You carry a 7.0 kg bag of groceries above the level floor at a constant velocity of 75 cm/s across a room that is room. How much work do you do on the bag in the process?

1.97J

Explanation:

Given parameters:

Mass of the groceries = 7kg

velocity of the bag = 75cm/s

Unknown:

Work done to move the bag  = ?

Solution:

Work done is the force applied to move a body through a distance in a specific direction:

     Work done = Force x distance

In this case, the work done is the kinetic energy applied in pulling the bag.

Kinetic energy is the energy in motion of a body.

 Work done  = kinetic energy =

where m is the mass

           v is the velocity

Now, convert the velocity from cm/s to m/s

   100cm = 1m

 75  x  = 0.75m/s

 Work done  = x 7 x 0.75² = 1.97J

the velocity you are looking for is made up of two parts: horizontally velocity, vh, and its vertical velocity, vv. the actual velocity of the ball will be these two parts added together, and because velocity is a vector then they will need to be added vectorially.  

neglecting air resistance etc etc.,  

the horizontal velocity component will be constant (because there is no accelerating force in the horizontal direction.  

vh = 8 ms-1  

the vertical velocity component has an accelerating force: 'g'.  

using v = u +at where a = g = 9.81 ms-2.  

the vertical component of velocity, vv = 0 + gt = vv =9.81 x 2  

vv = 19.62 ms-1 . the zero appears because the virtical component of velocity at time t=0 is zero. remember, the ball was thrown horizontally.  

how fast it will be moving (it actual path (being a parabola )) will be the vector sum of these two.  

adding vectorally gives: -  

v = sqr root (8^2 + 19.62^2) = sqr root(64+384.9) = 21.18 or 21.2 ms-1