1. A 1.0 kg block slides off the edge of a frictionless horizontal table with a

Question

1. A 1.0 kg block slides off the edge of a frictionless horizontal table with a speed of 3.0 m/s. It lands in the back of a child’s toy truck, 1.0 m below the table top, and a horizontal distance L away (see diagram below). The truck has a mass of 2.0 kg, is initially at rest, and can roll without friction on the floor. a. [6 points] Find the distance L. b. [1 point] True or false: After the block leaves the table, the block and truck can be considered to be a system of interacting objects. Since there is no friction, the only external forces on this system are gravitational forces and the normal force exerted by the floor on the truck. All the external forces are vertical, therefore the vertical component of the total momentum of the system can change, but the horizontal component of the system’s momentum is conserved. c. [3 points] Assuming the block stays on the truck after they collide, find the final speed of the truck.

Explanation / Answer

Problem Data

. mb = 1 Kg       vbo = 3 m/s    x axis

. y =1 m mT= 2 Kg     vTo= 0

.a) L=?

.b)

.c) vf = ?

.a) To find the distance we use kinematic

. y = voy t – ½ g t2          voy = 0       y= - ½ g t2      t2 = -2y/g     t2 = - 2 (-1)/9.8=0.2 s2

.   t= 0.45 s

. x = L = vbo t          x= 3 0.45 = 1.36 m

L= 1.36 m

.b)   True, since there are no external forces on the x axis, also the impact forces in the system are internal forces therefore do not change its momentum

.c) use conservation of momentum as the forces in the x axis are internal

     .    pi = pf

   .   pi = mb vbo+ mT vTo      vTo=0

. pf = (mb + mT ) vf

. mb vbo = (mb + mT ) vf                   vf= vbo mb/(mb + mT )      vf = 3     1/(2+1) = 1 m/s

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