Question

A 5000-lb truck is being used to lift a 1000 lb boulder B that is on a 200 lb pallet A. Knowing the acceleration of the truck is 1 ft/s2, determine (a) the horizontal force between the tires and the ground, (b) the force between the boulder and the pallet.

Answer 1

Answer:

Part a: The force between the tires and the ground is 765 lbf.

Part b: The force between the pallet and the boulder is 1016 lbf.

Explanation:

From the free body diagram on the Truck,  boulder and pallet level

• $a_T$ is the acceleration of truck which is 1 ft/s2
• $m_T$ is the mass of the truck which is 5000 lb or 155.28 slugs

• $m_b$ is the mass of the boulder which is 1000 lb or 31.06 slugs

• $m_a$ is the mass of the pallet which is 200 lb or 6.211 slugs
• $a_a =a_b$ is the acceleration of the pallet or boulder which is 0.5 ft/s2

Applying Newton's 2nd Law of Motion on pulley in vertical direction

                             $2T-(m_a+m_b)g=(m_a+m_b)a_a\\2T-(37.271)(32.2)=(37.271)(0.5)\\T=609.32 lb_f$

Part a

Applying Newton's 2nd Law of Motion on Truck in horizontal direction

                              $F-T=m_Ta_T\\F=609.32+(155.28)(1)\\F=765 lb_f$

So the force between the tires and the ground is 765 lbf.

Part b

Applying Newton's 2nd Law of Motion on Boulder in vertical direction

                               $F_{AB}-m_bg=m_ba_b\\F_{AB}=m_b(g+a_b)\\F_{AB}=31.056(32.2+0.5)\\F_{AB}=1016 lb_f$

So the force between the pallet and the boulder is 1016 lbf.