physics Sections 6.1,6.2, 6.3 and 6.4

Identify all the non-inertial reference frames from the list below:1. Feeling pushed forward when a car brakes2. Standing in line and throwing a ball to your friend riding a carousel3. Watching a cell phone be pushed off the dashboard to the right while your car turns left4. Playing on the merry-go-round at the playground, and holding on tightly because you feel like you're about to be flung off5. Pushing off from the ice to begin a speed skating race

#1, #3, and #4

A truck with 0.420 m radius tires travels at 32.0 m/s. What is the angular velocity of the rotating tires in radians per second? What is this in rev/min?

32/.42=76.2 rad/s; 76.2 / 2 / pi x 60= 728 rpm

Imagine a cannon that was capable of firing cannonballs from Florida, USA to Ontario, CAN. Assuming the cannonball is aimed directly at an obelisk due north in Canada, where would you anticipate it would land after being fired?

East of the obelisk

(a) Calculate the centripetal force exerted on a 900 kg car that negotiates a 500 m radius curve at 25.0 m/s. (b) Assuming an unbanked curve, find the minimum static coefficient of friction, between the tires and the road, static friction being the reason that keeps the car from slipping

Fc = mv^2/r = (900 kg (25 m/s)^2)/500 m = 1125 N us = ((25 m/s)^2)/(500 m) (9.8) = 0.13

How can you express centripetal force in terms of centripetal acceleration?

Fc=mac

The tires you choose to drive over icy roads will create more friction with the road than your summer tires. Give another example where more friction is desirable.

Jogging track prevent from slipping

Suppose a train is moving along a track. Is there a single, correct reference frame from which to describe the train's motion?

No, there is not a single, correct frame of reference because motion is a relative term.

Curves on some test tracks and race courses, such as the Daytona International Speedway in Florida, are very steeply banked. This banking, with the aid of tire friction and very stable car configurations, allows the curves to be taken at very high speed. To illustrate, calculate the speed at which a 100 m radius curve banked at 65.0° should be driven if the road is frictionless

Noting that tan 65.0º = 2.14, we obtain v = (100m * 9.8 * 2.14)^1/2 = 45.8 m/s

What is the relative orientation of the radius and tangential velocity vectors of an object in uniform circular motion?

Tangential velocity vector is always perpendicular to the radius of the circular path along which the object moves.

The clock on a clock tower has a radius of 1.0m What's the angle of rotation between the hour hand of the clock when it moves from 12:00pm to 3:00pm? What's the arc length along the outermost edge of the clock between the hour hand at these two times?

The angle of rotation at 12:00pm and 3:00pm are 0∘and 90∘respectively. Also, the arc length at 12:00pm and 3:00pm are 0m and 1.6m. The arc length can be obtained by using the relation Δ𝑠=𝑟Δ𝜃

A tennis player hits a ball with a racquet. The length of the player's arm plus racquet is 1.3m. The angle of rotation is 90∘. The swing takes a total of 0.50s. Assuming the player swings at a constant rate, what is the acceleration of the tip of the racquet?

The centripetal acceleration is 𝑎𝑐=𝑟𝜔^2. 13 m/s^2

How can object rotating counterclockwise have a positive angular acceleration?

The counterclockwise rotation of an object produces positive angular velocity. Therefore, when the object is speeding up and rotating counterclockwise, the angular acceleration is positive.

A Ford Focus with a cross-sectional area of 3.00 m^2 is driving on a highway at a speed of 88.0 km/hr, then accelerates to 113 km/hr to pass another car. How much more force does the motor have to supply to overcome air resistance at the higher speed? Assume the density of air the car is traveling through is 1.21 kg/m^3.

The engine must supply 227 N more force at 113 km/hr. FD1=CDAP/2 ((88 x 1000) / 3600)^2 FD2=CDAP/2((113 x 1000) / 3600)^2 FD2-FD1 = CDAP/2 [985.26 - 597.53] Drag Force = ((0.3(drag coefficient for cars) x 3 x 1.21) / 2) x 387.73 = 211 N Df approx 227 N

Calculate the centripetal force exerted on a 900kg car that rounds a 600m radius curve on horizontal ground at 25.0m/s. Static friction prevents the car from slipping. Find the magnitude of the frictional force between the tires and the road that allows the car to round the curve without sliding off in a straight line.

The frictional force is equal to the centripetal force. The centripetal force acting on the body can be obtained by using the relation 𝐹𝑐=𝑚𝑣^2/𝑟 938 N F, force of friction is the same as the centripetal force

Between static and kinetic friction between two surfaces, which has a greater value? Why?

The static friction has a greater value because the friction between the two surfaces is less when the two surfaces are in relative motion.

What is the speed of an object with a centripetal acceleration of 64m/s^2 going along a path of radius 3.0m? Assume the speed to be constant.

The velocity of the object can be obtained by using the relation 𝑎𝑐=𝑣^2/𝑟. The two signs indicate that the motion can be clockwise or counterclockwise. 14 m/s

Imagine that you are swinging a yoyo in a vertical clockwise circle in front of you, perpendicular to the direction you are facing. Now, imagine that the string breaks just as the yoyo reaches its bottommost position, nearest the floor. Which of the following describes the path of the yoyo after the string breaks?

The yoyo will fly to the left in the direction of the tangential velocity.

For an object traveling in a circular path at a constant angular speed, would the linear speed of the object change if the radius of the path increases?

Yes, because tangential speed depends on the radius.

What is the magnitude of the centripetal acceleration of a car following a curve of radius 500 m at a speed of 25.0 m/s (about 90 km/h)? Compare the acceleration with that due to gravity for this fairly gentle curve taken at highway speed.

ac = v^2 / r = (25 m/s)^2 / 500 m = 1.25 m/s^2

A 2.20 kg toy plane takes off with an acceleration of 3.30 m/s2. The engine supplies a force of 8.15 N. Determine the magnitude of drag force acting on the plane as it accelerates.

ma=8.15 - d d=8.15 - ma = 8.15 - (2.2)(3.3) = 8.15 - 7.26 = 0.89 N

Conventionally, for which direction of rotation of an object is angular acceleration considered positive?

the counterclockwise direction

True or False: Determining the mass of an object by counting the number of atoms and molecules in it is an impossible task. Therefore, the mass of an object is often derived from the object's weight as the force of gravity is almost constant, that is, uniform on the surface of Earth.

true

Calculate the centripetal acceleration of a point 7.50 cm from the axis of an ultracentrifuge spinning at 7.5 × 10^4rev/min.Determine the ratio of this acceleration to that due to gravity.

w = 7.50 x 10^4 x 2pi rad/ 1 rev x 1 min / 60 sec = 7854 rad/s ac = (0.0750m)(7854 rad/s)^2 = 4.63 x 10^6 m/s^2 ac/g = 4.63x10^6/9.80 = 4.72 x 10^5

How can you express a centripetal force in terms of angular velocity and the radius?

𝐹𝑐=𝑚𝑟𝜔^2

Calculate the angular velocity of a 0.300 m radius car tire when the car travels at 15.0m/s (about 54km/h)

𝜔=15.0m/s / 0.300 m=50.0 rad/s