A crate has a mass 24 kg. What applied force is required to produce an acceleration of 3m/s^2 if the frictional force is 90 N.
162 N
To determine the applied force required to produce the desired acceleration, we first need to calculate the net force acting on the crate. The net force is given by the equation:
Net force = Applied force - Frictional force
Since the frictional force is acting in the opposite direction to the desired motion, we need to subtract it from the applied force.
Given:
Mass of the crate (m) = 24 kg
Acceleration (a) = 3 m/s^2
Frictional force (F_friction) = 90 N
Step 1: Find the net force
Net force = Applied force - Frictional force
Step 2: Substitute the given values into the equation
Net force = Applied force - 90 N
Step 3: Substitute the equation for net force into Newton's second law of motion:
Net force = mass x acceleration
Step 4: Solve for the applied force
Applied force - 90 N = mass x acceleration
Rearranging the equation to solve for the applied force:
Applied force = mass x acceleration + 90 N
Step 5: Substitute the given values into the equation
Applied force = 24 kg x 3 m/s^2 + 90 N
Step 6: Calculate the applied force
Applied force = 72 N + 90 N
Applied force = 162 N
Therefore, an applied force of 162 N is required to produce an acceleration of 3 m/s^2, given a frictional force of 90 N.
To find the applied force required to produce a certain acceleration, we need to consider the forces acting on the crate.
The forces acting on the crate are the applied force (F), the frictional force (Ffr), and the weight of the crate (mg).
The weight of the crate can be calculated using the formula: weight = mass * acceleration due to gravity (g), where g is approximately 9.8 m/s² on Earth.
So, weight = 24 kg * 9.8 m/s² ≈ 235.2 N.
Now, let's analyze the forces acting on the crate:
1. The applied force (F) accelerates the crate, so it is in the same direction as the desired acceleration and can be written as F = ma, where m is the mass and a is the acceleration.
2. The frictional force (Ffr) opposes the motion of the crate and is given as 90 N.
3. The weight of the crate (mg) acts vertically downward.
Since the frictional force and the weight are perpendicular to the desired acceleration, they do not affect the calculation of the applied force required.
Therefore, the applied force required to produce an acceleration of 3 m/s² can be calculated as:
F = ma + Ffr
= (24 kg)(3 m/s²) + 90 N
= 72 N + 90 N
= 162 N.
So, an applied force of 162 N is required to produce an acceleration of 3 m/s², considering the given frictional force of 90 N and the mass of the crate.
net force= m*a
applied force-90=m*a
solve for applied force.