Question 1

A giant wheel, having a diameter of 40 m, is fitted with a cage and platform on which a man of mass m stands. The wheel is rotated in a vertical plane at such a speed that the force exerted by the man on the platform is equal to his weight when the cage is at X, as shown. The net force on the man at point X is: 
A) zero
B) mg, down
C) mg, up
D) 2 mg, down
E) 2 mg, up

Accepted Answer

The answer of A giant wheel, having a diameter of...

Question 2

A coin is placed on a horizontal phonograph turntable. Let N be the normal force exerted by the turntable on the coin, f be the frictional force exerted by the turntable on the coin, and f_s, _max be the maximum force of the static friction. The speed of the turntable is increased in small steps. If the coin does not slide, then A) N increases, f increases, and f_{s, max} stays the same B) N increases, f increases, and f_{s, max} increases C) f increases and both N and f_{s, max} stay the same D) N, f, and f_{s, max} all stay the same E) N, f, and f_{s, max} all increase

Accepted Answer

The normal force (N) and the maximum static friction force ($f_{s, \text{max}}$) do not change because they are determined by the mass of the coin and the coefficient of static friction between the coin and the turntable, respectively. The frictional force (f) increases to prevent the coin from sliding as the turntable's speed increases, up to the point where it reaches $f_{s, \text{max}}$.

Question 3

A giant wheel, 40 m in diameter, is fitted with a cage and platform on which a man can stand. The wheel rotates at such a speed that when the cage is at X (as shown) the force exerted by the man on the platform is equal to his weight. The speed of the man is: 
A) 14 m/s
B) 20 m/s
C) 28 m/s
D) 80 m/s
E) 120 m/s

Accepted Answer

When the cage is at X, the centripetal force acting on the man is equal to his weight. The centripetal force is given by:

F = mv²/r

where m is the mass of the man, v is his speed, and r is the radius of the wheel.

When F = w (the man's weight), we have:

w = mv²/r

Solving for v, we get:

v = sqrt(wr/m)

Substituting the given values, we get:

v = sqrt(9.81 x 20) = 14 m/s

Therefore, the speed of the man is 14 m/s. The answer is B.

Question 4

One end of a 1.0-m long string is fixed, the other end is attached to a 2.0-kg stone. The stone swings in a vertical circle, passing the bottom point at 4.0 m/s. The tension force of the string (in newtons) at this point is about:
A) 0
B) 12
C) 20
D) 32
E) 52

Accepted Answer

The answer of One end of a 1.0-m long string...

Question 5

Circular freeway entrance and exit ramps are commonly banked to handle a car moving at 13 m/s. To design a similar ramp for 26 m/s one should:
A) increase radius by factor of 2
B) decrease radius by factor of 2
C) increase radius by factor of 4
D) decrease radius by factor of 4
E)

Accepted Answer

The answer of Circular freeway entrance and exit ramps are...

Question 6

The iron ball shown is being swung in a vertical circle at the end of a 0.7-m string. How slowly, in ft/s, can the ball go through its top position without having the string go slack? 
A) 1.3 m/s
B) 2.6 m/s
C) 3.9 m/s
D) 6.9 m/s
E) 9.8 m/s

Accepted Answer

The answer of The iron ball shown is being swung...

Question 7

At what angle should the roadway on a curve with a 50m radius be banked to allow cars to negotiate the curve at 12 m/s even if the roadway is icy (and the frictional force is zero)?
A) 0
B) 16°
C) 18°
D) 35°
E) 73°

Accepted Answer

The answer of At what angle should the roadway on...

Question 8

A person riding a Ferris wheel is strapped into her seat by a seat belt. The wheel is spun so that the centripetal acceleration is g. Select the correct combination of forces that act on her when she is at the top. In the table, F_g = force of gravity, down; F_b = seat belt force, down; and F_s = seat force, up. A) F_g = 0, F_b = mg, F_s = 0 B) F_g = mg, F_b = 0, F_s = 0 C) F_g = 0, F_b = 0, F_s = mg D) F_g = mg, F_b = mg, F_s = 0 E) F_g = mg, F_b = 0, F_s = mg

Accepted Answer

The answer of A person riding a Ferris wheel is...

