Question

a man is moving with a 1500 kg car on a hilly road with 25 m/s velocity.the road creates an angle with ground 30 degree.but seeing a tree the car stops the car at 50m.what is the frictional force to stop the car?use work energy theorem

Answer 1

Answer on Question #50733, Physics, Mechanics - Kinematics - Dynamics

A man is moving with a 1500 kg car on a hilly road with 25 m/s velocity. The road creates an angle with ground 30 degree. But seeing a tree the car stops the car at 50m.what is the frictional force to stop the car? Use work energy theorem

Solution

By the work energy theorem:

$$E _ {k} + E _ {p} = W = F S$$

Where $S$ – traveled distance, $h = S \sin \alpha$ – vertical distance

$$\frac {m v ^ {2}}{2} + m g h = F S$$ $$\frac {m v ^ {2}}{2} + m g S \sin \alpha = F S \rightarrow F = \frac {m v ^ {2}}{2 S} + m g \sin \alpha$$

Finally, the frictional force is:

$$F = \frac {1 5 0 0 k g \cdot \left(2 5 \frac {m}{S}\right) ^ {2}}{2 \cdot 5 0 m} + 1 5 0 0 k g \cdot 9. 8 \frac {m}{S ^ {2}} \sin 3 0 {}^ {\circ} = 1 6 7 2 5 N$$

Answer: $F = 16725N$

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