Question 5.6: A car of mass 1000 kg, including its driver, is being pushed...
A car of mass 1000 kg, including its driver, is being pushed along a horizontal road by three people as indicated in the diagram. The car is moving in the direction PQ.
i) Calculate the total force exerted by the three people in the direction PQ.
ii) Calculate the force exerted overall by the three people in the direction perpendicular to PQ.
iii) Explain briefly why the car does not move in the direction perpendicular to PQ.
Initially the car is stationary and 5 s later it has a speed of 2 ms^{-1} in the direction PQ.
iv) Calculate the force of resistance to the car’s movement in the direction PQ assuming the three people continue to push as described above.
i) Resolving in the direction PQ, the components in newtons are:
Kelly 20 cos 15° = 193
Dean 270
Emma 240 cos 25° = 218
Total force in the direction PQ = 681 N.
ii) Resolving perpendicular to PQ (\uparrow) the components are:
Kelly -200 sin 15° = -51.8
Dean 0
Emma 240 sin 25° = 101.4
Total force in the direction perpendicular to PQ = 49.6 N.
iii) The car does not move perpendicular to PQ because the force in this direction is balanced by a sideways (lateral) friction force between the tyres and the road.
iv) To find the acceleration, a ms^{-2}, of the car:
v = u + at
\begin{matrix} 2 = 0 + 5a &\longleftarrow \boxed{ u = 0, v = 2,\ t = 5 }\end{matrix}
a = 0.4
When the resistance to motion in the direction QP is R N, the diagram shows all the horizontal forces acting on the car and its acceleration.
The resultant force in the direction PQ is (681 – R) N. So by Newton II
681 – R = 1000a
R = 681 – 400
The resistance to motion in the direction PQ is 281 N.
