Question
What is the force of friction acting on a 75 kg object moving at a constant velocity on a surface with a coefficient of kinetic friction of 0.45?
Answers
GPT-4o mini
To find the force of friction acting on the object, we can use the formula for the force of friction:
\[
f_k = \mu_k \times N
\]
where:
- \( f_k \) is the force of kinetic friction,
- \( \mu_k \) is the coefficient of kinetic friction, and
- \( N \) is the normal force.
For an object resting on a horizontal surface, the normal force \( N \) is equal to the weight of the object, which can be calculated using the formula:
\[
N = m \times g
\]
where:
- \( m \) is the mass of the object (75 kg),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)).
First, we calculate the normal force:
\[
N = 75 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 735.75 \, \text{N}
\]
Now, we can find the force of kinetic friction:
\[
f_k = 0.45 \times 735.75 \, \text{N} \approx 330.09 \, \text{N}
\]
Since the object is moving at a constant velocity, the force of friction equals the net force acting on it, which means the force of kinetic friction is balanced by any other forces (like applied forces) acting on the object.
Thus, the force of friction acting on the 75 kg object is approximately:
\[
\boxed{330.09 \, \text{N}}
\]
\[
f_k = \mu_k \times N
\]
where:
- \( f_k \) is the force of kinetic friction,
- \( \mu_k \) is the coefficient of kinetic friction, and
- \( N \) is the normal force.
For an object resting on a horizontal surface, the normal force \( N \) is equal to the weight of the object, which can be calculated using the formula:
\[
N = m \times g
\]
where:
- \( m \) is the mass of the object (75 kg),
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)).
First, we calculate the normal force:
\[
N = 75 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 735.75 \, \text{N}
\]
Now, we can find the force of kinetic friction:
\[
f_k = 0.45 \times 735.75 \, \text{N} \approx 330.09 \, \text{N}
\]
Since the object is moving at a constant velocity, the force of friction equals the net force acting on it, which means the force of kinetic friction is balanced by any other forces (like applied forces) acting on the object.
Thus, the force of friction acting on the 75 kg object is approximately:
\[
\boxed{330.09 \, \text{N}}
\]