Question

A 2510-kg car is coasting up a hill with a 10.0 degree incline at initial speed 20.0 m/s, when a squirrel suddenly darts out into the street ahead of it, and the driver slams on the brakes, causing the car to skid for 20.0 m before the brake is suddenly released and it continues coasting. The coefficient of kinetic friction between the tires and the pavement is 0.500.

Answer 1

given,

mass of the car = 2510 Kg

angle of inclination = 10°

initial speed = v₁ = 20 m./s

skid length = 20 m

coefficient of friction = 0.5

Using conservation of energy

`\Delta E = \Delta KE + \Delta U`

`\Delta E = (1)/(2)mv^2 + m g h`

h = d sin θ

`\Delta E = (1)/(2)mv^2- m g (dsin\theta)`

`\Delta E = (1)/(2)* 2510 * 20^2- 2510* 9.8 * (20 sin10^0)`

`\Delta E =416572.04\ J`

now, calculating the magnitude of frictional force is equal to

E = F_f d

`F_f = (E)/(d)`

`F_f = (416572.04)/(20)`

`F_f = 20828\ N`