1.

a)A 15.6 kg block is dragged over a rough, horizontal surface by a constant force of 72.2 N acting at an angle of angle 34.8� above the horizontal. The block is displaced 24.6 m and the coefficient of kinetic friction is 0.234.Find the work done by the 72.2 N force.The acceleration of gravity is 9.8 m/s2 .
Answer in units of J.

b)Find the magnitude of the work done by the force of friction.
Answer in units of J.

c)What is the sign of the work done by the frictional force?
1. negative
2. zero
3. positive

d)Find the work done by the normal force.
Answer in units of J.

e)What is the net work done on the block?
Answer in units of J.

a) The work done by a force is given by the equation W = F*d*cosθ, where W is the work, F is the force, d is the displacement, and θ is the angle between the force and displacement.

In this case, the force acting on the block is 72.2 N at an angle of 34.8 degrees above the horizontal. The displacement is 24.6 m.

So, the work done by the 72.2 N force is W = 72.2 N * 24.6 m * cos(34.8 degrees).

Calculating this, we find the work done is approximately 1445.7 J.

b) The magnitude of the work done by the force of friction can be found using the equation W = μ*N*d, where μ is the coefficient of kinetic friction, N is the normal force, and d is the displacement.

Given the coefficient of kinetic friction is 0.234, we need to find the normal force. The normal force can be calculated using the formula N = m*g, where m is the mass and g is the acceleration due to gravity.

The mass of the block is 15.6 kg, and the acceleration due to gravity is 9.8 m/s^2. So, the normal force is N = 15.6 kg * 9.8 m/s^2.

Calculating this, we find the normal force is approximately 152.88 N.

Now, we can calculate the work done by the force of friction using the equation W = μ*N*d. Plugging in the given values, we have W = 0.234 * 152.88 N * 24.6 m.

Calculating this, we find the magnitude of the work done by the force of friction is approximately 882.79 J.

c) The sign of the work done by the frictional force is negative because the frictional force acts opposite to the direction of displacement. So the correct answer is 1. negative.

d) The work done by the normal force is zero because the normal force is perpendicular to the displacement. In other words, the normal force does not contribute to the displacement of the block.

e) The net work done on the block is the sum of the work done by all the forces acting on it. In this case, the net work done is the sum of the work done by the 72.2 N force and the work done by the force of friction.

Net work = Work done by the 72.2 N force + Work done by the force of friction

Net work = 1445.7 J + (-882.79 J) (Note: Negative sign as the work done is in the opposite direction)

Calculating this, we find the net work done on the block is approximately 562.91 J.

To solve this problem, we need to break it down into different steps:

Step 1: Calculate the force of gravity acting on the block.
The force of gravity is given by the formula F_gravity = m * g, where m is the mass of the block and g is the acceleration due to gravity.
Given:
m = 15.6 kg
g = 9.8 m/s^2

Substituting the values into the formula, we have:
F_gravity = 15.6 kg * 9.8 m/s^2 = 152.88 N

Step 2: Calculate the vertical component of the applied force.
The vertical component of the force is given by the formula F_vertical = F_applied * sin(angle), where F_applied is the applied force and angle is the angle above the horizontal.
Given:
F_applied = 72.2 N
angle = 34.8 degrees

First, we need to convert the angle to radians:
angle_radians = 34.8 degrees * (π/180 radians/degree) = 0.608 radians

Substituting the values into the formula, we have:
F_vertical = 72.2 N * sin(0.608) = 43.4924 N

Step 3: Calculate the frictional force.
The frictional force is given by the formula F_friction = μ * F_normal, where μ is the coefficient of kinetic friction and F_normal is the normal force.
Given:
μ = 0.234

Since the block is on a horizontal surface, the normal force is equal to the force of gravity:
F_normal = F_gravity = 152.88 N

Substituting the values into the formula, we have:
F_friction = 0.234 * 152.88 N = 35.78712 N

Step 4: Calculate the horizontal component of the applied force.
The horizontal component of the force is given by the formula F_horizontal = F_applied * cos(angle), where F_applied is the applied force and angle is the angle above the horizontal.
Given:
F_applied = 72.2 N
angle = 34.8 degrees

