a 36.1 N crate is resting on the floor. When you push horizontally on the crate with a force of 16.9 N, it accelerates at 0.15 m/s2. How large is the frictional force acting on the crate?
F = m a
F = (36.1/9.8)* .15
F = .552 N
16.9 - friction force = .552
friction force = 16.35 N
(I suspect a typo in your problem statement by the way)
sum of forces-> F=ma
F(friction)= ufn* you don't need this
F(applied)-F(friction)=ma
f(a)-f(f)=ma
f(a)/ma=f(f)
add numbers
To find the frictional force acting on the crate, we need to use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration.
First, let's calculate the mass of the crate using the formula: mass = force / acceleration. The force acting on the crate is the applied force, which is 16.9 N, and the acceleration is 0.15 m/s^2.
mass = 16.9 N / 0.15 m/s^2
mass = 112.67 kg (approximately)
Now that we know the mass of the crate, we can find the frictional force acting on it. The frictional force can be calculated using the formula: frictional force = coefficient of friction * normal force.
However, we need to find the normal force first. The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the weight of the crate is the gravitational force acting on it. The formula for gravitational force is weight = mass * acceleration due to gravity.
acceleration due to gravity (g) = 9.8 m/s^2 (approximate value on Earth)
weight = mass * acceleration due to gravity
weight = 112.67 kg * 9.8 m/s^2
weight = 1105.93 N (approximately)
Since the crate is resting on the floor, the normal force exerted by the floor is equal to the weight of the crate, which is 1105.93 N.
Now we can calculate the frictional force using the formula: frictional force = coefficient of friction * normal force. However, we need one more piece of information - the coefficient of friction.
The coefficient of friction depends on the nature of the surfaces in contact. Since the question doesn't provide this information, we can't calculate the exact frictional force. However, we can calculate the maximum possible frictional force, also known as the static friction force. The maximum static friction force can be calculated using the formula: maximum static friction force = coefficient of static friction * normal force.
For now, let's assume a coefficient of static friction (µs) of 1. This value can range from 0 to 1, depending on the surfaces in contact.
maximum static friction force = 1 * 1105.93 N
maximum static friction force = 1105.93 N
So, based on the information provided, the maximum possible frictional force acting on the crate is 1105.93 N.