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

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

Question 1

Express the following measurement in complete decimal form, without using any unit prefixes: $$9.8\ \mu\mathrm{m}.$$

Accepted Answer

$$0.0000098\ \mathrm{m}$$

Question 2

A Montgolfier balloonist, moving up with a uniform speed of $$10.0\ \mathrm{m/s}$$, drops a bag of stones at an instant when the balloon is $$50.0\ \mathrm{m}$$ above the ground. What is the speed and position of the bag at $$0.50\ \mathrm{s}$$ after its release? (Assume $$g = 9.8\ \mathrm{m/s^2$}$$ and ignore air resistance.)

Accepted Answer

$$11.1\ \mathrm{m/s}$$ and $$41.1\ \mathrm{m}$$ above the ground

Question 3

The following graph represents the position of a vehicle on a straight road with respect to time. Determine the vehicle's instantaneous velocity at $$t = 15\ \mathrm{s}. ($$Assume the graph shows a positive slope at $$t=15\ \mathrm{s}.)$$

Accepted Answer

$$4.0\ \mathrm{m/s}$$

Question 4

The radius of Mars is $$3,389.5\ \mathrm{km}$$ and rotates once every $$24.6$$ hours. The radial acceleration at the equator must be larger than $$g$$ for items to leave the surface of the planet and enter space. What would be the needed rotational period on Mars for this to happen? ($$g on $$the surface of Mars is $$3.7\ \mathrm{m/s^2$})$$

Accepted Answer

$$11\ \mathrm{h}$$

Question 5

A rescue helicopter is flying horizontally at a height of $$150\ \mathrm{m}$$ above sea level to deliver emergency medical supplies to a boat in distress near the coast. The helicopter is traveling at a speed of $$100\ \mathrm{km/h}$$ parallel to the coastline. Neglecting air resistance, calculate the distance from the boat at which the supplies should be dropped to ensure they land accurately in the water close to the boat, taking into account the height from which they are dropped.

Accepted Answer

$$154\ \mathrm{m}$$

Question 6

The velocity of a drone is given by $$\vec{v}(t) = \left(2 + (0.8\,\mathrm{m/s^2$})t\right)\hat{i} + \left[1.5 - (1.2\,\mathrm{m/s^2$})t\right]\hat{j}. $$Find the magnitude and direction of the drone's velocity and acceleration $$3$$ seconds after launch.

Accepted Answer

Velocity $$= 7.025\ \mathrm{m/s}$$, $$41.07^\circ$$; Acceleration $$= 0.625\ \mathrm{m/s^2$}$$, $$275.12^\circ$$

Question 7

A $$1200\ \mathrm{kg}$$ stalled truck on a level parking lot is pushed by a small SUV of mass $$650\ \mathrm{kg} in a $$direction due north. The SUV is pushing on the truck with a $$2200\ \mathrm{N}$$ 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 8

Two physics enthusiasts devise an experiment in which a $$40-$$centimeter-long thread suspends a bar magnet ($$m = 10\ \mathrm{g}). $$When another bar magnet is brought close to the first one with the identical poles facing each other, they repel. If the second magnet is held in place it causes the hanging magnet to swing out to a $$15^\circ$$ angle and remain there. Determine the magnitude of the magnetic force that causes the repulsion between magnets (making it swing).

Accepted Answer

$$0.026\ \mathrm{N}$$

Question 9

A thin, uniform rod measuring $$60.0\ \mathrm{cm} in $$length and weighing $$0.400\ \mathrm{kg} is $$bent into a V-shape with a $$30.0^\circ$$ angle at its vertex. What would this bent rod's moment of inertia be at its vertex, which is an axis perpendicular to the plane of the V?

Accepted Answer

$$0.032\ \mathrm{kg\cdot m^2$}$$

Question 10

A child's entertainment equipment has a $$100.0\ \mathrm{cm}$$ long, thin and uniform rod of mass $$0.500\ \mathrm{kg}. $$Determine the moment of inertia of the rod pivoted about its center such that it spins perpendicular to its length.

