Find the normal reaction, $R \\ \\mathrm{N}$ between the block and the plane, to 2 decimal places.
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", "mustBeReduced": false, "showPrecisionHint": false, "minValue": "precround(kinetic_force,2)-0.1", "precision": "3", "customMarkingAlgorithm": "", "variableReplacements": [{"must_go_first": true, "part": "p0", "variable": "normal_force"}], "extendBaseMarkingAlgorithm": true, "correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "showCorrectAnswer": true, "type": "numberentry", "mustBeReducedPC": 0, "scripts": {}, "unitTests": [], "precisionPartialCredit": 0, "correctAnswerStyle": "plain", "precisionMessage": "You have not given your answer to the correct precision.", "marks": 1, "precisionType": "dp", "strictPrecision": false, "maxValue": "precround(kinetic_force,2)+0.1"}, {"allowFractions": false, "showCorrectAnswer": false, "type": "numberentry", "showFeedbackIcon": true, "prompt": "Using the values of force calculated in part b and c, calculate the change in kinetic energy of the block after it has moved {distance}m, to 2 decimal places.
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To find the normal reaction force $F_{N}$, we resolve the forces perpendicular to the plane.
$F_{N} = mg$
$F_{N} = $ {mass} kg * {gravity} ms$^{-2}$
The normal reaction force $F_{N} $ is equal to {precround(normal_force,3)} N.
\n
b)
To find the force needed to start the block moving $F_{S}$, we must factor the normal reaction force, calculated in a) against the co-efficient of static friction $\\mu _{S}$:
$F_{S} = F_{N} * \\mu _{S}$
$F_{S} = $ {precround(normal_force,3)} N * {static_friction}
The force need to start moving the block is $\\var{precround(static_force,3)}$ N.
c)
To find the force needed to keep the block moving, once it is in motion $F_{K}$, we must factor the normal reaction force, calculated in a) against the co-efficient of kinetic friction $\\mu _{K}$:
$F_{K} = F_{N} * \\mu _{K}$
$F_{S} = $ {precround(normal_force,3)} N * {kinetic_friction}
The forces need to start moving the block is $\\var{precround(kinetic_force,3)}$ N.
d)
To calculate the kinetic energy of the block at a distance of {distance}m, we must first calculate the difference between the forces in parts b) and c):
$F = F_{S} - F_{K}$
$F = $ {precround(static_force,3)} N - {precround(kinetic_force,3)} N
$F = $ {precround(motion_force,3)} N
Using this force, we can then calculate the work done on the block:
$KE = Work = F * d$
$W = $ {precround(motion_force,3)} N * {distance} m
The work done on the block, and thus the change in kinetic energy of the block is {precround(kinetic_energy,3)} Nm.
e)
To calculate the velocity of the block after {distance} m, we must re-arrange the equation for calculating kinetic energy:
$KE = 1/2 mv^{2}$
$v^{2} = 2 * KE$
$v = \\sqrt{2 * KE}$
$v = \\sqrt{2 * \\var{precround(kinetic_energy,3)}}$
The velocity of the block after {distance} m is {precround(velocity,3)} m/s.
A static block of given mass is sits on a flat plane with defined static and kinetic friction values. It is pushed with enough force to start it moving - calculate the speed of the block after a given distance.
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