Study the image.
A couch with two opposing forces. A friction force vector (surface on couch) marked 5 N points to the left. A push force vector (person on couch) marked 20 N points right.
If the couch has a mass of 45 kg, determine its acceleration.
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Responses
1.8 m/s2, to the right
1.8 m/s 2 , to the right
0.33 m/s2, to the right
0.33 m/s 2 , to the right
3 m/s2, to the right
3 m/s 2 , to the right
2.2 m/s2, to the right
2.2 m/s2, to the right
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To determine the acceleration of the couch, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration (F = ma).
In this case, the opposing forces are the friction force pointing to the left (-5 N) and the push force pointing to the right (+20 N). The net force acting on the couch can be calculated by subtracting the friction force from the push force:
Net force = 20 N - 5 N = 15 N
Now, we can plug in the mass of the couch (45 kg) and the net force (15 N) into the formula for acceleration:
Acceleration = Net force / mass
Acceleration = 15 N / 45 kg
Acceleration = 0.33 m/s^2
Therefore, the acceleration of the couch is 0.33 m/s^2, to the right.
To determine the acceleration of the couch, we need to consider the forces acting on it. In this case, there are two forces: the friction force and the push force.
The friction force vector is marked 5 N and it points to the left. This force opposes the motion of the couch. Since it is a friction force, we can assume it is equal to the coefficient of friction (μ) multiplied by the normal force (N). However, since the normal force is not given, we cannot directly calculate the coefficient of friction or the normal force from the information provided.
The push force vector is marked 20 N and it points to the right. This force is applied by the person on the couch and causes the couch to accelerate to the right.
We can use Newton's second law of motion to calculate the acceleration. The formula is:
F_net = m * a
where F_net is the net force acting on the object, m is the mass of the object, and a is the acceleration.
In this case, the net force is the vector sum of the friction force and the push force:
F_net = 20 N - 5 N = 15 N
Substituting this into the formula:
15 N = 45 kg * a
Solving for a:
a = 15 N / 45 kg = 0.33 m/s^2
Therefore, the acceleration of the couch is 0.33 m/s^2 to the right. Therefore, the correct answer is:
0.33 m/s^2, to the right