A horizontal force of 150 N is used to push a 43.5 kg packing crate a distance of 5.30 m on a rough horizontal surface. If the crate moves at constant speed, find each of the following.
(a) the work done by the 150 N force
(b) the coefficient of kinetic friction between the crate and the surface
(a) Well, let's calculate the work done by the 150 N force. Work is equal to force multiplied by distance, so W = F * d. Plugging in the given values, we get W = 150 N * 5.3 m. That's a whopping 795 J of work done!
(b) Now, let's find the coefficient of kinetic friction between the crate and the surface. Since the crate is moving at constant speed, we know that the force of friction is equal and opposite to the applied force. So the force of friction is also 150 N, but in the opposite direction.
According to Newton's second law, F_friction = μ * N, where μ is the coefficient of kinetic friction and N is the normal force. Since the crate is on a horizontal surface, the normal force is equal to the weight of the crate, which is given by N = m * g, where m is the mass of the crate and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Substituting the given values, we have 150 N = μ * 43.5 kg * 9.8 m/s^2. Solving this equation for μ, we find μ ≈ 0.343.
So, the coefficient of kinetic friction between the crate and the surface is approximately 0.343. Don't worry, this won't make the crate start telling jokes or anything!
To find the answers, we first need to calculate the work done by the 150 N force and then determine the coefficient of kinetic friction between the crate and the surface.
(a) Work done by the 150 N force:
The work done by a force can be calculated using the formula:
Work = Force x Distance x cos(angle)
Since the angle is not given in the problem, we assume it to be 0 degrees since it is stated that the crate moves horizontally. Therefore, the work can be calculated as:
Work = 150 N x 5.30 m x cos(0°)
Since cos(0°) = 1, the equation simplifies to:
Work = 150 N x 5.30 m
Calculating this, we get:
Work = 795 J
Therefore, the work done by the 150 N force is 795 Joules.
(b) Coefficient of kinetic friction:
We can use the following equation to calculate the coefficient of kinetic friction:
Frictional force = Coefficient of kinetic friction x Normal force
The normal force is the force exerted perpendicularly by the surface on the crate and is equal to the gravitational force acting on the crate since it is not accelerating vertically.
Normal force = mass x gravitational acceleration
Normal force = 43.5 kg x 9.8 m/s^2
Calculating this, we get:
Normal force = 426.3 N
Since the crate is moving at constant speed, the frictional force must be equal in magnitude and opposite in direction to the applied force.
Frictional force = Applied force = 150 N
Now we can substitute these values into the equation to calculate the coefficient of kinetic friction:
150 N = Coefficient of kinetic friction x 426.3 N
Dividing both sides by 426.3 N, we get:
Coefficient of kinetic friction = 150 N / 426.3 N
Calculating this, we get:
Coefficient of kinetic friction ≈ 0.352
Therefore, the coefficient of kinetic friction between the crate and the surface is approximately 0.352.
To find the answers, we need to apply some concepts from physics. Let's start with part (a) and find the work done by the 150 N force.
(a) Work is defined as the product of the force applied and the displacement of the object in the direction of the force. In this case, the force applied is 150 N, and the displacement of the crate is 5.30 m. Since the crate moves at a constant speed, we can assume that the force applied is equal to the frictional force opposing its motion.
Therefore, the work done by the 150 N force is given by:
Work = Force x Displacement x cos(theta)
Since the force and displacement are in the same direction, the angle between them (theta) is 0 degrees. This means that the cosine of theta is 1. Therefore, the equation simplifies to:
Work = Force x Displacement
Substituting the values we have:
Work = 150 N x 5.30 m
Work = 795 J
So, the work done by the 150 N force is 795 J.
Now, let's move on to part (b) and find the coefficient of kinetic friction between the crate and the surface.
The force of friction can be calculated using the equation:
Force of friction = coefficient of friction x normal force
In this case, the normal force is equal to the weight of the crate, which is given by:
Normal force = mass x gravity
Where mass is 43.5 kg and gravity is 9.8 m/s^2 (approximate value).
Normal force = 43.5 kg x 9.8 m/s^2
Normal force = 426.3 N
Since the crate is moving at a constant speed, the frictional force must be equal to the applied force, which is 150 N. Therefore:
Force of friction = 150 N
Using the equation for the force of friction, we can now solve for the coefficient of kinetic friction:
150 N = coefficient of friction x 426.3 N
Coefficient of friction = 150 N / 426.3 N
Coefficient of friction ≈ 0.352
So, the coefficient of kinetic friction between the crate and the surface is approximately 0.352.
(a) 150 N * (distance moved) = 150*5.3 J
(b) 150 N = M*g*Uk
Since there is no increase in speed, the two forces balance
Solve for the coefficient of kinetic friction, Uk