Question 1

A 20-g bead is attached to a light 120 cm-long string as shown in the figure. If the angle θ is measured to be 18°, what is the speed of the mass?

Accepted Answer

The answer of A 20-g bead is attached to a...

Question 2

When a spacecraft is launched from the earth toward the sun, at what distance from the earth will the gravitational forces due to the sun and the earth cancel? Earth's mass is $5.97 \times 10 ^ { 24 } \mathrm {~kg}$ the sun's mass is $1.99 \times 10^{30} \mathrm {~kg}$ and the Earth-sun distance is  1.5 x $10 ^ { 11 } \mathrm {~m}$

Accepted Answer

The answer of When a spacecraft is launched from the...

Question 3

A highway curve of radius  80 m is banked at $45 ^ { \circ }$ Suppose that an ice storm hits, and the curve is effectively frictionless. What is the speed with which to take the curve without tending to slide either up or down the surface of the road?

Accepted Answer

The speed to take a frictionless banked curve without sliding is given by $v = \sqrt{rg\tan(\theta)}$, where $r$ is the radius of the curve, $g$ is the acceleration due to gravity (approximately $9.8 \, \text{m/s}^2$), and $\theta$ is the banking angle. Plugging in the given values ($r = 80 \, \text{m}$, $\theta = 45^\circ$), we get $v = \sqrt{80 \times 9.8 \times \tan(45^\circ)} = \sqrt{80 \times 9.8} = \sqrt{784} = 28 \, \text{m/s}$.

Question 4

What is the gravitational force acting on a 59-kg person due to another 59-kg person standing  2.0 m away? We can model each person as a small sphere. $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

Accepted Answer

The gravitational force between two masses can be calculated using Newton's law of universal gravitation: $F = G \frac{m_1 m_2}{r^2}$, where $G = 6.67 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2$, $m_1 = 59 \, \text{kg}$, $m_2 = 59 \, \text{kg}$, and $r = 2.0 \, \text{m}$. Plugging these values into the formula gives $F = 6.67 \times 10^{-11} \times \frac{59 \times 59}{2.0^2} = 5.8 \times 10^{-8} \, \text{N}$.

Question 5

What is the magnitude of the gravitational force that two small  7.00-kg  balls exert on each other when they are  35.0 cm apart? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

Accepted Answer

The answer of What is the magnitude of the gravitational...

Question 6

A very dense 1500-kg point mass  (A)  and a dense 1200-kg point mass  (B)  are held in place  1.00 m apart on a frictionless table. A third point mass is placed between the other two at a point that is  20.0 cm from  B  along the line connecting  A  and  B . When the third mass is suddenly released, find the magnitude and direction (toward  A  or toward  B  ) of its initial acceleration. $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

Accepted Answer

The answer of A very dense 1500-kg point mass ...

Question 7

$\begin{array} { | c | c | c | c | c | } 
\hline & \text { Mass } & \text { Radius } & \text { Orbital radius } & \text { Orbital period } \
\hline \text { Moon A } & 4.0 \times 10 ^ { 20 } \mathrm {~kg} & \text { unknown } & 2.0 \times 10 ^ { 8 } \mathrm {~m} & 4.0 \times 10 ^ { 6 } \mathrm {~s} \
\hline \text { Moon B } & 1.5 \times 10 ^ { 20 } \mathrm {~kg} & 2.0 \times 10 ^ { 5 } \mathrm {~m} & 3.0 \times 10 ^ { 8 } \mathrm {~m} & \text { unknown } \
\hline
\end{array}$
Mithra is an unknown planet that has two moons,  A  and  B , in circular orbits around it. The table summarizes the hypothetical data about these moons. What is the magnitude of the maximum gravitational force that Moon A exerts on Moon B? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

Accepted Answer

The answer of \(\begin{array} { | c | c |...

Question 8

Two horizontal curves on a bobsled run are banked at the same angle, but one has twice the radius of the other. The safe speed (for which no friction is needed to stay on the run) for the smaller radius curve is  v . What is the safe speed on the larger-radius curve?

Accepted Answer

The safe speed on a banked curve depends on the radius of the curve and the banking angle. For a given angle, the safe speed is proportional to the square root of the radius. If one curve has twice the radius of the other, the safe speed for the larger-radius curve is $v \sqrt{2}$, because the square root of 2 times the radius results in a safe speed that is the square root of 2 times the original speed.

