Free Printable Resolving forces

1.

An aeroplane is flying horizontally and heading north through the air. Its speed through the air is a and the wind is blowing east with a speed b.

The speed over the ground is given by

a)

$a+b$

b)

$a^2+b^2$

c)

$\sqrt{a+b}$

d)

$\sqrt{a^2+b^2}$

2.

With reference to that same aeroplane, the angle from North at which the plane flies over the ground is given by

a)

$\cos^{-1}\left(\frac{a}{b}\right)$

b)

$\sin^{-1}\left(\frac{b}{a}\right)$

c)

$\tan^{-1}\left(\frac{a}{b}\right)$

d)

$\tan^{-1}\left(\frac{b}{a}\right)$

3.

The diagram shows the forces acting on a picture, of weight W, suspended by a cord.

The tension in the cord is T. Which of the following expressions shows the correct relationship between W and T?

a)

$W=2T\cos\theta$

b)

$W=T\cos\theta$

c)

$W=T\sin\theta$

d)

$W=2T\sin\theta$

4.

Read this one carefully:

The diagram shows the forces acting on an object on an inclined surface. The component of R parallel to the inclined surface is

a)

0

b)

W

c)

$R\cos\theta$

d)

$R\sin\theta$

5.

With this one, try drawing the diagram yourself to help you if you need it:

A football is kicked at 12 m s^-1 at an angle of 35° to the horizontal. The horizontal component of its velocity, in m s^-1, is given by

a)

$12\cos\ 35\degree$

b)

$12\sin35\degree$

c)

$\frac{12}{\cos35\degree}$

d)

$\frac{12}{\sin35\degree}$

6.

Again, try drawing the diagram yourself here to help you if you need to:

A model boat is crossing a stream. The stream is travelling east at a speed of 1.5 m $s^{-1}$ .The boat is heading north at a speed of 0.5 m $s^{-1}$ . The magnitude of the resultant velocity is given by

a)

$\left(1.5^2+0.5^2\right)\ m\ s^{-1}$

b)

$\sqrt{\left(1.5^2+0.5^2\right)}\ \ m\ s^{-1}$

c)

$\left(1.5\ +0.5\right)\ m\ s^{-1}$

d)

$\sqrt{\left(1.5+0.5\right)}\ m\ s^{-1}$

7.

Remember, do a diagram if you think it will help:

A body is acted on by a vertical force of 18 N and a horizontal force of 32 N.

The angle to the horizontal of the resultant force is given by

a)

$\cos^{-1}\left(\frac{18}{32}\right)$

b)

$\tan^{-1}\left(\frac{18}{32}\right)$

c)

$\sin^{-1}\left(\frac{32}{18}\right)$

d)

$\tan^{-1}\left(\frac{32}{18}\right)$

8.

A box of weight 150 N is placed on an inclined plane. The component of the box’s weight acting along the plane is given by W'. What would be the value of W', in Newtons?

a)

$\frac{150}{\cos15\degree}$

b)

$150\times\cos15\degree$

c)

$\frac{150}{\sin15\degree}$

d)

$150\times\sin15\degree$

9.

A student goes down a slide. Which of the diagrams correctly represents the forces acting on the student?

a)

A

b)

B

c)

C

d)

D

10.

The diagram above is a free-body force diagram for a hot air balloon when a wind is blowing. The size of the resultant force acting on the balloon is

a)

400 N

b)

500 N

c)

700 N

d)

9, 805 N

11.

Two forces F₁ and F₂ act on an object as in the diagram above.

If F₁ and F₂ are drawn to scale, the resultant force can be found by measuring the length of the resultant line F_R.

Which of the following diagrams shows the correct position of the line F_R?

a)

b)

c)

d)

12.

FINAL QUESTION: TAKE YOUR TIME. REMEMBER A DRAWING WILL HELP!

A Force F is resolved into two components, F_h and F_v at right angles to each other as in the diagram above. Which statement below is NOT true?

a)

Decreasing the angle θ will increase the size of F_h

b)

Increasing the angle θ will increase the size of Fv

c)

F_h and F_v have sizes that when added together give a total equal to the size of F.

d)

F_h and F_v have sizes that when added together give a total greater than the size of F.

Resolving forces

Total questions: 12

Worksheet time: 6mins

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