What is the force required to move a 22kg ccrate up an incline of 35 degrees, if the coefficient between the two surfaces is .30?
To determine the force required to move the crate up the incline, we can break down the problem into components.
1. Calculate the weight of the crate:
The weight of the crate can be calculated using the formula: weight = mass * gravitational acceleration. Given that the mass of the crate is 22 kg, and the gravitational acceleration is approximately 9.8 m/s^2, we can find the weight: weight = 22 kg * 9.8 m/s^2 = 215.6 N (approximately).
2. Determine the force of gravity acting parallel to the incline:
Since the incline is at an angle of 35 degrees, we can find the force of gravity acting along the incline by multiplying the weight of the crate by the cosine of the angle. So, the force of gravity along the incline is: force of gravity along incline = weight * cos(35 degrees).
3. Calculate the force of friction:
The force of friction is given by the equation: force of friction = coefficient of friction * normal force. The normal force is the perpendicular force exerted by the surface on the crate and can be calculated as: normal force = weight * cos(55 degrees), where 55 degrees is the angle of the incline relative to the horizontal. Finally, the force of friction is: force of friction = coefficient of friction * normal force.
4. Determine the force required to move the crate up the incline:
To move the crate up the incline, we need to overcome both the force of gravity and the force of friction. The force required to move the crate up the incline is the sum of these two forces: force required = force of gravity along incline + force of friction.
By following these steps, you can calculate the force required to move the 22 kg crate up the incline with a coefficient of friction of 0.30.