A man drags a table 4.25 m across the floor, exerting a constant force of 54.0 N, directed 28.0° above the horizontal.
I have found the work done by the applied force to be 202.6 J but I can't find the second part of the question which is below.
(b) How much work is done by friction? Assume the table's velocity is constant.
(b) Multiply the friction force by the distance the table moves. It will be a negative number.
Since the table does not accelerate, you know that the friction force must balance the horizontal component of the applied force. The answer to (b) is MINUS the value of the answer to (a)
To find the work done by friction, we need to determine the force of friction and the distance over which it acts.
The force of friction can be determined using the equation:
frictional force = coefficient of friction × normal force
However, we do not have the coefficient of friction or the normal force. We need to find these values first.
Since the table is being pulled horizontally, the normal force will act vertically and will be equal in magnitude and opposite in direction to the gravitational force exerted on the table.
The normal force can be calculated using the equation:
normal force = mass × gravitational acceleration
Assuming the mass of the table is 20 kg and the gravitational acceleration is approximately 9.8 m/s^2, we can calculate the normal force:
normal force = 20 kg × 9.8 m/s^2 = 196 N
Now that we have the normal force, we can calculate the force of friction using the equation:
frictional force = coefficient of friction × normal force
However, since we still don't know the coefficient of friction, we cannot calculate the force of friction directly. Instead, we can make an observation:
The table's velocity is constant, which means the net force acting on it must be zero, i.e., the applied force and the force of friction are equal in magnitude and opposite in direction.
Since we know the applied force is 54.0 N, the force of friction must also be 54.0 N. This is the force required to overcome friction and keep the table moving at a constant velocity.
Finally, we can calculate the work done by friction using the formula:
work done by friction = force of friction × distance
Given that the distance traveled by the table is 4.25 m:
work done by friction = 54 N × 4.25 m = 229.5 J
Therefore, the work done by friction is 229.5 J.
To find the work done by friction, we need to understand that friction always opposes motion. In this case, since the table is being dragged across the floor, the frictional force will act in the opposite direction of the applied force.
The work done by friction can be calculated using the formula:
Work (W) = Force (F) × Distance (d) × cos(theta)
where:
- Force (F) is the frictional force,
- Distance (d) is the distance over which the object is moved, and
- theta is the angle between the force and the direction of motion.
In this case, we are given:
- Force (F) = ? (since we are trying to find it)
- Distance (d) = 4.25 m (given in the question)
- theta = 180° (since the frictional force acts in the opposite direction)
Since the table's velocity is constant, the force of friction must be equal in magnitude to the applied force. Therefore, the force of friction is equal to 54.0 N (given in the question).
Now let's calculate the work done by friction:
W = Force (F) × Distance (d) × cos(theta)
W = 54.0 N × 4.25 m × cos(180°)
When calculating cos(180°), we find that it is equal to -1. Therefore, the equation becomes:
W = 54.0 N × 4.25 m × (-1)
Solving this equation will give us the work done by friction.
W = -229.5 J
Therefore, the work done by friction is -229.5 J. The negative sign indicates that the frictional force is acting in the opposite direction to the displacement, which is consistent with our understanding that friction opposes motion.