dynamics assignment

8/9/2019 Dynamics Assignment

1/3

Dynamics Assignment

1. A car which has run out of petrol is being towed by a breakdown truck along a straight

horizontal road. The truck has mass 1200 kg and the car has mass 800 kg. The truck is

connected to the car by a horizontal rope which is modelled as light and inextensible. The

trucks engine pro!ides a constant dri!ing force of 2"00 #. The resistances to motion of the

truck and the car are modelled as constant and of magnitude $00 # and "00 # respecti!ely. %ind

&a' the acceleration of the truck and the car((3)

&b' the tension in the rope.(3)

)hen the truck and car are mo!ing at 20 m s1

( the rope breaks. The engine of the truck

pro!ides the same dri!ing force as before. The magnitude of the resistance to the motion of the

truck remains $00 #.

&c' *how that the truck reaches a speed of 28 m s1

approximately $ s earlier than it would

ha!e done if the rope had not broken.(7)

(Total 13 marks)

2. A post is dri!en into the ground by means of a blow from a pile+dri!er. The pile+dri!er

falls from rest from a height of 1.$ m abo!e the top of the post.

&a' *how that the speed of the pile+dri!er ,ust before it hits the post is -.$ m s1

.(2)

The post has mass $ kg and the pile+dri!er has mass /8 kg. )hen the pile+dri!er hits the top of

the post( it is assumed that there is no rebound and that both then mo!e together with the same

speed.

&b' %ind the speed of the pile+dri!er and the post immediately after the pile+dri!er has

hit the post.(3)

The post is brought to rest by the action of a resisti!e force from the ground acting for 0.0$ s.

y modelling this force as constant throughout this time(

&c' find the magnitude of the resisti!e force((4)

&d' find( to 2 significant figures( the distance tra!elled by the post and the pile+dri!er

before they come to rest.(4)

(Total 13 marks)

Queen Elizabeth's School 1


2/3

Dynamics Assignment

3.

1 m

1 . " m

P

2 0

A m& k g '

B & 0 . " k g '

The diagram abo!e shows two particlesAandB( of mass mkg and 0." kg respecti!ely(

connected by a light inextensible string. 3nitiallyAis held at rest on a fixed smooth plane

inclined at 04 to the horizontal. The string passes o!er a small light smooth pulleyPfixed at

the top of the plane. The section of the string fromAtoPis parallel to a line of greatest slope of

the plane. The particleBhangs freely belowP. The system is released from rest with the string

taut andBdescends with acceleration -1

g.

&a' )rite down an e5uation of motion forB.(2)

&b' %ind the tension in the string.(2)

&c' 6ro!e that m= 2-1$

.(4)

&d' *tate where in the calculations you ha!e used the information thatPis a light smooth

pulley.(1)

7n release(Bis at a height of one metre abo!e the ground andAP = 1." m. The particleB

strikes the ground and does not rebound.

&e' alculate the speed ofB as it reaches the ground.(2)

&f' *how thatAcomes to rest as it reachesP.(5)

(Total 16 marks)



3/3

Dynamics Assignment

4.

1 - 4

This figure shows a lorry of mass 1$00 kg towing a car of mass 900 kg along a straight

horizontal road. The two !ehicles are ,oined by a light towbar which is at an angle of 1-to the

road. The lorry and the car experience constant resistances to motion of magnitude $00 # and

00 # respecti!ely. The lorrys engine produces a constant horizontal force on the lorry of

magnitude 1-00 #. %ind

&a' the acceleration of the lorry and the car(

(3)

&b' the tension in the towbar.(4)

)hen the speed of the !ehicles is $ m s1

( the towbar breaks. Assuming that the resistance to the

motion of the car remains of constant magnitude 00 #(

&c' find the distance mo!ed by the car from the moment the towbar breaks to the momentwhen the car comes to rest.

(4)

&d' *tate whether( when the towbar breaks( the normal reaction of the road on the car is

increased( decreased or remains constant. :i!e a reason for your answer.(2)

(Total 13 marks)


dynamics assignment

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