A 54 kg box is being pushed a distance of 7.0 m across the floor by a force P whose magnitude is 153 N. The force P is parallel to the displacement of the box. The coefficient of kinetic friction is 0.25. Determine the work done on the box by each of the four forces that act on the box. Be sure to include the proper plus or minus sign for the work done by each force.
applied force:
frictional force:
normal force:
gravity:
mg does 0 work because there is no motion up or down
the force up on the box, also mg, does no work because there is no motion up or down.
the 153 N does positive work = 153*7 Joules
the friction does negative work = -m g*.25*7
Well, well, let's break this down, shall we?
First up, the applied force. We have a parallel push happening here, so the work done by the applied force is simply the magnitude of the force times the displacement. In this case, it's 153 N multiplied by 7.0 m. You do the math, my friend! But don't forget the sign, it's gonna be positive.
Next, we have the frictional force. Now, this force is always a bit of a party pooper, slowing things down. The work done by friction can be found by multiplying the coefficient of kinetic friction (0.25) by the normal force (which we'll get to later) and the displacement (7.0 m). Make sure to throw in a minus sign to show that friction is all about taking things away.
Speaking of the normal force, it's like the bouncer at a club making sure things don't go out of control. In this case, it's equal to the weight of the box, which is just the mass (54 kg) multiplied by the acceleration due to gravity (9.8 m/s^2). Don't forget the minus sign when you calculate the work done by the normal force because it's opposing the displacement.
Finally, we have the force of gravity. It may not be directly in the game since it's perpendicular to the displacement, but we can still find the work done by it. The work done by gravity is zero because its force and the displacement are perpendicular. No work, no problem!
So there you have it, my friend. Grab a calculator and crunch those numbers to find the work done by each of these forces. And don't forget to let your humor flow while doing those calculations!
To determine the work done on the box by each of the four forces, we need to use the formula for work:
Work = Force * Distance * cos(angle)
For simplicity, let's assume that the angle between each force and the displacement of the box is 0 degrees, meaning they are parallel.
1. Applied force (P):
The work done by the applied force can be calculated using the formula:
Work = P * Distance * cos(0)
= P * Distance
Given that P = 153 N and Distance = 7.0 m, we can calculate the work done by the applied force as follows:
Work = 153 N * 7.0 m
= 1071 N·m (or Joules)
So, the work done by the applied force is 1071 Joules.
2. Frictional force:
The work done by the frictional force can also be calculated using the formula:
Work = frictional force * Distance * cos(0)
= frictional force * Distance
To find the frictional force, we need to calculate the normal force. The normal force is the force exerted perpendicular to the surface of contact, which in this case is the weight of the box.
3. Normal force:
The normal force can be calculated using the formula:
Normal force = Weight of the box
Weight of the box = mass * gravity acceleration
Given that the mass of the box is 54 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the normal force as follows:
Normal force = 54 kg * 9.8 m/s^2
= 529.2 N
Therefore, the normal force exerted on the box is 529.2 N.
4. Gravity:
The work done by gravity can be calculated using the formula:
Work = Weight * Distance * cos(0)
= Weight * Distance
To calculate the work done by gravity, we need to find the weight of the box:
Weight of the box = mass * gravity acceleration
Given that the mass of the box is 54 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight of the box as follows:
Weight of the box = 54 kg * 9.8 m/s^2
= 529.2 N
Therefore, the work done by gravity is:
Work = 529.2 N * 7.0 m
= 3704.4 N·m (or Joules)
So, the work done by gravity is 3704.4 Joules.
In summary, the work done by each force on the box is as follows:
- Applied force: 1071 Joules
- Frictional force: frictional force * Distance
- Normal force: N/A (the normal force does no work as it is perpendicular to the displacement)
- Gravity: 3704.4 Joules
To determine the work done on the box by each force, we need to use the equation:
Work = Force x Distance x cos(theta)
Where:
- Work is the work done on the box.
- Force is the magnitude of the force.
- Distance is the displacement of the box.
- cos(theta) is the angle between the force vector and the displacement vector.
Now, let's calculate the work done by each force:
1. Applied force (P):
The magnitude of the applied force is 153 N, and it is parallel to the displacement of the box. Therefore, the angle (theta) between the force and displacement vectors is 0 degrees.
So, the work done by the applied force is:
Work (P) = P x Distance x cos(0)
= 153 N x 7.0 m x cos(0)
= 1071 Joules
Since the force and displacement are in the same direction, the work done by the applied force is positive.
2. Frictional force:
The frictional force can be determined using the equation:
Frictional force = coefficient of kinetic friction x normal force
The coefficient of kinetic friction is given as 0.25. To find the normal force, we need to consider the weight of the box.
3. Normal force:
The normal force is the force exerted by the floor perpendicular to the box's surface. In this case, it is equal to the weight of the box, which can be calculated using:
Weight = mass x acceleration due to gravity
Where the mass of the box is 54 kg, and the acceleration due to gravity is 9.8 m/s^2.
Weight = 54 kg x 9.8 m/s^2
= 529.2 N
Therefore, the normal force acting on the box is 529.2 N.
4. Gravity:
The force of gravity acts vertically downward. Since the box is being pushed horizontally, the angle between the force of gravity and the displacement is 90 degrees.
So, the work done by gravity is:
Work (gravity) = Weight x Distance x cos(90)
= 529.2 N x 7.0 m x cos(90)
= 0 Joules
As there is no horizontal displacement in the direction of the force of gravity, the work done by gravity is zero.
Now, let's calculate the work done by the frictional force:
Frictional force = 0.25 x Normal force
= 0.25 x 529.2 N
= 132.3 N
The angle between the frictional force and the displacement is 180 degrees, as the force of friction opposes the motion. Thus, the work done by the frictional force is:
Work (friction) = Frictional force x Distance x cos(180)
= 132.3 N x 7.0 m x cos(180)
= -924.6 Joules
Since the angle is 180 degrees and cos(180) = -1, the work done by the frictional force is negative.
Therefore, the work done on the box by each force is as follows:
- Applied force: +1071 Joules
- Frictional force: -924.6 Joules
- Normal force: 0 Joules
- Gravity: 0 Joules