A worker pushed a 33 kg block 6.1 m along a level floor at constant speed with a force directed 23° below the horizontal. if the
coefficient of kinetic friction between block and floor was 0.20, what were (a) the work done by the worker's force and (b) the increase in thermal energy of the block-floor system?
The work done occurs only in the direction the block was moved - horizontally. Work is given by:
W = F(h) * d
Where F(h) is the force applied in that direction (horizontal) and d is the distance in that direction. In this case, F(h) is the horizontal component of the applied force, F(app). However, the question doesn't give us F(app), so we need to find it some other way.
Since the block is moving at a constant speed, we know the horizontal forces must be balanced so that the net force is 0. This means that F(h) must be exactly balanced by the friction force, f. We can express F(h) as a function of F(app):
F(h) = F(app)cos(23)
Friction is a little trickier - since the block is being PUSHED into the ground a bit by the vertical component of the applied force, F(v), the normal force, N, is actually a bit more than mg:
N = mg + F(v) = mg + F(app)sin(23)
Now we can get down to business and solve for F(app) - as mentioned above:
F(h) = f F(h) = uN F(h) = u * (mg + F(v)) F(app)cos(23) = 0.20 * (33 * 9.8 + F(app)sin(23)) F(app) = 76.8
Now that we have F(app), we can find the exact value of F(h):
Velocity is defined as the rate of change of displacement.
velocity is a vector quantity, that means it requires both magnitude and direction to completely explain the velocity.
For example, the velocity is 5 ms due east, it means an object is moving with speed 5 ms in the direction of east. We can say that the object covers the displacement of 5 m in one second due east.