Accepted Answer

$$0.0042\ \mathrm{kg\cdot m^2$}$$

Question 11

A metal piece of mass $$M is $$extended to form a planar rectangular sheet. If the length of the sheet $$L is $$twice the width, find the moment of inertia about an axis perpendicular to the sheet and passing through one of the four corners.

Accepted Answer

$$(7/12)ML^2$$

Question 12

A $$35\ \mathrm{kg}$$ dog begins to cautiously tread on a $$6.2\ \mathrm{m}$$ long, $$58\ \mathrm{kg}$$ wooden plank that is supported by two support beams. With safety in mind, determine the nearest distance the dog can approach the right end of the wooden plank without causing it to topple over.

Accepted Answer

$$2.83\ \mathrm{m}$$

Question 13

A $$3.5\ \mathrm{kg}$$ block when placed on a spring compresses it to $$25\ \mathrm{cm}. $$The spring is $$33\ \mathrm{cm}$$ long and is placed vertically with one end fixed on the ground. Determine the spring constant.

Accepted Answer

$$137\ \mathrm{N/m}$$

Question 14

A rocket scientist is developing a rocket to be launched vertically from the surface of the earth. The rocket will have a total mass of $$275,000\ \mathrm{kg}. $$The rocket engine generates $$3.5 	imes 10^6$\ \mathrm{N} of $$thrust and consumes all of the fuel in $$340$$ seconds at a constant rate. Consider that all the fuel has been consumed. What would be (i) the speed of the rocket during the vertical takeoff and (ii) the speed of the rocket if it were launched in a region of space where the effect of gravitation is negligible?

Accepted Answer

$$2687\ \mathrm{m/s}$$; $$3544\ \mathrm{m/s}$$

Question 15

A bullet with a mass of $$80\ \mathrm{g} is $$fired horizontally into a block of wood with a mass of $$800\ \mathrm{g}$$, causing the block to slide forward with a velocity of $$2.5\ \mathrm{m/s}. $$The bullet gets embedded in the wood. Determine the initial speed of the bullet before it collides with the block of wood which is initially at rest.

Accepted Answer

$$27.5\ \mathrm{m/s}$$

Question 16

You are strolling around one evening when a $$50\ \mathrm{g}$$ marble is launched horizontally at $$15.0\ \mathrm{m/s}$$ from a $$12\ \mathrm{m}$$ high point in a tall building (point A). Weight is the only force acting on the stone during the flight. Calculate the magnitude and direction of the rate of change of the stone's angular momentum about your feet (point H) the moment it is launched.

Accepted Answer

$$11\ \mathrm{kg\cdot m^2$/s^2$$}$, out of the page

Question 17

A man having a mass of $$55\ \mathrm{kg} is $$riding a bike weighing $$30\ \mathrm{kg}. $$There is a box with a mass of $$15\ \mathrm{kg}$$ kept on the rear seat of the bike. The man is initially riding the bike at $$9.0\ \mathrm{m/s}$$ and suddenly increases the speed to $$12.0\ \mathrm{m/s}. $$Due to this, the box falls behind the bike. Determine the velocity of the falling box immediately after it falls off of the bike.

Accepted Answer

$$9.0\ \mathrm{m/s}$$

Question 18

You obtain a massless spring from an old umbrella having a force constant, $$k = 1000\ \mathrm{N/m}. $$Out of sheer fun, you place the spring to rest vertically with one of its ends lying on a bench. Next, you release a block of mass $$0.50\ \mathrm{kg}$$ from a height of $$1.5\ \mathrm{m} ($$measured from the spring's top end) directly above the spring. Determine the maximum compression that occurs on the spring.

Accepted Answer

$$0.0606\ \mathrm{m}$$

Question 19

In a simulation of orbital mechanics, a model space station module of mass $$2.0\ \mathrm{kg} is $$tethered to a central pivot by a strong, lightweight cable $$10\ \mathrm{m}$$ long. Initially, the module orbits the pivot in a horizontal plane at a speed of $$5.0\ \mathrm{m/s}. To $$simulate a maneuver to a higher orbit speed for docking purposes, the cable is gradually pulled in, reducing the orbit's radius to $$6.0\ \mathrm{m}. $$Determine the work done to achieve this higher orbit speed.

Accepted Answer

$$44\ \mathrm{J}$$

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