Question 1

Express $9.8\ \mu\mathrm{m}$ in complete decimal form, using only meters and no unit prefixes.

Accepted Answer

$0.0000098\ \mathrm{m}$

Question 2

The Recommended Dose Allowance (RDA) for the trace metal lead through diet is $0.000114\ \mathrm{g/day}$. Express this dose in micrograms per day.

Accepted Answer

$114\ \mathrm{micrograms/day}$

Question 3

Following the rules of significant figures, simplify the expression $\frac{21.8}{16.9}$.

Accepted Answer

$1.3$

Question 4

A school bus is heading to school at a constant velocity. After covering a distance of $140\ \mathrm{m}$ in $5.0\ \mathrm{s}$, the driver applies brakes on a traffic signal and comes to rest in $4.0\ \mathrm{s}$. Determine the magnitude of its acceleration in (i) $\mathrm{m/s^2}$ and (ii) in terms of the gravitational constant $g$.

Accepted Answer

i) $8.4\ \mathrm{m/s^2}$, ii) $0.4g$

Question 5

Suppose a particle's position depends on time and it moves according to the equations $x = \frac{1}{3}t^3 - t^2\ \mathrm{m}$ and $y = \frac{1}{4}t^4 - t^2\ \mathrm{m}$. Determine where the particle is at (i) $t = 0\ \mathrm{s}$ and (ii) $t = 6\ \mathrm{s}$. Also, find its speed at $t = 6\ \mathrm{s}$.

Accepted Answer

i) $\vec{r} = (0\hat{i} + 0\hat{j})\ \mathrm{m}$, v = $1\ \mathrm{m/s}$; ii) $\vec{r} = (36\hat{i} + 3\hat{j})\ \mathrm{m}$, v = $24.1\ \mathrm{m/s}$

Question 6

A drone is initially at rest at the origin point, coordinates $(0,0)$, and begins to move across the $xy$-plane. It accelerates at a constant rate, described by the vector $\vec{a} = (5.0\hat{i} + 7.0\hat{j})\ \mathrm{m/s^2}$. What is the drone's speed as a function of time?

Accepted Answer

$8.6t\ \mathrm{m/s}$

Question 7

Recently, there are reports of people throwing plastics on the waters of a local lagoon. To address this, caretakers check the area by using drones. The velocity of a drone can be expressed as a function of time, and it is described by the equation $\vec{v}(t) = \left[12\frac{\mathrm{m}}{\mathrm{s}} + (0.0928\frac{\mathrm{m}}{\mathrm{s}^3})t^2\right]\hat{i} + \left[20.5\frac{\mathrm{m}}{\mathrm{s}} - (1.035\frac{\mathrm{m}}{\mathrm{s}^2})t\right]\hat{j}$. Find the magnitude and direction of the drone's velocity and acceleration $3$ seconds after launch.

Accepted Answer

Velocity = $17.025\ \mathrm{m/s}$, $41.07^\circ$; Acceleration = $6.235\ \mathrm{m/s^2}$, $275.12^\circ$

Question 8

Plants depend on the explosive mechanism for seed dispersal. A pod opens up explosively on a level ground firing a seed with an initial velocity of $55\ \mathrm{m/s}$ at $54.0^\circ$ above the horizontal. Assuming negligible air resistance, find the seed's horizontal and vertical components of acceleration and velocity at the highest point in its trajectory.

Accepted Answer

$v_x = 32.3\ \mathrm{m/s}$; $v_y = 0\ \mathrm{m/s}$; $a_x = 0\ \mathrm{m/s^2}$; $a_y = -9.8\ \mathrm{m/s^2}$

Question 9

A thief steals some precious diamonds preserved as ancient treasures in a museum. The security comes to know about the robbery and they carry out a search operation for the stolen diamonds. The thief finds himself locked inside as all the entrances and exits are sealed. In order to save himself from getting caught along with the diamonds he has to throw the diamond pouch to his partner who is outside the gate as shown in the figure. Determine the angle at which the pouch needs to be thrown so that it safely reaches the partner thief. (Assume the horizontal distance is $5.8\ \mathrm{m}$ and the vertical height is $2.0\ \mathrm{m}$.)

Accepted Answer

$42.3^\circ$

Question 10

Suppose a person with a height of $1.72\ \mathrm{m}$ is centrifuged to a maximum acceleration of $9g$ using a horizontal arm that is $7.50\ \mathrm{m}$ long. Assuming the head of the person is positioned at the outermost end of the centrifuge arm, calculate the required revolutions per minute (rev/min) to generate an acceleration of $9g$.

Accepted Answer

$1.87\ \mathrm{RPM}$

Question 11

When a vehicle takes off abruptly, you will jerk backward. To gain a better comprehension of the process, you place a box on a frictionless surface at the back of a pick-up truck. There is no mechanism to secure the box. Explain what happens when the pick-up truck takes off.

Accepted Answer

The box does not accelerate but will remain at constant velocity (at rest) until it hits the back of the pick-up.

Question 12

A 1200 kg stalled truck on a level parking lot is pushed by a small SUV of mass 650 kg in a direction due north. The SUV is pushing on the truck with a 2200 N horizontal force. Determine the magnitude of the force applied to the SUV by the truck.

Accepted Answer

$2.20 	imes 10^3\ \mathrm{N}$

Question 13

The figure shows an iron slab of mass $4.0\ \mathrm{kg}$ attached to a box having a mass of $5.0\ \mathrm{kg}$ via a massless string. The pulley connecting them has a mass of $150\ \mathrm{g}$ and a radius of $10\ \mathrm{cm}$. Calculate the magnitude of acceleration experienced by the iron slab if it has a force of $25\ \mathrm{N}$ applied toward the left. Also, calculate the magnitude of tension(s) in different parts of the string. Consider the pulley and the horizontal surface to be frictionless.

Accepted Answer

$a = 2.6\ \mathrm{m/s^2}$, $T_1 = 36\ \mathrm{N}$, $T_2 = 13\ \mathrm{N}$

Question 14

An interior decorator is rearranging furniture and needs to move a $75\ \mathrm{kg}$ bookcase across a hardwood floor. The coefficient of kinetic friction between the bookcase and the hardwood floor is $\mu_k = 0.3$. The decorator applies a force of $250\ \mathrm{N}$ by dragging to slide the bookcase. Calculate the bookcase's acceleration given that the force is applied at an angle $	heta = 5^\circ$ to the horizontal.

Accepted Answer

$0.5\ \mathrm{m/s^2}$

Question 15

An automobile of mass $1200\ \mathrm{kg}$ travels at $14\ \mathrm{m/s}$ around a flat curve with a radius of $50\ \mathrm{m}$. What is the bare minimum coefficient of friction that the tires must have with the ground in order for the car to turn?

Accepted Answer

$0.375$

Physics Fundamentals: Measurement, Kinematics, Dynamics, and Applications

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