A mass of 45kg is sitting at the bottom of an incline plane which is 5.5m long has a coefficient of friction of .65 and which meets the horizontal at an angle of 32deg. A force of 812N is applied to the mass so as to accelerate the mass up the inclined plane. What will be the velocity of this object when it reaches the top of the incline?
To find the velocity of the object when it reaches the top of the incline, we need to consider several factors such as the force applied, the frictional force, and the incline itself.
First, we can find the gravitational force acting on the object using the equation: F = m * g, where m is the mass and g is the acceleration due to gravity (approximately 9.8 m/s^2).
F = 45 kg * 9.8 m/s^2 = 441 N
Next, we need to calculate the frictional force using the equation: f_friction = coefficient of friction * normal force. The normal force can be found using the equation: N = m * g * cos(theta), where theta is the angle of the incline.
N = 45 kg * 9.8 m/s^2 * cos(32°) ≈ 380.91 N
f_friction = 0.65 * 380.91 N ≈ 247.6 N
Now, we can calculate the net force acting on the object by subtracting the frictional force from the applied force:
net force = applied force - frictional force
net force = 812 N - 247.6 N = 564.4 N
After finding the net force, we can calculate the acceleration of the object using the equation: a = net force / mass.
acceleration = 564.4 N / 45 kg = 12.54 m/s^2
Finally, we can use the kinematic equation: v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity (0 m/s in this case), a is the acceleration, and s is the distance traveled (5.5 m in this case).
v^2 = 0 + 2 * 12.54 m/s^2 * 5.5 m
v^2 = 138.09 m^2/s^2
v ≈ √138.09 ≈ 11.75 m/s
Therefore, the velocity of the object when it reaches the top of the incline will be approximately 11.75 m/s.