Forces and Gravity

Two coccal bacteria, each with a mass of $9.5 \times 10^{-16}$ kg, are separated by a distance of $1 \mu m$. What is the gravitational force between them, given $G = 6.67 \times 10^{-11} Nm^2/kg^2$?

If the radius of a planet is doubled, how does the free fall acceleration ($g$) at the surface change, assuming the planet's mass remains constant?

A sphere with a mass of 20 kg is placed on the Earth's surface where $g = 9.8 m/s^2$. What is the weight of the sphere?

A box rests on a horizontal surface. A force of 15 N is applied upwards, while gravity exerts a force of 11 N downwards on the box. What is the normal force exerted by the surface on the box?

Which of the following best describes the direction of the normal force exerted by a surface on an object?

What primarily causes the force of friction between two surfaces in contact?

What is the primary role of static friction?

An object is placed on a slope. As the angle of the slope increases, how does the magnitude of the normal force acting on the object change?

Which statement accurately describes the difference between scalar and vector quantities?

A force vector is represented by $\vec{F}$. Which of the following represents the magnitude of this vector?

What does the negative of a vector represent?

Two displacement vectors, one 5m and the other 3m, are acting along the same line. If they point in the same direction, what is the magnitude of the resultant vector?

When resolving a vector into its components, what information do the components provide?

What is the significance of the algebraic sign ( + or − ) of a vector component?

Which of the following is a false statement about vector magnitudes?

If two vectors of magnitudes 3N and 4N are added, what is the minimum magnitude of the resultant vector?

A car travels 5 km east, then 3 km south, and finally 2 km west. What is the magnitude and direction of the car's resultant displacement?

A hiker travels 100 m north and then 50 m east. What is the magnitude and direction of the hiker's displacement?

Which of the following is NOT a fundamental force?

What determines an object's motion when multiple forces act upon it?

An object experiences two forces: 10N to the right and 4N to the left. What is the net force acting on the object?

According to Newton's First Law, what condition must be met for an object's velocity to remain constant?

Which of the following best exemplifies inertia?

A force vector has a magnitude of 15 N and is directed 30° above the +x-axis. What is the magnitude of its y-component?

In a free-body diagram, which forces should be included?

A displacement vector has an x-component of -5.0 m and a y-component of +8.0 m. In which quadrant does this vector lie?

Given a vector with a magnitude of 20 units and an angle of 60° with respect to the x-axis, what are the approximate magnitudes of its x and y components?

Vector A has components $A_x = -3$ and $A_y = 4$. What is the angle of this vector with respect to the positive x-axis?

Which trigonometric function is defined as the ratio of the opposite side to the hypotenuse in a right triangle?

A vector has a negative x-component and a negative y-component. In which quadrant does this vector lie?

Vector A has a magnitude of 10 and makes an angle of 30 degrees with the positive x-axis. Vector B has a magnitude of 15 and makes an angle of 120 degrees with the positive x-axis. What is the x-component of the resultant vector A + B?

A projectile is launched with an initial velocity $v_0$ at an angle $\theta$ with respect to the horizontal. Assuming negligible air resistance, what is the y-component of the projectile's velocity at the highest point of its trajectory?

When adding vectors $\vec{A}$ and $\vec{B}$ to obtain $\vec{C}$, which of the following statements is always true?

In a scenario where multiple forces are acting on an object, what is the purpose of creating a free-body diagram?

A force $\vec{F_1}$ of 30 N acts on an object at an angle of 30° above the +x axis, and a force $\vec{F_2}$ of 40 N acts on the same object along the +y axis. What is the approximate magnitude of the resultant force?

In the context of vector addition, what does 'resolving a force into components' mean?

Consider three forces acting on an object: $\vec{F_1} = 20\hat{i}$ N, $\vec{F_2} = -10\hat{j}$ N, and $\vec{F_3} = -5\hat{i} + 5\hat{j}$ N. What is the x-component of the resultant force?

An object has two forces acting on it: 50 N at 0 degrees and 30 N at 90 degrees. What is the approximate angle of the resultant force with respect to the x-axis?

A person is pulling a box with a force of 100 N at an angle of 60 degrees above the horizontal. What is the horizontal component of the force?

When should you exclude a force from a free-body diagram?

Two spheres, each with a mass of 30 kg, are separated by a center-to-center distance of 0.05 m. Which of the following best approximates the gravitational force between them?

A radio transmitter's power output is changed such that the new power, $P$, is four times the initial power, $P_0$. By what factor has the power increased?

If the kinetic energy of an object increases by 25%, by what factor is the new kinetic energy, $E_f$, related to the original kinetic energy, $E_0$?

The speed of a car decreases by 10% after the driver applies the brakes. If the initial speed was $v_0$, what is the final speed, $v_f$, in terms of $v_0$?

An object's momentum increases by 300%. By what factor has its momentum increased?

A scientist measures the length of a bacterium under a microscope and finds its length has decreased by 5%. If the original length was $L_0$, what is the new length, $L_f$?

The population of a town increases by 8% in one year. If the initial population was $P_0$, what is the final population, $P_f$, at the end of the year?

Coccal bacteria, with a mass of approximately $9.5 × 10^{-13}$ g each and a radius of approximately $0.5 \mu m$ each, form Diplococcal bacteria. Estimate the gravitational force between these two adjacent bacteria.