Substituting the values into the formula, we have:
F_horizontal = 72.2 N * cos(0.608) = 60.4189 N

Step 5: Calculate the work done by the applied force.
The work done by a force is given by the formula W = F * d * cos(θ), where F is the force, d is the displacement, and θ is the angle between the force and displacement vectors.
Given:
F = 72.2 N
d = 24.6 m
θ = 34.8 degrees

First, we need to convert the angle to radians:
θ_radians = 34.8 degrees * (π/180 radians/degree) = 0.608 radians

Substituting the values into the formula, we have:
W_applied = 72.2 N * 24.6 m * cos(0.608) = 1648.6297 J
(rounded to 4 decimal places)

Step 6: Calculate the work done by the frictional force.
The work done by a force is given by the formula W = F * d * cos(θ), where F is the force, d is the displacement, and θ is the angle between the force and displacement vectors.
In this case, the force of friction is always opposite to the direction of motion, so the angle between the force and displacement vectors is 180 degrees.

Given:
F_friction = 35.78712 N
d = 24.6 m
θ = 180 degrees

First, we need to convert the angle to radians:
θ_radians = 180 degrees * (π/180 radians/degree) = π radians

Substituting the values into the formula, we have:
W_friction = -35.78712 N * 24.6 m * cos(π) = -880.4136 J
(rounded to 4 decimal places)

Since the work done by the frictional force is in the opposite direction of the displacement, it is negative.

Step 7: Calculate the work done by the normal force.
The work done by the normal force is determined by the displacement of the block, which is in the vertical direction. Since the normal force is perpendicular to the displacement, the work done by the normal force is zero.

W_normal = 0 J

Step 8: Calculate the net work done on the block.
The net work done on the block is the sum of the work done by all the forces acting on it.

Net work = W_applied + W_friction + W_normal
Substituting the values calculated in steps 5, 6, and 7, we have:
Net work = 1648.6297 J + (-880.4136 J) + 0 J = 768.2161 J
(rounded to 4 decimal places)

Answer:
a) The work done by the 72.2 N force is 1648.6297 J.
b) The magnitude of the work done by the force of friction is 880.4136 J.
c) The sign of the work done by the frictional force is negative.
d) The work done by the normal force is 0 J.
e) The net work done on the block is 768.2161 J.

To solve this problem, we can break it down into several parts:

a) To find the work done by the 72.2 N force, we need to calculate the component of the force parallel to the displacement and multiply it by the displacement.

The component of the force parallel to the displacement is given by: F_parallel = F * cos(angle)
F_parallel = 72.2 N * cos(34.8 degrees)

Next, we calculate the work done by multiplying the parallel force by the displacement:
Work = F_parallel * displacement
Work = (72.2 N * cos(34.8 degrees)) * 24.6 m

Calculating this expression will give us the work done by the force of 72.2 N.

b) To find the magnitude of the work done by the force of friction, we need to calculate the frictional force and multiply it by the displacement.

The frictional force can be found using the formula:
Frictional force = coefficient of kinetic friction * normal force
Frictional force = 0.234 * (mass * acceleration due to gravity)

Then, we calculate the work done by the frictional force using the formula:
Work = Frictional force * displacement

This will give us the magnitude of the work done by the force of friction.

c) The sign of the work done by the frictional force depends on the direction of the force compared to the displacement. Since the force of friction acts opposite to the direction of motion, the work done by the frictional force will be negative.

d) To find the work done by the normal force, we need to calculate the normal force and multiply it by the displacement. The normal force is equal in magnitude and opposite in direction to the force of gravity, which can be calculated as (mass * acceleration due to gravity). Then, we calculate the work using the formula: Work = Normal force * displacement.

e) The net work done on the block is calculated by adding up the work done by all individual forces acting on it. The net work is the sum of the work done by the 72.2 N force, the work done by the force of friction, and the work done by the normal force. Net Work = Work (72.2 N force) + Work (frictional force) + Work (normal force).