A grocery cart with a mass of 18 kg is pushed at constant speed along an aisle by a force F = 12 N. The applied force acts at a 20° angle to the horizontal. Find the work done by each of the forces on the cart if the aisle is 17 m long.
a)work done by the applied force=?
b)work done by the frictional force
c)work done by the normal force
d)work done by the gravitational force
i am trying.i actually answered one of my own questions earlier after looking further into class notes.sorry if it seemed like im using it to harvest ansewrs.i just have avery large assignment.n these are the few that i didn't get.and only needed hints as to what to do, not nessesarily the answer.
To determine the work done by each force on the grocery cart, we can use the formula:
Work = Force * Distance * cos(θ)
where Force is the magnitude of the force acting on the object, Distance is the distance over which the force is applied, and θ is the angle between the force and the direction of motion.
a) To find the work done by the applied force, we have F = 12 N and θ = 20°. The distance over which the force is applied is 17 m. Plugging these values into the formula:
Work = 12 N * 17 m * cos(20°)
Using a calculator, we find the work done by the applied force to be approximately 199.04 J.
b) The frictional force opposes the motion of the cart. Since the cart is moving at a constant speed, the net force on the cart is zero, which means the frictional force must be equal in magnitude but opposite in direction to the applied force. Therefore, the work done by the frictional force is:
Work = -12 N * 17 m * cos(180° - 20°)
Simplifying the cosine term:
Work = -12 N * 17 m * cos(160°)
Computing this value, we find the work done by the frictional force to be approximately -193.52 J. The negative sign indicates that the work done by the frictional force is in the opposite direction of the displacement.
c) The normal force is the force exerted by the aisle surface on the cart, perpendicular to the surface. Since the cart is moving horizontally at a constant speed, there is no vertical acceleration, and therefore, the normal force does no work. Thus, the work done by the normal force is zero.
d) The gravitational force acts vertically downward on the cart. However, the aisle is horizontal, so the displacement of the cart is perpendicular to the direction of the gravitational force. Therefore, the work done by the gravitational force is also zero.