A 15kg object takes 26.3 meters to stop because of friction. Assume no skidding. If the frictional force is 60 N, what is the initial velocity of the object?
the work done in stopping is... f * d
... 60 * 26.3 = ? J
the work equals the initial kinetic energy of the object... ½ m v²
60 * 26.3 = ½ * 15 * v²
v = √(8 * 26.3) m/s
be aware of significant figures...
To calculate the initial velocity of the object, we first need to understand the concept of frictional force and the equations of motion involved.
Frictional force is a force that opposes the motion of an object when it is in contact with a surface. In this case, the frictional force is responsible for stopping the object.
The equation that relates the frictional force to the normal force (which is the force exerted by a surface that is perpendicular to it) is given by:
Frictional force = μ * Normal force
Here, μ (pronounced as mu) represents the coefficient of friction, which depends on the surfaces in contact. In the given problem, the frictional force is already provided as 60 N.
Since the object is brought to rest due to friction, the frictional force must be equal to the force that was initially driving the object forward, which is the force of inertia.
The force of inertia, F, can be calculated using the formula:
Force of inertia = Mass * Acceleration
Since the object is slowing down (due to friction), the acceleration is negative. Hence, we have:
Force of inertia = Mass * (-Acceleration)
In this case, the mass of the object is given as 15 kg.
Now, we can set up an equation using the given information:
Frictional force = Force of inertia
60 N = 15 kg * (-Acceleration)
Solving for the acceleration, we get:
Acceleration = -60 N / 15 kg
Acceleration = -4 m/s²
Finally, we can use the equation of motion to find the initial velocity (v₀) of the object:
Final velocity² = Initial velocity² + 2 * Acceleration * Distance
Since the object comes to a stop (final velocity = 0), the equation becomes:
0 = v₀² + 2 * (-4 m/s²) * 26.3 m
Simplifying further, we have:
0 = v₀² - 209.2 m²/s²
Now, we can solve for v₀:
v₀² = 209.2 m²/s²
v₀ = √(209.2) m/s = 14.5 m/s
Therefore, the initial velocity of the object is approximately 14.5 m/s.