems>Q 54

In designing circular rides for amusement parks, mechanical engineers must consider how small variations in certain parameters can alter the net force on a passenger. Consider a passenger of mass

m

riding around a horizontal circle of radius

r

at speed

v

. What is the variation

d F

in the net force magnitude for (a) a variation

d r

in the radius with

v

held constant, (b) a variation

d v

in the speed with

r

held constant, and (c) a variation

d T

in the period with

r

held constant?

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Principles Of Physics International Student Version>Chapter 6 - Force and Motion-II>Problems>Q 55

A bolt is threaded onto one end of a thin horizontal rod, and the rod is then rotated horizontally about its other end. An engineer monitors the motion by flashing a strobe lamp onto the rod and bolt, adjusting the strobe rate until the bolt appears to be in the same eight places during each full rotation of the rod (as shown in figure). The strobe rate is $2000$ flashes per second; the bolt has mass $33 g$ and is at radius $4.0 cm .$ What is the magnitude of the force on the bolt from the rod?

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Principles Of Physics International Student Version>Chapter 6 - Force and Motion-II>Problems>Q 56

A banked circular highway curve is designed for traffic moving at

65 km h^{- 1}

. The radius of the curve is

200 m

. Traffic is moving along the highway at

40 km h^{- 1}

on a rainy day. What is the minimum coefficient of friction between tires and road that will allow cars to take the turn without sliding off the road? (Assume the cars do not have negative lift.)

Important Questions on Force and Motion-II

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