a 2.0kg object is pulled horizontally by a force of 6.3N along the floor where the coefficient of kinetic friction is o.24. what is the object acceleration
Wo = mg = 2kg * 9.8N/kg = 19.6 N. = Wt.
of the object.
Fo = 19.6 N @ 0 Deg.
Fp = 19.6*sin(0) = 0 = Force parallel
to floor.
Fv = 19.6*cos(0) = 19.6 N. = Force perpendicular to floor.
Fn = Fap - Fp - u*Fv,
Fn = 6.3 - 0 - 0.24*19.6 = 1.6 N. = Net
force.
a = Fn / m = 1.6 / 2 = 0.80 m/s^2.
Why did the object go to see a therapist? Because it was feeling quite strained by all the friction in its life!
Now, to calculate the object's acceleration, we need to consider the forces acting on it. The force of friction is given by the equation F_friction = μ * N, where μ is the coefficient of friction and N is the normal force.
Since the object is being pulled horizontally, the normal force is equal to its weight, which is given by the equation N = m * g, where m is the mass of the object and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Plugging in the values, we have:
N = (2.0 kg) * (9.8 m/s^2) = 19.6 N
Now we can calculate the force of friction:
F_friction = (0.24) * (19.6 N) = 4.704 N
The net force acting on the object is equal to the applied force minus the force of friction:
Net force = 6.3 N - 4.704 N = 1.596 N
Finally, we can use Newton's second law (F = m * a) to solve for acceleration:
1.596 N = (2.0 kg) * a
a = 1.596 N / 2.0 kg ≈ 0.798 m/s^2
So, the object's acceleration is approximately 0.798 m/s^2.
To find the object's acceleration, we need to calculate the net force acting on the object. The net force is the difference between the applied force and the force of friction.
Step 1: Calculate the force of friction
Given:
- Coefficient of kinetic friction (μ) = 0.24
- Normal force (N) = weight of the object = mass (m) * acceleration due to gravity (g) = 2.0 kg * 9.8 m/s^2
Force of friction (Ffriction) = μ * N
Calculate N:
N = m * g = 2.0 kg * 9.8 m/s² = 19.6 N
Calculate Ffriction:
Ffriction = 0.24 * 19.6 N
Step 2: Calculate the net force
Given:
- Applied force (Fapplied) = 6.3 N
Net force (Fnet) = Fapplied - Ffriction
Substituting the given values:
Fnet = 6.3 N - (0.24 * 19.6 N)
Step 3: Calculate the object's acceleration
Using Newton's second law of motion, F = m * a, we can rearrange the formula to solve for acceleration (a):
Fnet = m * a
Substituting the calculated value for Fnet:
6.3 N - (0.24 * 19.6 N) = 2.0 kg * a
Now, solve for a:
a = (6.3 N - 4.704 N) / 2.0 kg
a = 1.596 N / 2.0 kg
a ≈ 0.798 m/s²
Therefore, the object's acceleration is approximately 0.798 m/s².
To find the object's acceleration, we need to consider the forces acting on the object.
First, let's find the force of friction using the coefficient of kinetic friction and the normal force. The normal force is the force exerted by a surface to support the weight of an object resting on it, which is equal to the object's weight in this case.
Step 1: Calculate the normal force (N)
Since the object is on the floor, the normal force is equal to the weight of the object (mg), where m is the mass of the object and g is the acceleration due to gravity (9.8 m/s^2).
In this case, the object's weight (mg) will be (2.0 kg * 9.8 m/s^2).
Weight (mg) = 2.0 kg * 9.8 m/s^2 = 19.6 N
So, the normal force (N) is 19.6 N.
Step 2: Calculate the force of friction (f)
The force of friction (f) is equal to the coefficient of kinetic friction (μk) multiplied by the normal force (N).
Force of friction (f) = μk * N
= 0.24 * 19.6 N
So, the force of friction (f) is 4.704 N.
Step 3: Calculate the net force (Fnet)
The net force (Fnet) acting on the object is the difference between the applied force and the force of friction.
Net force (Fnet) = applied force - force of friction
= 6.3 N - 4.704 N
So, the net force (Fnet) is 1.596 N.
Step 4: Calculate the object's acceleration (a)
From Newton's second law of motion, we know that the acceleration (a) of an object is equal to the net force (Fnet) divided by the mass (m) of the object.
Acceleration (a) = net force (Fnet) / mass (m)
= 1.596 N / 2.0 kg
So, the object's acceleration (a) is 0.798 m/s^2.