Q: Consider a vehicle's motion along a linear path, and the graph below illustrates its position as a function of time. Determine the instants if any where the velocity of the object becomes zero.

$$t = 10\ \mathrm{s}$$ \text{ and } t = 25\ \mathrm{s}$

Q: Shown below are three boats being pulled along the x-axis on a frictionless surface via ropes. If the magnitude of the pull force applied is $$480\ \mathrm{N}$$, calculate the tension in each rope.

$$T_A = 360.0\ \mathrm{N}$$ \text{ and } T_B = 260.0\ \mathrm{N}$

Q: A container being lowered from a crane is held in place by a light steel cable that makes an angle of $$58.0^\circ$$ from the vertical and a horizontal synthetic cable. If the container has a mass $$m = 4520\ \mathrm{kg}$$, determine the tension $$T_1 in $$the slanted cable and the tension $$T_2 in $$the horizontal cable.

$$T_1 = 4.43$$ \times $$10^4$$\ \mathrm{N},\ $$T_2 = 2.35$$ \times $$10^4$$\ \mathrm{N}$$

Q: An exoplanet has a mean radius equal to $$0.09$$ times the radius of Earth and a mass equal to $$0.00023$$ times the mass of Earth. What would be the gravitational acceleration at the exoplanet's surface?

$$g_{\text{exoplanet}} = 0.084\ \mathrm{m/s^2$}$$

Q: A satellite with a mass of $$5.0 \times 10^3$\ \mathrm{kg} is $$moving at a speed of $$2.5 \times 10^3$\ \mathrm{m/s}. $$Due to a major technical issue, the satellite explodes into 3 fragments. One of the fragments with a mass of $$75 \times 10^1$\ \mathrm{kg}$$ continues forward at a speed of $$1.5 \times 10^3$\ \mathrm{m/s}. $$The second fragment moves in the backward direction at a speed of $$0.5 \times 10^3$\ \mathrm{m/s}. $$Find the speed and direction in which the third fragment moves, if the mass of the second fragment is $$6.0 \times 10^2$\ \mathrm{kg}.$$

$$1.56 \times 10^3$\ \mathrm{m/s}$$, -x direction

Q: A $$20\ \mathrm{kg}$$ crate is being pulled up a $$20^\circ$$ incline with a constant velocity by a force $$F at an $$angle of $$15^\circ$$ below the horizontal. Determine the work done by the weight ($$W_g$$), normal force ($$W_N) $$and applied force ($$W_F) on $$the crate as it travels $$10\ \mathrm{m}$$ along the incline.

$$W_g = -6.7 \times 10^2$\ \mathrm{J},\ W_N = 0\ \mathrm{J},\ W_F = 6.7 \times 10^2$\ \mathrm{J}$$

Question 1

Determine the number of gallons of diesel used in Arizona in one day. The average mileage of a car is approximately 30 miles per gallon, and each car is driven an average of 12,000 miles annually. There are four cars for every five people and there is an estimated $$7 	imes 10^6$ people in the state of Arizona. Answer in three significant figures.

Accepted Answer

$$6.14 	imes 10^4$ gal/day

Question 2

A van of Swift (a company that delivers packages) was initially parked at Cornelia Street. Then, it starts moving with an acceleration of $$3.2\ \mathrm{m/s^2$}. At $$the instant it has started moving, a van of its competitor, Thunder, traveling with a constant speed of $$22.0\ \mathrm{m/s}$$, overtakes and passes the van of Swift. What is the speed of the van of Swift when it overtakes the van of Thunder?

Accepted Answer

$$44\ \mathrm{m/s}$$

Question 3

Consider a vehicle's motion along a linear path, and the graph below illustrates its position as a function of time. Determine the instants if any where the velocity of the object becomes zero.

Accepted Answer

$$t = 10\ \mathrm{s}$$ 	ext{ and } t = 25\ \mathrm{s}$

Question 4

Imagine a rock at the ridge of a mountain incline at a $$22^\circ$$ angle below the horizontal, with an initial velocity of $$6.0\ \mathrm{m/s}. If $$the mountain's edge is $$13\ \mathrm{m}$$ above the ground, calculate the horizontal distance between the base of the mountain to the point at which the rock hits the ground.

