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16. Exercises

From Mechanics

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Two particles travel towards each other along a straight line. One has mass 3 kg and speed 4 ms-1. The other has mass 5kg and speed 2 <math>\text{m}{{\text{s}}^{-1}}</math>. When they collide the 3kg mass is brought to rest. What happens to the 5kg mass ?
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Two particles travel towards each other along a straight line. One has mass 3 kg and speed 4 <math>\text{m}{{\text{s}}^{-1}}</math>. The other has mass 5kg and speed 2 <math>\text{m}{{\text{s}}^{-1}}</math>. When they collide the 3kg mass is brought to rest. What happens to the 5kg mass ?
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A toy train, of mass 200 grams, is moving along a straight track at 1.8 <math>\text{m}{{\text{s}}^{-1}}</math>, when it collides with a stationary truck of mass, of mass 300 grams, during the collision the trucks are coupled together. Find the speed of the truck after the collision.
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A toy train, of mass 200 grams, is moving along a straight track at 1.8 <math>\text{m}{{\text{s}}^{-1}}</math>, when it collides with a stationary truck of mass, of mass 300 grams, during the collision the truck is coupled to the train. Find the speed of the truck after the collision.
</div>{{#NAVCONTENT:Answer|Answer 16.4|Solution|Solution 16.4}}
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Two particles, ''A'' and ''B'', have velocities (<math>4\mathbf{i}-V\mathbf{j}</math>) <math>\text{m}{{\text{s}}^{-1}}</math> and (<math>2\mathbf{i}+V\mathbf{j}</math>) <math>\text{m}{{\text{s}}^{-1}}</math> respectively. The mass of ''A'' is ''m'' and the mass of ''B'' is <math>\lambda m</math>. After the collision, the particles move together with velocity (<math>3\mathbf{i}+2\mathbf{j}</math>) <math>\text{m}{{\text{s}}^{-1}}</math>.
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Two particles, ''A'' and ''B'', have velocities (<math>5\mathbf{i}+V\mathbf{j}</math>) <math>\text{m}{{\text{s}}^{-1}}</math> and (<math>2\mathbf{i}-V\mathbf{j}</math>) <math>\text{m}{{\text{s}}^{-1}}</math> respectively. The mass of ''A'' is ''m'' and the mass of ''B'' is <math>\lambda m</math>. After the collision, the particles move together with velocity (<math>3\mathbf{i}-2\mathbf{j}</math>) <math>\text{m}{{\text{s}}^{-1}}</math>.
a) Find <math>\lambda </math>.
a) Find <math>\lambda </math>.

Current revision

       Theory          Exercises      



Exercise 16.1


A car, of mass 1000 kg, is travelling at 20 ms−1, when it drives into a truck, of mass 4000 kg, which was moving at 10 ms−1 in the same direction. After the collision the two vehicles move together. Find the speed of the vehicles after the collision.

Answer | Solution


Exercise 16.2

A child of mass 40 kg stands on a skate board, of mass 2 kg. Initially both are at rest. The boy jumps off so that he travels horizontally at 3 ms−1. Find the speed of the skateboard.

Answer | Solution



Exercise 16.3

Two particles travel towards each other along a straight line. One has mass 3 kg and speed 4 ms−1. The other has mass 5kg and speed 2 ms−1. When they collide the 3kg mass is brought to rest. What happens to the 5kg mass ?

Answer | Solution



Exercise 16.4

A toy train, of mass 200 grams, is moving along a straight track at 1.8 ms−1, when it collides with a stationary truck of mass, of mass 300 grams, during the collision the truck is coupled to the train. Find the speed of the truck after the collision.

Answer | Solution



Exercise 16.5

Two particles are travelling towards each other when they collide. One has mass 2kg and was travelling at 5 ms−1 before the collision and the other has mass 3 kg and a velocity of 6 ms−1 before the collision. The 2kg mass changes direction and moves at 2 ms−1 after the collision. Describe how the 3kg mass moves after the collision.


Answer | Solution



Exercise 16.6

Two particles A and B, have masses 2 kg and 3kg respectively. Before a collision between the two particles, they have velocities (9i+5j) ms−1 and (−3i+4j) ms−1 respectively, where i and j are perpendicular unit vectors. During the collision the two particles coalesce and move together after the collision.

Find the velocity of the particles after the collision.


Answer | Solution


Exercise 16.7

Two identical particles, A and B are travelling in perpendicular directions when they collide. Particle A is travelling at 5 ms−1 and B at 8 \displaystyle \text{m}{{\text{s}}^{-1}} when they collide. During the collision the particles coalesce to form a single particle.

a) Find the speed of the combined particle after the collision.

b) Find the angle between the velocity of A before the collision and the velocity of the combined particle after the collision.


Answer | Solution a | Solution b


Exercise 16.8

Red and white snooker balls have the same mass. A white ball is moving at 1 \displaystyle \text{m}{{\text{s}}^{-1}}, when it collides with a red ball which is at rest. After the collision the white ball travels at 0.8 \displaystyle \text{m}{{\text{s}}^{-1}} and it is deflected through 60\displaystyle {}^\circ from its original path. Find the speed of the red ball after the collision.

Answer | Solution


Exercise 16.9

Two particles, A and B, have velocities (\displaystyle 8\mathbf{i}+7\mathbf{j}) \displaystyle \text{m}{{\text{s}}^{-1}} and \displaystyle U\mathbf{i}+V\mathbf{j} respectively when they collide. After the collision A travels in the direction of \displaystyle \mathbf{i} at 5 \displaystyle \text{m}{{\text{s}}^{-1}} and B travels in the direction of \displaystyle \mathbf{j} at 2 \displaystyle \text{m}{{\text{s}}^{-1}}. Given that the mass of A is twice the mass of B, find U and V.

Answer | Solution

Exercise 16.10

Two particles, A and B, have velocities (\displaystyle 5\mathbf{i}+V\mathbf{j}) \displaystyle \text{m}{{\text{s}}^{-1}} and (\displaystyle 2\mathbf{i}-V\mathbf{j}) \displaystyle \text{m}{{\text{s}}^{-1}} respectively. The mass of A is m and the mass of B is \displaystyle \lambda m. After the collision, the particles move together with velocity (\displaystyle 3\mathbf{i}-2\mathbf{j}) \displaystyle \text{m}{{\text{s}}^{-1}}.

a) Find \displaystyle \lambda .

b) Find V.


Answer | Solution a | Solution b

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