An object with a mass of 0.75 kg is projected over a horizontal surface with a speed of 2.5 m/s. It then comes to rest after 3.0 s.
(d) What is the value of kinetic friction?
The value of kinetic friction can be calculated using the equation F = ma, where F is the force of friction, m is the mass of the object, and a is the acceleration. In this case, the acceleration is the change in velocity (2.5 m/s) divided by the time (3.0 s), which is 0.83 m/s2. Therefore, the force of friction is 0.75 kg x 0.83 m/s2 = 0.62 N.
To find the value of kinetic friction, we need to use the equation:
F_k = μ_k * N
where F_k is the force of kinetic friction, μ_k is the coefficient of kinetic friction, and N is the normal force.
First, let's determine the normal force. The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, since the object is on a horizontal surface, the normal force is equal to the weight of the object.
Weight = mass * gravitational acceleration
Weight = 0.75 kg * 9.8 m/s^2
Weight = 7.35 N
Since the object comes to rest, this means that the force of kinetic friction is equal in magnitude but opposite in direction to the net force acting on the object. The net force can be calculated using Newton's second law:
Net force = mass * acceleration
In this case, the net force is 0 (since the object comes to rest), so:
0 = 0.75 kg * acceleration
Solving for acceleration:
acceleration = 0 m/s^2
Since the object comes to rest, the acceleration is zero. Therefore, the force of kinetic friction equals zero, and the value of kinetic friction is 0 N.
To find the value of kinetic friction, let's go through the steps:
1. Recall the equation for kinetic friction:
F_k = μ_k * N
Where F_k is the force of kinetic friction, μ_k is the coefficient of kinetic friction, and N is the normal force.
2. Find the normal force acting on the object. The normal force is the force exerted by a surface to support the weight of an object resting on it. In this scenario, since the object comes to rest on a horizontal surface, the normal force is equal to the weight of the object:
N = m * g
Where m is the mass of the object and g is the acceleration due to gravity. Using the given mass of 0.75 kg, and the standard value of g as 9.8 m/s^2, we can calculate the normal force.
3. Calculate the acceleration of the object. When an object comes to rest, its final velocity is zero. Therefore, using the equation of motion:
v = u + a * t
Where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Rearranging the equation, we have:
a = (v - u) / t
Plugging in the values given (v = 0 m/s, u = 2.5 m/s, and t = 3.0 s), we can calculate the acceleration.
4. Calculate the force of kinetic friction. Now that we have the normal force and the acceleration, we can use the equation for kinetic friction:
F_k = μ_k * N
Plugging in the values for the normal force and acceleration, we need to solve for the coefficient of kinetic friction, μ_k.
By going through these steps, we can find the value of kinetic friction for the given scenario.