Accepted Answer

$$7.9\ \mathrm{m}$$

Question 5

Twenty magic balls each weighing a quarter of a kilogram are contained in a thin bag of negligible weight. This bag of magic balls is carried by a $$90\ \mathrm{kg}$$ floating genie descending with a constant downward velocity of $$8\ \mathrm{m/s}. $$One of the magic balls is thrown from the bag initially at $$4\ \mathrm{m/s}$$ perpendicularly to the downward path of the genie. This is measured relative to a stationary speed meter in the bag. After $$12\ \mathrm{s}$$ the genie sees the thrown magic ball bounce for the first time. Calculate how far the genie was from the ground when the magic ball was thrown. Assume that the genie continues his descent at a constant speed of $$8\ \mathrm{m/s}$$ and he can be treated like a point-like object.

Accepted Answer

$$860.1\ \mathrm{m}$$

Question 6

Shown below are three boats being pulled along the x-axis on a frictionless surface via ropes. If the magnitude of the pull force applied is $$480\ \mathrm{N}$$, calculate the tension in each rope.

Accepted Answer

$$T_A = 360.0\ \mathrm{N}$$ 	ext{ and } T_B = 260.0\ \mathrm{N}$

Question 7

An iron slab of mass $$4.0\ \mathrm{kg} is $$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 a force of $$25\ \mathrm{N} is $$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

$$a = 2.8\ \mathrm{m/s^2$},\ T_1$ = 36\ \mathrm{N},\ T_2$ = 14\ \mathrm{N}$$

Question 8

A $$50.0\ \mathrm{N}$$ animal salt block is at rest on a horizontal floor. The coefficients of static and kinetic friction between the block and the floor are $$0.54$$ and $$0.36$$ respectively. A goat pushes on the block applying a horizontal force of magnitude $$12.0\ \mathrm{N}. $$Determine the magnitude of the friction force if the block is at rest when the push is applied.

Accepted Answer

$$12.0\ \mathrm{N}$$

Question 9

A container being lowered from a crane is held in place by a light steel cable that makes an angle of $$58.0^\circ$$ from the vertical and a horizontal synthetic cable. If the container has a mass $$m = 4520\ \mathrm{kg}$$, determine the tension $$T_1 in $$the slanted cable and the tension $$T_2 in $$the horizontal cable.

Accepted Answer

$$T_1 = 4.43$$ 	imes $$10^4$$\ \mathrm{N},\ $$T_2 = 2.35$$ 	imes $$10^4$$\ \mathrm{N}$$

Question 10

An exoplanet has a mean radius equal to $$0.09$$ times the radius of Earth and a mass equal to $$0.00023$$ times the mass of Earth. What would be the gravitational acceleration at the exoplanet's surface?

Accepted Answer

$$g_{	ext{exoplanet}} = 0.084\ \mathrm{m/s^2$}$$

Question 11

On a basketball court, a basketball player recorded a standing vertical leap of $$125\ \mathrm{cm}. $$Imagine that this player was given the opportunity to travel to a spherical celestial object in outer space. The mass per unit volume of the celestial object is $$2.2\ \mathrm{g/cm^3$}. $$Calculate the maximum radius of the celestial object, allowing the player to escape by jumping vertically.

Accepted Answer

$$28.5\ \mathrm{km}$$

Question 12

A toy car of mass $$250\ \mathrm{g} is $$rolling on a circular vertical loop of diameter $$10.0\ \mathrm{m}. $$The coefficient of kinetic friction between the car and the loop is $$0.45. At $$the top of the loop, the speed of the car is $$0.25\ \mathrm{m/s}. $$Determine the magnitude of the tangential acceleration at the top of the loop.

Accepted Answer

$$-0.81\ \mathrm{m/s^2$}$$

Question 13

The motor of a hand-held sander machine applies a steady torque $$	au to $$the disk, enhancing its angular velocity by $$1.5\ \mathrm{rad/s}$$ each second. The moment of inertia of the disk is $$3.0\ \mathrm{kg\cdot m^2$}. $$Calculate the torque $$	au.$$

Accepted Answer

$$2.0\ \mathrm{N\cdot m}$$

Question 14

A building employs a dual counterweight system with two elevator cars. Elevator Car A has a mass of $$1200\ \mathrm{kg}$$ and starts at the tenth floor. Elevator Car B, with a mass of $$1250\ \mathrm{kg}$$, begins at the second floor. They are connected by a steel cable that runs over a pulley that is free to rotate about a fixed axis at the top of the shaft. The pulley is a solid cylinder with a radius of $$0.80\ \mathrm{m}$$ and a mass of $$100\ \mathrm{kg}. $$Find the acceleration of each elevator car as they move in the shaft.

