Question

A truck driver slams on the brakes and the momentum of the truck changes from <89000, 0, 0 > kg·m/s to < 33000, 0, 0> kg·m/s in 3.3 seconds due to a constant force of the road on the wheels of car. As a vector, write the net force exerted on the truck by the surroundings. N

Answer 1

The net force exerted on the truck by the surroundings is calculated using the change in momentum and the time interval. It is found to be approximately <-16970, 0, 0> Newtons.

Step-by-step explanation:

To find the net force exerted on the truck by the surroundings, we need to use the change in momentum (Δp) and the time (Δt) over which the change occurs. The change in momentum is obtained by subtracting the final momentum vector from the initial momentum vector. In this case:

Δp = <33000, 0, 0> kg·m/s - <89000, 0, 0> kg·m/s = <-56000, 0, 0> kg·m/s

The time interval Δt is given as 3.3 seconds. The net force (F) can be calculated using Newton's second law in its impulse-momentum form:

F = Δp / Δt

The net force vector is:

F = <-56000, 0, 0> kg·m/s / 3.3 s = <-16969.7, 0, 0> N

Therefore, the net force exerted on the truck by the surroundings as a vector is approximately <-16970, 0, 0> Newtons.

Answer 2

<-16969.7, 0, 0> N

Step-by-step explanation:

`p_2` = Final momentum = < 33000, 0, 0> kg·m/s

`p_1` = Initial momentum = <89000, 0, 0> kg·m/s

t = Time taken = 3.3 seconds

Impulse is given by

`J=p_2-p_1\\\Rightarrow Ft=p_2-p_1\\\Rightarrow F=(p_2-p_1)/(t)\\\Rightarrow F=(< 33000, 0, 0>-<89000, 0, 0>)/(3.3)\\\Rightarrow F=(<-56000, 0, 0>)/(3.3)\\\Rightarrow F=<-16969.7, 0, 0>\ N`

The net force exerted on the truck is <-16969.7, 0, 0> N