Lab 1018

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course Phy 201

10/24 6 pmLab-related questions

`qx001. Suppose a car of mass m coasts along a slight constant incline.

If the magnitudes of its accelerations while traveling up, and down, the incline are respectively a_up and a_down, then what is the magnitude of the frictional force acting on it?

What therefore is the coefficient of friction?

****a_up =205.25 cm/s^2 (this is the average of my trials) then mu=205.25 cm/s^2/980 cm/s^2=0.21

a_down=-83.7 cm/s^2 (average) then mu=-83.7 cm/s^2/980 cm/s^2=-0.09 (can mu be negative?)

mu multiplied by the normal force gives you the magnitude of the frictional force, not its direction

there is also the parallel component of the weight, which always acts down the incline

the acceleration is due to the net force, which includes both frictional force and the parallel component of the weight

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`qx002. Give your data for the acceleration of the car down the incline, and its acceleration up the incline:

****A_down=68.2 cm/s^2 and 98.8 cm/s^2

a_up=-226 cm/s^2, -178 cm/s^2,- 219.5 cm/s^2, -198.8 cm/s^2

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`qx003. What therefore is the acceleration down, and what is the acceleration up?

****a_down= 83.7 cm/s^2, a_up=-205.25 cm/s^2

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`qx004. The only forces acting on the coasting care are the component of its weight parallel to the incline, and the frictional force. The former is always directed down the incline. Let the direction down the incline be chosen as the positive direction.

What is the direction of the frictional force as the car coasts down the incline?

****The direction of friction force coasting down the incline is negative or up the incline.

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What is the direction of the frictional force as the car coasts up the incline?

****The direction of frictional force is positive.

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Is the net force on the car greater when it coasts down the incline, or when it coasts up?

****the net force of the car is greater when it coasts down the incline.

when the car is coasting up the incline the frictional force and parallel component of the weight are both down the incline, so they reinforce one another

when the car is coasting up the incline the frictional force and parallel component of the weight are in opposite directions, which results in a net force of lesser magnitude

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`qx005. This question asks for symbols, but the expressions are short and everyone should answer this question:

Let wt_parallel stand for the parallel component of the weight and f_frict for the magnitude of the frictional force.

• What is the expression for the net force on the car as it travels up the incline?

• What is the expression for the net force on the car as it travels down the incline?

• What is the difference in the two expressions?

****Fnet=wt_parallel*acceleration –f_frict

Fnet=wt_parallet*acceleration +f_frict

The difference would be +/- f_frict

you have the correct expressions

if you subtract the first from the second you end up with 2 * f_frict:

wt_parallet*acceleration +f_frict - (wt_parallet*acceleration - f_frict) = 2 * f_frict

`qx006. If the mass of your car and its load is 120 grams, then based on your calculated accelerations:

• What is the magnitude of the net force on the car as it travels down the incline?

****F(net)=ma; Fnet=120 g*83.7 cm/s^2=10044 g*cm/s^2

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• What is the magnitude of the net force on the car as it travels up own the incline?

****Fnet=120 g* -205.25 cm/s^2=24630 g*cm/s^2

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• What is the difference between the magnitudes of these two forces?

****14586 g*cm/s^2

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• What do you therefore conclude is the force due to friction?

****Is the force due to friction, the difference between the 2?

the difference is double the force of friction

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• What would be the corresponding coefficient of friction?

**** if a_down= 83.7 cm/s^2, a_up=-205.25 cm/s^2, then mu for each respectively is 83.7cm/s^2/980 cm/s^2= .085 and down is -205.25 cm/s^2/980cm/s^2=0.21

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`qx007. A car and magnet, with total mass m, coasts down an incline. A magnet at distance L from the position of release brings the car to rest (just for an instant) after it has coasted a distance `ds, during which its vertical position decreases by distance `dy. If energy lost to friction is negligible, then

• What is the change in the car's gravitational potential energy from release to the instant of rest? ****PEgrav=m g * `dy

good but PE decreases, so the change would be - m g `dy; note that `dy is a distance and not a displacement

• What is the change in the car's magnetic potential energy between these two points?

****`PEmag=mg *(`ds-L)

no energy is lost to friction, and KE is zero at release and also at position L

so between these two points `dW_noncons = 0 and `dKE = 0

it follows that `dPE = 0

the loss of gravitational PE is therefore exactly balanced by the gain in magnetic PE

the change in magnetic PE is therefore + m g `dy

If the incline is slight, then the normal force on the car is very nearly equal and opposite its weight. If the coefficient of friction is mu, then how do your answers to the above two questions change?

`qx008. Assume your car, which has mass 120 grams, coasted 20 cm down an incline of slope .05, and that the coefficient of friction was .03. At the end of the incline, 25 cm from the initial position of the car, is a magnet, which brings the car to rest for an instant, at the end of its 20 cm displacement.

• How far did the car descend in the vertical direction, based on the 20 cm displacement and the slope .05?

• By how much did its gravitational PE therefore change?

• Assuming that the normal force is very nearly equal to the car's weight, what was the frictional force on the car?

• How much work did friction therefore do on the car?

• In the absence of the repelling magnet, how much KE would you therefore expect the car to have at the end of the 20 cm?

• How much magnetic PE do you therefore think is present at the instant of rest?

• What do you think will happen next to this magnetic PE?

*****I am very uncertain of how to calculate the above problem based on the fact I’m not sure I got the previous problem correct.

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you got the change in PE, except for the - sign

see my note

then see how you can do on this problem

You're doing well. See my notes and feel free to follow up with additional questions.

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