Question 9

Two identical tiny balls of highly compressed matter are  1.50 m apart. When released in an orbiting space station, they accelerate toward each other at $2.00 \mathrm {~cm} / \mathrm { s } ^ { 2 }$
What is the mass of each of them? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

Accepted Answer

The answer of Two identical tiny balls of highly compressed...

Question 10

As a 70-kg person stands at the seashore gazing at the tides (which are caused by the Moon), how Iarge is the gravitational force on that person due to the Moon? The mass of the Moon is  7.35 x $10 ^ { 22 } \mathrm {~kg}$ the distance to the Moon is $3.82 \times 10 ^ { 8 } \mathrm {~m}$ and $G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } .$

Accepted Answer

The answer of As a 70-kg person stands at the...

Question 11

A curved portion of highway has a radius of curvature of 65 m. As a highway engineer,
you want to bank this curve at the proper angle for a steady speed of 22 m/s.
(a) What banking angle should you specify for this curve?
(b) At the proper banking angle, what normal force and what friction force does the
highway exert on a 750-kg car going around the curve at the proper speed?

Accepted Answer

The answer of A curved portion of highway has a...

Question 12

A car traveling at a steady 20 m/s rounds an 80-m radius horizontal unbanked curve with the tires on the verge of slipping. What is the maximum speed with which this car can round a second
Unbanked curve of radius 320 m if the coefficient of static friction between the car's tires and the
Road surface is the same in both cases?

Accepted Answer

The maximum speed $v$ at which a car can round a curve without slipping is given by the formula $v = \sqrt{\mu rg}$, where $\mu$ is the coefficient of static friction, $r$ is the radius of the curve, and $g$ is the acceleration due to gravity. Since $\mu$ and $g$ are constants, the maximum speed is directly proportional to the square root of the radius of the curve. Given that the car can travel at 20 m/s around an 80-m radius curve, for a curve with a radius four times larger (320 m), the maximum speed would be double, because the square root of 4 is 2. Therefore, the maximum speed for the 320-m radius curve is $20 m/s \times 2 = 40 m/s$.

Question 13

A 600-kg car is going around a banked curve with a radius of 110 m at a steady speed of 24.5 m/s. What is the appropriate banking angle so that the car stays on its path without the assistance of
Friction?

Accepted Answer

The appropriate banking angle can be found using the formula for the centripetal force required to keep the car moving in a circle of radius $r$ at speed $v$, which is given by $F_c = \frac{mv^2}{r}$, where $m$ is the mass of the car, $v$ is its velocity, and $r$ is the radius of the curve. For a banked curve without friction, the centripetal force is provided by the component of the gravitational force acting down the slope of the bank, which depends on the banking angle $\theta$. The correct relationship that equates the gravitational force component to the necessary centripetal force, and allows solving for $\theta$, is $\tan(\theta) = \frac{v^2}{rg}$, where $g$ is the acceleration due to gravity (approximately $9.8 m/s^2$). Substituting the given values ($v = 24.5 m/s$, $r = 110 m$, $g = 9.8 m/s^2$) into this formula and solving for $\theta$ yields an angle of approximately $29.1^\circ$.

Question 14

A 20-g bead is attached to a light 120-cm-long string as shown in the figure. This bead moves in a horizontal circle with a constant speed of 1.5 m/s. What is the tension in the string if the angle θ is
Measured to be 25°?

Accepted Answer

The answer of A 20-g bead is attached to a...

Question 15

A small 175-g ball on the end of a light string is revolving uniformly on a frictionless
surface in a horizontal circle of diameter 1.0 m. The ball makes 2.0 revolutions every 1.0 s.
(a) What are the magnitude and direction of the acceleration of the ball?
(b) Find the tension in the string.

Accepted Answer

The answer of A small 175-g ball on the end...

Question 16

In a carnival ride, passengers stand with their backs against the wall of a cylinder. The cylinder is set into rotation and the floor is lowered away from the passengers, but they remain stuck against
The wall of the cylinder. For a cylinder with a 2.0-m radius, what is the minimum speed that the
Passengers can have so they do not fall if the coefficient of static friction between the passengers
And the wall is 0.25?

Accepted Answer

The answer of In a carnival ride, passengers stand with...

Question 17

What is the proper banking angle for an Olympic bobsled to negotiate a  100-m radius turn at 35  m/s without skidding?

