What acceleration would a 35 KG box have if we pushed it with a force of 275 N across a surface that has a coefficient of friction of .7?
M*g = 35 * 9.8 = 343 N. = Wt. of box = Normal force(Fn ).
Fk = u*Fn = 0.7 * 343 = 240 N. = Force of kinetic friction.
Fap-Fk = M*a.
275-240 = 35a, a = ?.
To determine the acceleration of the box, we can use Newton's second law of motion, which states that the force exerted on an object is equal to the mass of the object multiplied by its acceleration.
Step 1: Calculate the frictional force.
The frictional force can be determined using the formula:
Frictional Force = Coefficient of Friction × Normal Force
The normal force is the force exerted by the surface on the box, which in this case is equal to the weight of the box (mass × gravitational acceleration).
Given:
Coefficient of Friction = 0.7
Mass = 35 kg
Gravitational acceleration = 9.8 m/s^2
Normal Force = Mass × Gravitational acceleration
Normal Force = 35 kg × 9.8 m/s^2
Normal Force = 343 N
Frictional Force = Coefficient of Friction × Normal Force
Frictional Force = 0.7 × 343 N
Frictional Force = 240.1 N
Step 2: Calculate the net force.
The net force on the box is the difference between the applied force and the frictional force.
Given:
Applied Force = 275 N
Frictional Force = 240.1 N
Net Force = Applied Force - Frictional Force
Net Force = 275 N - 240.1 N
Net Force = 34.9 N
Step 3: Calculate the acceleration.
Using Newton's second law of motion:
Net Force = Mass × Acceleration
Given:
Net Force = 34.9 N
Mass = 35 kg
Net Force = Mass × Acceleration
34.9 N = 35 kg × Acceleration
Solving for acceleration:
Acceleration = 34.9 N / 35 kg
Acceleration ≈ 0.997 m/s^2
Therefore, the acceleration of the 35 kg box would be approximately 0.997 m/s^2 when pushed with a force of 275 N across a surface with a coefficient of friction of 0.7.
To determine the acceleration of the box, we need to apply 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.
First, we need to calculate the net force on the box. The net force can be determined by subtracting the force of friction from the applied force.
The force of friction can be found using the equation:
Force of Friction = Coefficient of Friction × Normal Force
The normal force is the force exerted by a surface perpendicular to the object. In this case, it is equal to the weight of the box, which can be found using the equation:
Weight = Mass × Gravitational Acceleration
Given:
Mass (m) = 35 kg
Coefficient of Friction (µ) = 0.7
Applied Force (F) = 275 N
Gravitational Acceleration (g) = 9.8 m/s²
1. Calculate weight:
Weight = Mass × Gravitational Acceleration
Weight = 35 kg × 9.8 m/s²
2. Calculate the force of friction:
Force of Friction = Coefficient of Friction × Normal Force
Force of Friction = 0.7 × Weight
3. Calculate the net force:
Net Force = Applied Force - Force of Friction
4. Calculate the acceleration:
Acceleration = Net Force / Mass
Let's plug in the values to calculate the acceleration:
1. Weight = 35 kg × 9.8 m/s² = 343 N
2. Force of Friction = 0.7 × 343 N = 240.1 N
3. Net Force = 275 N - 240.1 N = 34.9 N
4. Acceleration = 34.9 N / 35 kg
The acceleration of the 35 kg box, when pushed with a force of 275 N across a surface with a coefficient of friction of 0.7, is approximately 1 m/s².