Maths Question

A van of mass 1200kg is towing a car of mass 800kg up a slope inclined at 8 degree to the horizontal. The resistance to motion of the van may be modelled by a single force of magnitude 500N acting parallel to the slop. For the car the resistance may be modelled by a single force of magnitude 200 N acting parallel to the slope. The van is travelling at a constant speed.State one assumption that you have made,find in either order
a) the tension in teh towrope between van and the car
b) the driving force acting on the van

The driving force acting on the can is now increased to 4000N. Find the time taken for the van to increase its speed fromm 10ms^-1 to 14ms^-1?

Reply 1

Jonny W

Assumption: the car and van are not accelerating.

(a)
Because the car is not accelerating, there is no resultant force on it. Let T be the tension in the towrope. Resolving parallel to the slope,

T
= 200 + 800g sin(8)
= 1300 (2 sf)

(b)
Because the van is not accelerating, there is no resultant force on it. Let D be the driving force acting on the van. Resolving parallel to the slope,

D
= T + 500 + 1200g sin(8)
= 700 + 2000g sin(8)
= 3400 (2 sf)

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Let a be the common acceration of the car and van. Then

2000a = 4000 - 200 - 500 - 2000g sin(8)

Time taken to increase speed
= 4/a
= 14s (2 sf)