Ball in a box

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From users who are members of Maths Support Wiki - Mechanics :

Christian Lawson-Perfect	said	Ready to use	8 years, 8 months ago
Amy Chadwick	said	Needs to be tested	8 years, 10 months ago

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Christian Lawson-Perfect 8 years, 8 months ago

Gave some feedback: Ready to use

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Christian Lawson-Perfect 8 years, 8 months ago

Saved a checkpoint:

Some more typos fixed.

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Christian Lawson-Perfect 8 years, 10 months ago

Saved a checkpoint:

Fixed "madnitude" to "magnitude" in part a.

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Christian Lawson-Perfect commented 8 years, 10 months ago

A diagram would really help here!

The statement could be made easier to understand. Maybe something like

A box is being lifted upwards by a crane. It is accelerating at a rate of $a \, \mathrm{ms^{-2}}$ upwards.

A ball of mass $m\, \mathrm{kg}$ is resting inside the box.

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Amy Chadwick 8 years, 10 months ago

Gave some feedback: Needs to be tested

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Amy Chadwick 8 years, 10 months ago

Created this.

There is only one version of this question that you have access to.

Question statement

A ball of mass $\var{mass}kg$ is in a box which accelerates upwards at a rate of $\var{a} \, \mathrm{ms}^{-2}$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

mass	integer	16
a	number	1.25
g	number	9.8
decelerate	number	1.7

Automatically regenerate variables?

Name

Data type

Value

A random number between and (inclusive) with step size

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: `integer`

This variable doesn't seem to be used anywhere.

Advice

a)

We resolve $F=ma$ in the upwards positive direction as acceleration is acting vertically upwards, the normal reaction, $R \ \mathrm{N}$ , will act in the opposite direction to the weight of the ball.

$\begin{align} F & = ma \\ R - mg &= ma \\ R & = mg + ma \\ & = \left(\var{mass}\times \var{g}\right) + \left(\var{mass} \times \var{a}\right) \\ & = \var{precround(mass*g + mass*a,3)}. \end{align}$

The normal reaction on the ball has magnitude $\var{precround(mass*g + mass*a,3)} \ \mathrm{N}$ .

b)

We resolve $F=ma$ in the upwards positive direction. The normal reaction force, $R$ , will act in the opposite direction to the weight of the ball. This time however the box is decelerating so $a=\var{-decelerate} \, \mathrm{ms^{-2}}$ .

$\begin{align} F & = ma \\ R - mg &= ma \\ R & = mg + ma \\ & = \left(\var{mass}\times \var{g}\right) + \left(\var{mass} \times \var{-decelerate}\right) \\ & = \var{precround(mass*g - mass*decelerate,3)}. \end{align}$

The normal reaction on the ball has magnitude $\var{precround(mass*g - mass*decelerate,3)} \, \mathrm{N}$ .

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This question is used in the following exams:

Dynamics - Forces by Amy Chadwick in Maths Support Wiki - Mechanics.
My first exam by Elisabeth Grieger in Elisabeth's workspace.
Dynamics - Forces by Simon Thomas in Mechanics.

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Christian Lawson-Perfect 8 years, 8 months ago

Christian Lawson-Perfect 8 years, 8 months ago

Christian Lawson-Perfect 8 years, 10 months ago

Christian Lawson-Perfect commented 8 years, 10 months ago

Amy Chadwick 8 years, 10 months ago

Amy Chadwick 8 years, 10 months ago

Error in variable testing condition

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Warning

Generated value: `integer`

Parts

Number entry

Advanced settings

a)

b)

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Ball in a box

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 8 years, 8 months ago

Christian Lawson-Perfect 8 years, 8 months ago

Christian Lawson-Perfect 8 years, 10 months ago

Christian Lawson-Perfect commented 8 years, 10 months ago

Amy Chadwick 8 years, 10 months ago

Amy Chadwick 8 years, 10 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Number entry

Advanced settings

a)

b)

Generated value: `integer`