suppose the
you push with a 40-N horizontal force on a 4-kg mass resting on a horizontal surface against a horizontal friction force of 24N. show that the acceleration is 4 m/s2
8999
To find the acceleration of the mass, we can use Newton's second law of motion, which states that the acceleration of an object is equal to the net force acting on it divided by its mass.
Step 1: Identify the known values:
- Force applied (F) = 40 N
- Mass (m) = 4 kg
- Friction force (f) = 24 N
Step 2: Calculate the net force:
The net force can be calculated by subtracting the friction force from the applied force:
Net force = Force applied - Friction force
Net force = 40 N - 24 N
Net force = 16 N
Step 3: Calculate the acceleration:
Using Newton's second law, we can now determine the acceleration:
Acceleration = Net force / Mass
Acceleration = 16 N / 4 kg
Acceleration = 4 m/s²
Therefore, the acceleration of the mass is 4 m/s².
To show that the acceleration of the mass is 4 m/s^2, we need to use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. The formula for Newton's second law is:
F_net = m * a
where F_net is the net force, m is the mass, and a is the acceleration.
In this case, the net force acting on the object is the difference between the applied force and the friction force. The applied force is 40 N, and the friction force is 24 N. Therefore, the net force can be calculated as:
F_net = applied force - friction force
F_net = 40 N - 24 N
F_net = 16 N
Now, we can substitute the values of the net force and the mass into Newton's second law equation and solve for the acceleration:
16 N = 4 kg * a
To isolate the acceleration, we need to divide both sides of the equation by the mass:
a = 16 N / 4 kg
a = 4 N/kg
The unit N/kg is equivalent to m/s^2, so we have:
a = 4 m/s^2
Hence, the acceleration of the 4-kg mass is indeed 4 m/s^2 when a 40-N horizontal force is applied against a 24-N horizontal friction force.