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Mechanics 1 - Dynamics/Connected Particles

A revision aid for Kinematics (Edexcel Mechancis 1)
by

Lydia Blain

on 11 March 2013

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Transcript of Mechanics 1 - Dynamics/Connected Particles

June 2009, Q6 A car of mass 800 kg pulls a trailer of mass 200 kg along a straight horizontal road using a light towbar which is parallel to the road. The horizontal resistances to motion of the car and the trailer have magnitudes 400 N and 200 N respectively. The engine of the car produces a constant horizontal driving force on the car of magnitude 1200 N. Find

(a)the acceleration of the car and trailer, (3)
(b)the magnitude of the tension in the towbar. (3)

The car is moving along the road when the driver sees a hazard ahead. He reduces the force produced by the engine to zero and applies the brakes. The brakes produce a force on the car of magnitude F newtons and the car and trailer decelerate. Given that the resistances to motion are unchanged and the magnitude of the thrust in the towbar is 100 N,
(c)find the value of F. (7) June 2010, Q6 Edexcel Mechanics 1
revision resource Connected
Particles Dynamics Edexcel Mechanics 1
revision tool for chapter 3. Dynamics is the study of moving objects and the forces acting on them. This revision resource considers problems in vovling connected particles. Work through the questions and tutorial resources provided. At the end of the revision process you should be ready to try some past exam questions. You should allocate a minimum of 2 hours for your connected particles revision. January 2007, Q7 Examiner top tip:
If you are unsure where to begin, start by writing the equation of motion (applying F=ma) to each individual particle first and then to the whole system.
Generally if you want the acceleration it will be quickest to consider the whole system (as tension won't be included), but if you want tension you will need to have an equation for one, or both particles. Two particles A and B have masses 5m and km respectively, where k < 5. The particles are connected by a light inextensible string which passes over a smooth light fixed pulley. The system is held at rest with the string taut, the hanging parts of the string vertical and with A and B at the same height above a horizontal plane, as shown in Figure 4. The system is released from rest. After release, A descends with acceleration 1⁄4 g.

(a) Show that the tension in the string as A descends is (3)
(b) Find the value of k. (3)
(c) State how you have used the information that the pulley is smooth. (1)

After descending for 1.2 s, the particle A reaches the plane. It is immediately brought to rest by the impact with the plane. The initial distance between B and the pulley is such that, in the subsequent motion, B does not reach the pulley.

(d) Find the greatest height reached by B above the plane. (7) The figure above shows two particles P and Q, of mass 3 kg and 2 kg respectively, connected by a light inextensible string. Initially P is held at rest on a smooth fixed plane inclined at 30° to the horizontal. The string passes over a small smooth light pulley A fixed at the top of the plane. The part of the string from P to A is parallel to a line of greatest slope of the plane. The particle Q hangs freely below A. The system is released from rest with the string taut.

(a)Write down an equation of motion for P and an equation of motion for Q. (4)
(b)Hence show that the acceleration of Q is 0.98 m s–2. (2)
(c)Find the tension in the string. (2)
(d)State where in your calculations you have used the information that the string is inextensible. (1)

On release, Q is at a height of 0.8 m above the ground. When Q reaches the ground, it is brought to rest immediately by the impact with the ground and does not rebound. The initial distance of P from A is such that in the subsequent motion P does not reach A. Find

(e)the speed of Q as it reaches the ground, (2)
(f)the time between the instant when Q reaches the ground and then instant when the string becomes taut again. (5) Examiner top tip:
Mechanics is a subject that requires a lot of diagrams. Don't get lazy and cut corners. Learn the standard diagrams for a given topic so that you can draw them without having to think for too long.
Use standard letters to simplify your work and include these in your diagrams.
Forces:
•T for tension
•W for weight
•R for reaction (N for normal reaction or contact force can get confused with N for Newtons)
•F for friction or resistance to motion
•Fmax for limiting friction
This will make your work much easier to follow, save you time and possibly less mistakes. Spot the mistake! Look at the exam solution below. See if you can spot the mistake. Then see if you can find the correct answer. a=0.6 (m/s)
T=320 (N)
F=900 (N) Did you get the correct answer?
If not, watch the video solution. a) T-3gsin30=3a
(b) a=0.98
(c) T=17.6 or 18
(d) acceleration of P & Q the same
(e) v=1.25 or 1.3
(f) t=0.51 Did you get the correct answer?
If not, watch the video solutions. Examiner top tip:

When asked to state the assumptions you have made, remember;
•The string is light - (This is a common reply when dealing with connected particles where a string passes over a pulley. If the string were not light then the mass would change and therefore the acceleration would not be constant).
•The string is inextensible - (An inextensible string will mean that when two particles are connected, as one moves with acceleration a, then the other moves also with the same acceleration a)
•The pulley is smooth - (When a string passes over a smooth pulley the tensions in the string are the same on either side) Did you spot it? Part (b) was incorrect.
The component of weight down the slope has not been included. The correct value of mu was 0.693 or 0.69 Did you get the correct answer?
If not, watch the video tutorial. a) Show that.
b) k=3
c) Tensions are the same
d) s=4 (m)
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