Simon's copy of Particle in vertical equilibrium, accelerating horizontally

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Simon Thomas 5 years, 11 months ago

Created this as a copy of Particle in vertical equilibrium, accelerating horizontally.

Name	Status	Author	Last Modified
Particle in vertical equilibrium, accelerating horizontally	Ready to use	Amy Chadwick	24/08/2016 10:50
Particle in vertical equilibrium, accelerating horizontally	Needs to be tested	Chris Graham	08/12/2016 11:23
Simon's copy of Particle in vertical equilibrium, accelerating horizontally	draft	Simon Thomas	29/04/2019 09:19

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Question statement

Consider the following diagram of a particle of mass $K \ \mathrm{kg}$ , moving left-to-right. The forces $A, B, C$ and $D$ are acting upon it, producing a horizontal acceleration of $a \, \mathrm{ms^{-2}}$

The acceleration due to gravity is $9.8 \, \mathrm{ms}^{-2}$ . Answer all the following questions to 3 decimal places.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	number	5.5
K	integer	6
FA	number	2.5
FD	integer	6
a2	number	2.75
K2	integer	4
FA2	number	44
downforce	integer	19
FD2	integer	4

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Name

Data type

Value

A random number between and (inclusive) with step size

Description

acceleration

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

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Generated value: `number`

5.5

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Parts

Part a) Gap-fill
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Part b) Number entry
Part c) Number entry

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Suppose that the acceleration $a = \var{a}$ and the mass of the particle $K = \var{K} \ \mathrm{kg}$ . Find the force $C \ \mathrm{N}$ if $A = \var{FA}\ \mathrm{N}$ .

$C =$ Unnamed gap $\mathrm{N}$

Advice

(a)

To find the resultant force in a certain direction when there is more than one force acting on an object you can resolve the forces. You resolve in the direction of acceleration. Using the letter $R$ , with an arrow will indicate the direction the forces are being resolved in, for example $R(\rightarrow)$ .

In this case $R(\rightarrow)$ means apply $F=ma$ in the horizontal direction, where we treat forces and accelerations to the right as positive, and to the left as negative. So we need to resolve the equation

$\begin{align}F & = ma \\ C - \var{FA} & = \var{K} \times \var{a} \\ C & = \var{K*a} + \var{FA} \\ & = \var{K*a + FA}. \end{align}$

Here the forces, $F=C - \var{FA}$ because $\var{FA}$ is acting in the opposite direction to $C$ . The mass is $m=\var{K}$ and the acceleration is $a=\var{a}$ . Therefore $C = \var{K*a+FA}\ \mathrm{N}$ .

(b)

In this case we resolve in the direction perpendicular to acceleration so we use $R(\uparrow)$ which means apply $F=ma$ in the vertical direction, where acceleration, $a=0$ because there is no vertical acceration.

$\begin{align} F & = ma \\ B - \var{FD}g & = \var{K} \times 0 \\ B & = 0 + \left(\var{FD} \times 9.8\right) \\ & = \var{FD*9.8} \end{align}$
Here the forces,

$F=B - \var{FD}g$ because

$\var{FD}g$ is acting downwards which is the opposite direction to

$B$ . Therefore

$B = \var{FD*9.8} \ \mathrm{N}$ .

(c)

It is easier to take the positive direction as the direction of the acceleration. Therefore we use $R(\leftarrow)$ because we are decelerating.

$\begin{align} F & = ma \\ \var{FA2} - C & = \var{K2} \times \var{a2} \\ C & = \var{FA2} - \left( \var{K2} \times \var{a2} \right) \\ & = \var{FA2 - K2*a2}. \end{align}$

Here the forces, $F = \var{FA2} - C$ because $\var{FA2}$ is in the direction of acceleration and $C$ is acting in the opposite direction. The mass is $m = \var{K2}$ and $a=\var{a2}$ . Therefore $C = \var{FA2 - K2*a2} \ \mathrm{N}$ .

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This question is used in the following exam:

Dynamics - Forces by Simon Thomas in Mechanics.

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Simon's copy of Particle in vertical equilibrium, accelerating horizontally

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Simon Thomas 5 years, 11 months ago

Error in variable testing condition

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Generated value: `number`

Parts

Gap-fill

(a)

(b)

(c)

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Simon's copy of Particle in vertical equilibrium, accelerating horizontally

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Simon Thomas 5 years, 11 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

(a)

(b)

(c)

Generated value: `number`