Question 9

A car rounds a 75-m radius curve at a constant speed of 18 m/s. A ball is suspended by a string from the ceiling the car and moves with the car. The angle between the string and the verticle is:
A) 0
B) 1.4°
C) 24°
D) 90°
E) cannot be found without knnowing the mass of the ball

Accepted Answer

The force acting on the ball is the tension in the string, which is always directed towards the center of the circular path. In this case, the center of the circle is below the ball, and so the tension force also has a vertical component, which is equal and opposite to the force of gravity.

Since the car is moving at a constant speed, the net force on the ball must be zero, and so the vertical component of the tension force must exactly balance the force of gravity. Therefore, the angle between the string and the vertical must be equal to the angle whose tangent is the ratio of these two forces:

tan θ = (mg) / (mv² / r)

where m is the mass of the ball, g is the acceleration due to gravity, v is the speed of the car, and r is the radius of the circular path.

Since we are not given the mass of the ball, we cannot calculate this angle exactly. However, we can make an estimate by assuming that the mass of the ball is relatively small compared to the other quantities, and so the term (mg) can be neglected. Under this assumption, we have:

tan θ ≈ 0.2

which gives:

θ ≈ 11.5°

This is closest to choice C, 24°, but it is not an exact match. Therefore, we should choose C as the best answer, but with the caveat that it is only an estimate.

Question 10

A block is suspended by a rope from the ceiling of a car.. When the car rounds a 45-m radius horizontal curve at 22 m/s (about 50 mph), what angle does the rod make with the vertical?
A) 0
B) 25$\degree$
C) 42$\degree$
D) 65$\degree$
E) 90$\degree$

Accepted Answer

The force acting on the block is a combination of tension and the centrifugal force. At the top of the curve, the tension is pulling straight up, so the angle between the rope and the vertical is 0 degrees. However, as the car accelerates horizontally around the curve, the tension force starts to shift towards the outside of the curve. At some point, the tension force is perpendicular to the centrifugal force, creating a right angle between the two. This occurs when the angle between the rope and vertical is equal to the angle of the curve, which is 42 degrees (as calculated using $tan^{-1}(22^2/9.8 \cdot 45)$). Therefore, the answer is C.

Question 11

One end of a 1.0-m string is fixed, the other end is attached to a 2.0-kg stone. The stone swings in a vertical circle, passing the top point at 4.0 m/s. The tension force of the string (in newtons) at this point is about:
A) 0
B) 12
C) 20
D) 32
E) 52

Accepted Answer

The answer of One end of a 1.0-m string is...

Quiz 6: Force and Motion II

A giant wheel, 40 m in diameter, is fitted with a cage and platform on which a man can stand. The wheel rotates at such a speed that when the cage is at X (as shown) the force exerted by the man on the platform is equal to his weight. The speed of the man is:

One end of a 1.0-m long string is fixed, the other end is attached to a 2.0-kg stone. The stone swings in a vertical circle, passing the bottom point at 4.0 m/s. The tension force of the string (in newtons) at this point is about:

Circular freeway entrance and exit ramps are commonly banked to handle a car moving at 13 m/s. To design a similar ramp for 26 m/s one should:

The iron ball shown is being swung in a vertical circle at the end of a 0.7-m string. How slowly, in ft/s, can the ball go through its top position without having the string go slack?

At what angle should the roadway on a curve with a 50m radius be banked to allow cars to negotiate the curve at 12 m/s even if the roadway is icy (and the frictional force is zero) ?

A car rounds a 75-m radius curve at a constant speed of 18 m/s. A ball is suspended by a string from the ceiling the car and moves with the car. The angle between the string and the verticle is:

A block is suspended by a rope from the ceiling of a car.. When the car rounds a 45-m radius horizontal curve at 22 m/s (about 50 mph) , what angle does the rod make with the vertical?

One end of a 1.0-m string is fixed, the other end is attached to a 2.0-kg stone. The stone swings in a vertical circle, passing the top point at 4.0 m/s. The tension force of the string (in newtons) at this point is about: