Newton's Second Law of Motion - Basic Problem

Question

Please do provide a detailed step-by-step solution and a final answer.

1. A truck with a mass of 3,500 kg, including the passengers, has an engine that produces a net horizontal force of 525 N. Assuming that there is no other forces involve in the motion, find the following:

a.) acceleration of the truck

b.) starting from rest, how long will it take for the truck to reach the velocity of 11.5 m/s?

2. An object with a mass m1 accelerates at 8.0 m/s2 when a force F is applied. A second object with a mass m2 accelerates at 4.0 m/s2 when the same force F is applied to it.

a.) Find the value of the ratio m2/m1.

b.) Find the acceleration of the combined mass under the action of force F.

Answer 1

Question 1

a) Since the engine is the only force acting, the net force is 525 N.

F_net=ma

525=3500a

a=525/3500

a=0.15 m/s²

b) Using v=v₀+at

11.5=0+(0.15)t

t=11.5/0.15

t=76.7 seconds

Question 2

For the first mass F=m1(8)

m1=F/8

For the second mass F=m2(4)

m2=F/4

a) Therefore m2/m1 =(F/4)/(F/8) = 8/4 = 2

b) The combined mass is now m2 + m1 = F/8 + F/4 = 3F/8

Using F = (Combined Mass) x a

a= F/(3F/8)

a= 8/3 m/s² or 2.67 m/s²