Block sliding along a slope (static friction defines force)

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Tom Stallard

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Tom Stallard 8 years, 3 months ago

Created this as a copy of Block sliding down a slope with friction (with graphic).

Name	Status	Author	Last Modified
Block sliding down a slope	Ready to use	Amy Chadwick	16/01/2017 09:29
John's copy of Block sliding down a slope	draft	John Bridges	18/09/2016 23:52
Block sliding down a slope with friction (with graphic)	draft	Tom Stallard	04/10/2023 20:56
Block sliding along a slope (static friction defines force)	draft	Tom Stallard	15/01/2019 17:16
simon's copy of Block sliding down a slope (with graphic)	Ready to use	simon warwick	09/02/2018 13:49
Block sliding down a frictionless slope (with graphic)	draft	Tom Stallard	18/09/2017 18:13
Block has friction (static or kinetic)	draft	Tom Stallard	12/01/2019 12:10
Josh's copy of Block sliding down a frictionless slope (with graphic)	draft	Josh Lim	01/07/2019 11:57
A1: Block has friction (static or kinetic)	draft	Tom Stallard	12/01/2019 13:29
Simon's copy of Block sliding down a slope	draft	Simon Thomas	29/04/2019 10:27

There are 6 other versions that do you not have access to.

Question statement

{draw_block()}

A block of mass $\var{mass}\mathrm{kg}$ slides over a rough horizontal plane. The mass begins at rest. The acceleration due to gravity is g=9.8 ms $^{-2}$ . $\mu _{S}$ is {static_friction}.

Give any introductory information the student needs.

			Name	Type	Generated Value

gravity

number

9.8

			Name	Type	Generated Value

mass	number	7.8
static_friction	number	0.67
distance	integer	10
kinetic_friction	number	0.49

			Name	Type	Generated Value

normal_force	number	76.44
static_force	number	51.2148
kinetic_force	number	37.4556
motion_force	number	13.7592
kinetic_energy	number	137.592
velocity	number	5.939696962

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
9.8

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `number`

9.8

→ Used by:

normal_force

This variable doesn't seem to be used anywhere.

Advice

a)

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.

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.

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This question is used in the following exam:

Week 1 additional practice questions by Tom Stallard in Tom's workspace.

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Block sliding along a slope (static friction defines force)

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Tom Stallard 8 years, 3 months ago

Error in variable testing condition

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Generated value: `number`

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Error

Block sliding along a slope (static friction defines force)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Tom Stallard 8 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Number entry

Advanced settings

Generated value: `number`