3 A constant resistance of magnitude 1400 N acts on a car of mass 1250 kg .
- The car is moving along a straight level road at a constant speed of \(28 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
Find, in kW , the rate at which the engine of the car is working.
- The car now travels at a constant speed up a hill inclined at an angle of \(\theta\) to the horizontal, where \(\sin \theta = 0.12\), with the engine working at 43.5 kW .
Find this speed.
- On another occasion, the car pulls a trailer of mass 600 kg up the same hill. The system of the car and the trailer is modelled as particles connected by a light inextensible cable. The car's engine produces a driving force of 5000 N and the resistance to the motion of the trailer is 300 N . The resistance to the motion of the car remains 1400 N .
Find the acceleration of the system and the tension in the cable.
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A block of mass 8 kg is placed on a rough plane which is inclined at an angle of \(18 ^ { \circ }\) to the horizontal. The block is pulled up the plane by a light string that makes an angle of \(26 ^ { \circ }\) above a line of greatest slope. The tension in the string is \(T \mathrm {~N}\) (see diagram). The coefficient of friction between the block and plane is 0.65 . - The acceleration of the block is \(0.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
Find \(T\).
- The block is initially at rest.
Find the distance travelled by the block during the fourth second of motion.