A ball of mass m kg is rolled up a slope at an angle θ to the horizontal, where sin θ = 2 5 . The ball passes a point A with speed 7 m s - 1 . A point B is 5 m further up the slope than point A . Find the time between passing $B$ on the way up and returning to B on the way down.

Draw the force-free body diagram as given below Now compare the force values in the parallel to the incline slope - m g sin θ = m a a = - g sin θ = - 2 5 × 10 = - 4 m / s 2 Now use the constant acceleration formula as follows s = u t + 1 2 a t 2 s = 5 m , u = 7 m / s , a = - 4 m / s 2 , t = ? 5 = 7 t - 2 t 2 2 t 2 - 7 t + 5 = 0 2 t - 5 t - 1 = 0 t = 1 s o r 2 . 5 s The ball at B at t = 1 s and t = 2 . 5 s so the timing between passing B on the way up and down is 1 . 5 s .

A van of mass 2000 kg is towed from rest by two ropes. One pulls with a tension of 130 N at 10 ° to the direction of motion and the other acts at 15 ° to the direction of motion. Find the distance covered in 10 s .

Here Force-free body diagram is as given below Now here we have to compare the value of the force in the perpendicular direction For vertical direction T sin 15 ° = 130 sin 10 ° T = 130 sin 10 ° sin 15 ° For horizontal direction 130 cos 10 ° + T cos 15 ° = 2000 a a = 130 cos 10 ° + 130 sin 10 ° sin 15 ° cos 15 ° 2000 a = 0 . 106 m / s 2 Now here we use the constant acceleration formula as given below s = u t + 1 2 a t 2 u = 0 , s = ? , a = 0 . 106 m / s 2 , t = 10 s s = 0 + 1 2 × 0 . 106 × 10 2 = 5 . 31 m

HARD

AS and A Level

IMPORTANT

Earn 100

A buoy of mass $12 kg$ is on the surface of a lake. The tide pushes it with a force of $25 N$ and the wind pushes it with a force of $15 N,$ as shown in the diagram. The buoy moves in the direction shown. Find the value of $θ$ and the acceleration.

Important Questions on Forces in Two Dimensions

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 3 - Forces in Two Dimensions>EXERCISE 3D>Q 12

A girl pulls a toy car of mass

0.8 kg

by a string along a horizontal path. The tension in the string is

3 N

and the string is held at an angle of

40 °

above the horizontal. There is air resistance of

2 N .

Find the time taken to reach a speed of

2 m s^{- 1}

from rest.

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 3 - Forces in Two Dimensions>EXERCISE 3D>Q 13

A shopper drags a trolley of mass

25 kg

from rest along horizontal ground. The shopper is pulling the trolley by a force of

30 N

with his arm, which is at

15 °

above the horizontal. There is friction of

10 N .

Find the speed of the trolley after being pulled a distance of

6 m .

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 3 - Forces in Two Dimensions>EXERCISE 3D>Q 14

A ball of mass $3 kg$ is rolled with initial speed $4 m s^{- 1}$ up a slope at an angle $10 °$ to the horizontal.

Find the maximum distance up the slope the ball reaches.

MEDIUM

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 3 - Forces in Two Dimensions>EXERCISE 3D>Q 14

A ball of mass $3 kg$ is rolled with initial speed $4 m s^{- 1}$ up a slope at an angle $10 °$ to the horizontal.

What assumptions have been made to answer the question?

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 3 - Forces in Two Dimensions>EXERCISE 3D>Q 15

A cyclist of mass

70 kg

(including her bicycle) arrives at an uphill stretch of road of length

30 m

with an angle

9 °

to the horizontal, travelling at

10 m s^{- 1} .

She exerts a force of

15 N

parallel to the slope and there is wind resistance of

5 N

against her. Find the time taken to reach the top of the slope.

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 3 - Forces in Two Dimensions>EXERCISE 3D>Q 16

A ball of mass

m kg

is rolled up a slope at an angle

θ

to the horizontal, where

\sin θ = \frac{2}{5} .

The ball passes a point

A

with speed

7 m s^{- 1} .

A point

B

5 m

further up the slope than point

A .

Find the time between passing $B$ on the way up and returning to

B

on the way down.

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 3 - Forces in Two Dimensions>EXERCISE 3D>Q 17

A van of mass

2000 kg

is towed from rest by two ropes. One pulls with a tension of

130 N

10 °

to the direction of motion and the other acts at

15 °

to the direction of motion. Find the distance covered in

10 s .

HARD

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Mechanics Course Book>Chapter 3 - Forces in Two Dimensions>EXERCISE 3D>Q 18

A ship of mass

15000 kg

is moving due east at

2 m s^{- 1}

when it starts being towed by a tugboat. The wind is blowing it on a bearing of

60 °,

so the tugboat exerts a force of

5000 N

on a bearing of

100 °

to make the ship continue to go east. Find the speed of the ship after

5 s .

A buoy of mass 12 kg is on the surface of a lake. The tide pushes it with a force of 25 N and the wind pushes it with a force of 15 N, as shown in the diagram. The buoy moves in the direction shown. Find the value of θ and the acceleration.

Important Questions on Forces in Two Dimensions

Learn and Prepare for any exam you want !

A buoy of mass $12 kg$ is on the surface of a lake. The tide pushes it with a force of $25 N$ and the wind pushes it with a force of $15 N,$ as shown in the diagram. The buoy moves in the direction shown. Find the value of $θ$ and the acceleration.