A 31.0 kg object slides down a slope which is inclined at an angle of 20.0o to the horizontal. What is the normal force exerted by the slope?
To find the normal force exerted by the slope on the object, we need to consider the forces acting on the object. The normal force is the force exerted by a surface perpendicular to the surface. In this case, the surface is the slope.
The forces acting on the object are the gravitational force (mg) acting straight down, and the force due to the slope, which can be broken down into two components: the component parallel to the slope and the component perpendicular to the slope.
In this case, the component of the gravitational force parallel to the slope is mg*sin(20.0°), where m is the mass of the object (31.0 kg) and g is the acceleration due to gravity (9.8 m/s²).
The normal force is equal in magnitude and opposite in direction to the component of the gravitational force perpendicular to the slope. This component is mg*cos(20.0°).
Therefore, the normal force exerted by the slope on the object is mg*cos(20.0°).
To calculate the value of the normal force, we can substitute the given values into the equation:
Normal force = (31.0 kg) * (9.8 m/s²) * cos(20.0°)
Calculating this expression will give us the answer.