Using $F=ma$ to find magnitudes of unknown forces acting on an accelerating body.

Three forces act on a particle. You're given the magnitude of one, and the directions of all three. Find the magnitudes of the other two forces.

A particle is in equilibrium on an incline. Four forces are acting on it. You're given the angle of the incline and three forces. Resolve the forces to find the angle and magnitude of the other force.

Determine the resultant of three random 2-D vectors.  

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.

A block of given mass is sits on a flat plane with defined static and kinetic friction values. Randomly, it does one of two things, it is either:

1) pushed with enough force to start it moving - calculate the force on the block or the static friction.

2) moving over a distance - calculate the work done or the kinetic friction

(are these uneven calculations)

A block of given mass is sits on a flat plane with defined static and kinetic friction values. Randomly, it does one of two things, it is either:

1) pushed with enough force to start it moving - calculate the force on the block or the static friction.

2) moving over a distance - calculate the work done or the kinetic friction

(are these uneven calculations)

Find the solution of a first order separable differential equation of the form $a\sin(x)y'=by\cos(x)$.

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Students seem to freak out when their answer is not written exactly the same as the answer provided. This question tries to enforce that $(x-y)=-(y-x)$ and $\frac{a-b}{c-d}=\frac{b-a}{d-c}$

These practice questions cover:

• resolving axial forces in a truss structure
• stress & strain in a closed thin-walled pressure vessel (an example of 2D plane stress)
• use of Mohr's circle for determining principal stresses for a 2D plane stress case
• calculation of invariants for general 3D stress case, leading to von Mises stress and principal stresses

Students seem to freak out when their answer is not written exactly the same as the answer provided. This question tries to enforce that $(x-y)=-(y-x)$ and $\frac{a-b}{c-d}=\frac{b-a}{d-c}$

Students seem to freak out when their answer is not written exactly the same as the answer provided. This question tries to enforce that $(x-y)=-(y-x)$ and $\frac{a-b}{c-d}=\frac{b-a}{d-c}$

No description given

No description given

Find the solution of a first order separable differential equation of the form $a\sin(x)y'=by\cos(x)$.

A copy of Amy Chadwicks block question, with adaptions to provide a diagram for the student.

A block of given mass is sliding down the plane, with given acceleration. Find the normal reaction force, the coefficient of friction, and the distance travelled before reaching a given speed.

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Two masses in a box which is attached to a string. Finding acceleration by modelling the two masses as the whole system. Find forces exerted by the two masses.

These practice questions cover:

• resolving axial forces in a truss structure
• stress & strain in a closed thin-walled pressure vessel (an example of 2D plane stress)
• use of Mohr's circle for determining principal stresses for a 2D plane stress case
• calculation of invariants for general 3D stress case, leading to von Mises stress and principal stresses

Resolving forces in a simple truss, and 2D stresses in a uniaxially loaded bar.

A block of given mass is sliding down the plane with a given acceration. Find the normal reaction force, the parallel force and the missing value of a and mu.

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A block of given mass is sliding down the plane, with given acceleration. Find the normal reaction force, the coefficient of friction, and the distance travelled before reaching a given speed.

A mass is resting on a rough plane. Given the angle of the plane and the mass of the object, find the normal reaction force and hence the coefficient of friction.

Find the $x$ and $y$ components of the resultant force on an object, when multiple forces are applied at different angles.

Using $F=ma$ to find magnitudes of unknown forces acting on an accelerating body.

A mass is resting on a rough plane. Given the angle of the plane and the mass of the object, find the normal reaction force and hence the coefficient of friction.

Simultaneous Equations

rebelmaths

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