Question

A car and a truck have kinetic energies of 8*10^5 J and 9*10^5 respectively.If they brought to halt at the same distance,find the ratio of forces applied to both the vechiles.

Answer 1

Hey 

ΔE = W 

8 x 10⁵ = F1 x d 

9 x 10⁵ = F2 x d 

F1 : F2 = 8 x 10⁵ : 9 x 10⁵ = 8 : 9 = 8/9 

Answer 2

Given:

The kinetic energy of the car = 8 X 10⁵ J

The kinetic energy of the truck = 9 X 10⁵ J

The stopping distance of the car = The stopping distance of the truck

To Find:

The ratio of forces applied to both the vehicles

Solution:

The ratio of forces applied to the car and the truck is 8/9.

The work-energy theorem states that the total work done on a body is equal to the change in kinetic energy of the body.

Mathematically, if W joules of work change the initial velocity u of a body of mass m to v then,

W = 1/2 m (v² - u²)

Since in the question, after applying forces on the vehicles they come to rest

⇒ The final velocities of both the vehicles = 0 m/s

Applying the formula,

W$_c_a_r$ / W$_t_r_u_c_k$ = KE$_c_a_r$ / KE$_t_r_u_c_k$

= 8 X 10⁵ / 9 X 10⁵

= 8 /9

Replacing work done = Force X stopping distance,

F$_c_a_r$ . d / F$_t_r_u_c_k$ . d = 8 / 9

or The force applied on car / The force applied on truck = 8 / 9