A 50 kg object is moving under the action of a force along a horizontal floor at a constant speed of 4m/s. If the cofficient of sliding friction is 0.5 find the rate of workdone done by the force
The rate of work done by the force can be calculated using the formula:
Power = Force x Velocity
However, since the object is moving at a constant speed, the net force acting on it must be zero, meaning that the force applied is equal in magnitude but opposite in direction to the frictional force:
F = frictional force
F = μmg (where μ is the coefficient of sliding friction, m is the mass of the object, and g is the acceleration due to gravity)
F = 0.5 x 50 x 9.81
F = 245.25 N
Therefore, the rate of work done by the force is:
Power = F x v
Power = 245.25 x 4
Power = 981 W or 0.981 kW
So the rate of work done by the force is 0.981 kW.
To find the rate of work done by the force, we need to calculate the magnitude of the force first. The force that opposes the motion is the force of sliding friction.
The equation for the force of sliding friction is given by:
force of sliding friction = coefficient of sliding friction * normal force
The normal force is equal to the weight of the object, which can be calculated by multiplying the mass (50 kg) by the acceleration due to gravity (9.8 m/s^2):
normal force = mass * acceleration due to gravity
normal force = 50 kg * 9.8 m/s^2
normal force = 490 N
Now, we can calculate the force of sliding friction:
force of sliding friction = coefficient of sliding friction * normal force
force of sliding friction = 0.5 * 490 N
force of sliding friction = 245 N
Since the object is moving at a constant speed, the applied force (propelling force) is equal to the force of sliding friction:
applied force = force of sliding friction = 245 N
The work done by a force can be calculated using the formula:
work done = force * distance * cosine(theta)
In this case, the force and displacement are along the same line, so the angle between them (theta) is 0 degrees. Hence, the cosine(theta) is 1.
Considering that the object is moving at a constant speed, there is no displacement occurring (distance = 0 m).
Therefore, the work done by the force is:
work done = force * distance * cosine(theta)
work done = 245 N * 0 m * 1
work done = 0 Joules
Hence, the rate of work done by the force in this scenario is 0 Joules.