A 2.0 kg mass is sliding on a flat surface, with an initial speed of 20 m/s, and a coefficient of friction of 0.2. what is the magnitude of its acceleration? I know the answer is 2.0 m/s^2, but can someone show me how ?
a=force/mass=.2*mg/m=.2*9.8=you do it. I hope your teacher is not using for g 10.0 (no where on the Earth is it that value).
To find the magnitude of the acceleration, we will use the equation:
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 of the object.
The net force can be calculated using the equation:
F_net = F_applied - F_friction
Where F_applied is the applied force on the object and F_friction is the force of friction acting on the object. The force of friction can be calculated using the equation:
F_friction = μ * N
Where μ is the coefficient of friction and N is the normal force acting on the object.
The normal force is the force exerted by the surface on the object perpendicular to the surface. On a flat surface, the normal force is equal in magnitude and opposite in direction to the gravitational force, which can be calculated using:
N = m * g
Where g is the acceleration due to gravity.
Now, we can substitute the expressions for F_friction and N into the equation for F_net:
F_net = F_applied - μ * m * g
Since the object is on a flat surface and there is no applied force in this case, the equation becomes:
F_net = - μ * m * g
Now, we can substitute the given values into the equation to find F_net:
F_net = - (0.2) * (2.0 kg) * (9.8 m/s^2)
F_net = - 3.92 N
Since the acceleration acts in the opposite direction to the initial velocity, the magnitude of the acceleration is equal to the magnitude of the net force divided by the mass:
a = |F_net| / m = |-3.92 N| / (2.0 kg) = 1.96 m/s^2
Rounding to the appropriate number of significant figures, the magnitude of the acceleration is approximately 2.0 m/s^2.
To find the magnitude of acceleration of the mass, you can use the equation:
\[ a = \frac{f}{m} \]
where \( a \) represents acceleration, \( f \) represents the net force acting on the object, and \( m \) represents the mass of the object.
In this case, we need to calculate the net force acting on the object. The net force acting on the object is the difference between the force applied and the frictional force. The force applied is the product of mass and acceleration:
\[ F_{\text{applied}} = m \times a \]
The frictional force can be calculated using the equation:
\[ f_{\text{friction}} = \mu \times N \]
where \( \mu \) represents the coefficient of friction and \( N \) represents the normal force.
In this scenario, the mass of the object is given as 2.0 kg, and the coefficient of friction is 0.2. The normal force is equal to the weight of the mass, which is the product of mass and gravitational acceleration:
\[ N = m \times g \]
Given that the acceleration due to gravity (\( g \)) is approximately 9.8 m/s\(^2\), we can calculate the normal force as:
\[ N = 2.0 \, \text{kg} \times 9.8 \, \text{m/s}^2 \]
Once we have calculated the normal force (\( N \)), we can find the magnitude of the frictional force (\( f_{\text{friction}} \)), which is equal to:
\[ f_{\text{friction}} = 0.2 \times N \]
Finally, we can subtract the frictional force from the applied force to find the net force acting on the object. With this value, we can calculate the acceleration using the formula \( a = \frac{f}{m} \).
Let's plug in the values and calculate step by step:
1. Calculate the normal force:
\( N = 2.0 \, \text{kg} \times 9.8 \, \text{m/s}^2 \)
2. Calculate the frictional force:
\( f_{\text{friction}} = 0.2 \times N \)
3. Calculate the net force:
\( f_{\text{net}} = F_{\text{applied}} - f_{\text{friction}} \)
4. Calculate the acceleration:
\( a = \frac{f_{\text{net}}}{m} \)
By following these steps and performing the calculations, you will find that the magnitude of the acceleration is indeed 2.0 m/s\(^2\).