Accepted Answer

The proper banking angle ($\theta$) for a bobsled (or any vehicle) to negotiate a turn without skidding can be found using the formula for the centripetal force required for circular motion, which is provided by the gravitational force component acting down the slope of the bank. This is given by $\tan(\theta) = \frac{v^2}{rg}$, where $v$ is the velocity, $r$ is the radius of the turn, and $g$ is the acceleration due to gravity (approximately $9.8 m/s^2$). Plugging in the given values ($v = 35 m/s$, $r = 100 m$), we get $\tan(\theta) = \frac{(35)^2}{100 \times 9.8}$, which simplifies to $\tan(\theta) \approx 1.225$. Solving for $\theta$ gives $\theta \approx 51^\circ$.

Question 18

The curved section of a speedway is a circular arc having a radius of 190 m. This curve is properly banked for racecars moving at 34 m/s. At what angle with the horizontal is the curved part of the
Speedway banked?

Accepted Answer

The correct answer is A because the angle of banking is given by the equation tan(theta) = v^2 / rg, where v is the speed of the car, r is the radius of the curve, and g is the acceleration due to gravity. Plugging in the given values, we get tan(theta) = (34 m/s)^2 / (190 m * 9.8 m/s^2) = 0.602. Taking the arctangent of both sides, we get theta = 32 degrees.

Question 19

A future use of space stations may be to provide hospitals for severely burned persons. It is very painful for a badly burned person on Earth to lie in bed. In a space station, the effect of gravity can
Be reduced or even eliminated. How long should each rotation take for a doughnut-shaped
Hospital of 200-m radius so that persons on the outer perimeter would experience 1/10 the normal
Gravity of Earth?

Accepted Answer

The answer of A future use of space stations may...

Question 20

A highway curve of radius  100 m, banked at an angle of $45 ^ { \circ }$ may be negotiated without friction at a speed of

Accepted Answer

The answer of A highway curve of radius  100...

Quiz 5: Circular Motion; Gravitation

A 20-g bead is attached to a light 120 cm-long string as shown in the figure. If the angle θ is measured to be 18°, what is the speed of the mass?

A highway curve of radius 80 m is banked at 45∘45 ^ { \circ }45∘ Suppose that an ice storm hits, and the curve is effectively frictionless. What is the speed with which to take the curve without tending to slide either up or down the surface of the road?

What is the magnitude of the gravitational force that two small 7.00-kg balls exert on each other when they are 35.0 cm apart? (G=6.67×10−11 N⋅m2/kg2)\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)(G=6.67×10−11 N⋅m2/kg2)

Two horizontal curves on a bobsled run are banked at the same angle, but one has twice the radius of the other. The safe speed (for which no friction is needed to stay on the run) for the smaller radius curve is v . What is the safe speed on the larger-radius curve?

A 600-kg car is going around a banked curve with a radius of 110 m at a steady speed of 24.5 m/s. What is the appropriate banking angle so that the car stays on its path without the assistance of Friction?

A 20-g bead is attached to a light 120-cm-long string as shown in the figure. This bead moves in a horizontal circle with a constant speed of 1.5 m/s. What is the tension in the string if the angle θ is Measured to be 25°?

A small 175-g ball on the end of a light string is revolving uniformly on a frictionless surface in a horizontal circle of diameter 1.0 m. The ball makes 2.0 revolutions every 1.0 s. (a) What are the magnitude and direction of the acceleration of the ball? (b) Find the tension in the string.

What is the proper banking angle for an Olympic bobsled to negotiate a 100-m radius turn at 35 m/s without skidding?

The curved section of a speedway is a circular arc having a radius of 190 m. This curve is properly banked for racecars moving at 34 m/s. At what angle with the horizontal is the curved part of the Speedway banked?

A highway curve of radius 100 m, banked at an angle of 45∘45 ^ { \circ }45∘ may be negotiated without friction at a speed of

A highway curve of radius 80 m is banked at $45 ^ { \circ }$ Suppose that an ice storm hits, and the curve is effectively frictionless. What is the speed with which to take the curve without tending to slide either up or down the surface of the road?

What is the magnitude of the gravitational force that two small 7.00-kg balls exert on each other when they are 35.0 cm apart? $\left( G = 6.67 \times 10 ^ { - 11 } \mathrm {~N} \cdot \mathrm { m } ^ { 2 } / \mathrm { kg } ^ { 2 } \right)$

A highway curve of radius 100 m, banked at an angle of $45 ^ { \circ }$ may be negotiated without friction at a speed of