The magnitude of each force is 283 N, the
force on the right is applied at an angle 41�
and the mass of the block is 27 kg. The
coefficient of friction is 0.283.
The acceleration of gravity is 9.8 m/s2 .
27 kg
μ = 0.283
283 N
41� degrees
283 N
What is the magnitude of the resulting acceleration?
Answer in units of m/s2
Well, if we're talking about acceleration, I guess we could say it's "going at full speed ahead." But in all seriousness, let's break this down.
The force applied on the right is 283 N at an angle of 41 degrees. We need to find the horizontal component of this force, which can be calculated using trigonometry.
Using some fancy math, we find that the horizontal component of the force is 283 N * cos(41 degrees). Now, we also have friction in play, which opposes the motion. The force of friction can be calculated using the equation: force of friction = coefficient of friction * normal force.
The normal force is just the weight of the block, which is equal to its mass times the acceleration due to gravity (27 kg * 9.8 m/s^2). So, the force of friction is 0.283 * (27 kg * 9.8 m/s^2).
Now let's put all the forces together. We know that the net force (resultant force) is equal to the force on the right minus the force of friction. Since force equals mass times acceleration (F = m * a), we can set up an equation:
283 N * cos(41 degrees) - (0.283 * (27 kg * 9.8 m/s^2)) = 27 kg * acceleration.
Now we can solve for acceleration by rearranging the equation:
acceleration = (283 N * cos(41 degrees) - (0.283 * (27 kg * 9.8 m/s^2))) / 27 kg.
After crunching the numbers, the magnitude of the resulting acceleration is roughly equal to the numerical value we get from this equation. So let's plug it in and calculate the answer!
Just remember to carry the units along the way, because we don't want our acceleration to be left hanging out there without any companions. So the units for acceleration would be m/s^2.
Hope that helps! Keep on accelerating (figuratively, of course).
To find the magnitude of the resulting acceleration, we need to consider the forces acting on the block. The forces acting on the block are the applied force, the force of friction, and the force of gravity.
First, let's find the force of friction. The force of friction can be calculated using the equation:
force of friction = coefficient of friction * normal force
The normal force is the force exerted by the surface on the block and is equal to the force of gravity acting on the block.
normal force = mass * acceleration due to gravity
normal force = 27 kg * 9.8 m/s^2
normal force = 264.6 N
force of friction = 0.283 * 264.6 N
force of friction = 74.80 N
Now, let's analyze the forces in the horizontal direction. The applied force on the right can be resolved into two components: one acting horizontally and one acting vertically.
horizontal component of applied force = applied force * cos(angle)
horizontal component of applied force = 283 N * cos(41 degrees)
horizontal component of applied force = 216.20 N
The net force in the horizontal direction is given by:
net force = horizontal component of applied force - force of friction
net force = 216.20 N - 74.80 N
net force = 141.40 N
Now, we can use Newton's second law to find the resulting acceleration:
net force = mass * acceleration
141.40 N = 27 kg * acceleration
acceleration = 141.40 N / 27 kg
acceleration ≈ 5.24 m/s^2
Therefore, the magnitude of the resulting acceleration is approximately 5.24 m/s^2.
To find the magnitude of the resulting acceleration, we need to consider the forces acting on the block.
1. Start by calculating the gravitational force acting on the block. The gravitational force can be calculated using the formula:
F_gravity = mass * acceleration due to gravity
F_gravity = 27 kg * 9.8 m/s^2 (given: mass = 27 kg, acceleration due to gravity = 9.8 m/s^2)
F_gravity = 264.6 N
2. Next, we need to determine the frictional force acting on the block. The frictional force can be calculated using the formula:
F_friction = coefficient of friction * F_normal
where F_normal is the normal force acting on the block. The normal force can be calculated as:
F_normal = F_gravity
F_normal = 264.6 N
F_friction = 0.283 * 264.6 N (given: coefficient of friction = 0.283)
F_friction = 74.8378 N (round to 74.84 N)
3. Now, we can determine the net force acting on the block. The net force is the difference between the applied force on the right and the frictional force. Since the applied force is at an angle, we need to calculate the horizontal and vertical components:
F_applied_horizontal = F_applied * cos(angle)
F_applied_horizontal = 283 N * cos(41 degrees)
F_applied_horizontal = 283 N * 0.753 (rounded to 3 decimal places)
F_applied_horizontal = 213.399 N (round to 213.4 N)
F_net_horizontal = F_applied_horizontal - F_friction
F_net_horizontal = 213.4 N - 74.84 N
F_net_horizontal = 138.56 N (round to 138.6 N)
4. Finally, we can calculate the acceleration using Newton's second law of motion:
F_net_horizontal = mass * acceleration
138.6 N = 27 kg * acceleration
acceleration = 138.6 N / 27 kg
acceleration = 5.133 m/s^2 (rounded to 3 decimal places)
Therefore, the magnitude of the resulting acceleration is 5.133 m/s^2.
Fr = 283N.[41o] + 283N.[0o]
X = 283*cos41 + 283 = 496.6 N.
Y = 283*sin41 = 185.7 N.
Fr^2 = X^2 + Y^2
Fr^2 = 496.6^2+185.7^2 = 281,096.05
Fr = 530.2 N.
Ff = u*mg = 0.283 * 264.6 = 74.9 N.
a = (Fr-Ff)/m=(530.2-74.9)/27=16.9 m/s^2