Accepted Answer

$$0.15\ \mathrm{m/s^2$}$$

Question 15

The worker in the workplace has a safe limit to lift objects weighing $$160\ \mathrm{N} (16 kg) at $$places of work. The worker can lift weights greater than $$160\ \mathrm{N}$$ using a trolley. You may consider a $$1.5\ \mathrm{m}$$ long trolley, weighing $$100\ \mathrm{N}$$ and the center of gravity located at $$0.6\ \mathrm{m}$$ from the axle. Assume the load's center of mass is located $$0.6\ \mathrm{m}$$ from the axle. What is the source of the force that enables the worker to lift more weight using the trolley?

Accepted Answer

The force from the lever arm

Question 16

A block is on a merry-go-round. Its position is given by $$(x, y, z) = (3.0, 4.0, 5.0)\ \mathrm{m}$$, and its velocity can be expressed as $$(4.0, -3.2, -3.8)\ \mathrm{m/s}. If $$the mass of the block is $$5.2\ \mathrm{kg}$$, determine its angular momentum with respect to the origin.

Accepted Answer

$$(160.1\ \hat{i} - 45\ \hat{j} - 103.0\ \hat{k})\ \mathrm{kg\cdot m^2$/s}$$

Question 17

A motor-driven floor scrubber has a mass of $$1.5\ \mathrm{kg}$$ and a diameter of $$430\ \mathrm{mm}. $$The scrubber rotates about an axle attached to its center. The scrubber sweeps an angle as a function of time given by $$	heta(t) = At^3$ + Bt$$, $$	heta is in $$radians, $$t in $$seconds, and $$A$$ and $$B$$ are equal to $$0.820$$ and $$0.710$$, respectively. Determine the units of $$A$$ and $$B.$$

Accepted Answer

A: $$\mathrm{$$rad/s^3$$}$$; B: $$\mathrm{rad/s}$$

Question 18

A satellite with a mass of $$5.0 	imes 10^3$\ \mathrm{kg} is $$moving at a speed of $$2.5 	imes 10^3$\ \mathrm{m/s}. $$Due to a major technical issue, the satellite explodes into 3 fragments. One of the fragments with a mass of $$75 	imes 10^1$\ \mathrm{kg}$$ continues forward at a speed of $$1.5 	imes 10^3$\ \mathrm{m/s}. $$The second fragment moves in the backward direction at a speed of $$0.5 	imes 10^3$\ \mathrm{m/s}. $$Find the speed and direction in which the third fragment moves, if the mass of the second fragment is $$6.0 	imes 10^2$\ \mathrm{kg}.$$

Accepted Answer

$$1.56 	imes 10^3$\ \mathrm{m/s}$$, -x direction

Question 19

A boy is riding his bicycle moving north at $$6.0\ \mathrm{m/s}. $$There is wind flowing in the direction $$30^\circ$$ west of south exerting a force of $$4.5\ \mathrm{N}. $$Consider there is no rolling friction but static friction which will save the boy from skidding sideways. Calculate the minimum value of the static friction coefficient that will help move towards the north. Consider the combined mass of the boy and his bicycle is $$35\ \mathrm{kg}.$$

Accepted Answer

$$0.008$$

Question 20

A $$20\ \mathrm{kg}$$ crate is being pulled up a $$20^\circ$$ incline with a constant velocity by a force $$F at an $$angle of $$15^\circ$$ below the horizontal. Determine the work done by the weight ($$W_g$$), normal force ($$W_N) $$and applied force ($$W_F) on $$the crate as it travels $$10\ \mathrm{m}$$ along the incline.

Accepted Answer

$$W_g = -6.7 	imes 10^2$\ \mathrm{J},\ W_N = 0\ \mathrm{J},\ W_F = 6.7 	imes 10^2$\ \mathrm{J}$$

Physics Final Exam Study Guide: Motion, Forces, Energy, and Rotation

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